Internet DRAFT - draft-huelsing-cfrg-hash-sig-xmss
draft-huelsing-cfrg-hash-sig-xmss
Crypto Forum Research Group A. Huelsing
Internet-Draft TU Eindhoven
Intended status: Informational D. Butin
Expires: September 24, 2015 TU Darmstadt
S. Gazdag
genua mbH
A. Mohaisen
Verisign Labs
March 23, 2015
XMSS: Extended Hash-Based Signatures
draft-huelsing-cfrg-hash-sig-xmss-00
Abstract
This note describes the eXtended Merkle Signature Scheme (XMSS), a
hash-based digital signature system. It follows existing
descriptions in scientific literature. The note specifies the WOTS+
one-time signature scheme, a single-tree (XMSS) and a multi-tree
variant (XMSS^MT) of XMSS. Both variants use WOTS+ as a main
building block. XMSS provides cryptographic digital signatures
without relying on the conjectured hardness of mathematical problems.
Instead, it is proven that it only relies on the properties of
cryptographic hash functions. XMSS provides strong security
guarantees and, besides some special instantiations, is even secure
when the collision resistance of the underlying hash function is
broken. It is suitable for compact implementations, relatively
simple to implement, and naturally resists side-channel attacks.
Unlike most other signature systems, hash-based signatures withstand
attacks using quantum computers.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
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Internet-Drafts are draft documents valid for a maximum of six months
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material or to cite them other than as "work in progress."
This Internet-Draft will expire on September 24, 2015.
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Copyright Notice
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Conventions Used In This Document . . . . . . . . . . . . 5
2. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Data Types . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. Operators . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3. Functions . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4. Strings of Base-w Numbers . . . . . . . . . . . . . . . . 6
2.5. Member Functions . . . . . . . . . . . . . . . . . . . . 7
3. Primitives . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1. WOTS+ One-Time Signatures . . . . . . . . . . . . . . . . 8
3.1.1. WOTS+ Parameters . . . . . . . . . . . . . . . . . . 8
3.1.1.1. WOTS+ Hashing Functions . . . . . . . . . . . . . 9
3.1.2. WOTS+ Chaining Function . . . . . . . . . . . . . . . 9
3.1.3. WOTS+ Private Key . . . . . . . . . . . . . . . . . . 9
3.1.4. WOTS+ Public Key . . . . . . . . . . . . . . . . . . 10
3.1.5. WOTS+ Signature Generation . . . . . . . . . . . . . 10
3.1.6. WOTS+ Signature Verification . . . . . . . . . . . . 11
3.1.7. Pseudorandom Key Generation . . . . . . . . . . . . . 12
4. Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1. XMSS: eXtended Merkle Signature Scheme . . . . . . . . . 13
4.1.1. XMSS Parameters . . . . . . . . . . . . . . . . . . . 13
4.1.2. XMSS Hash Functions . . . . . . . . . . . . . . . . . 14
4.1.3. XMSS Private Key . . . . . . . . . . . . . . . . . . 14
4.1.4. L-Trees . . . . . . . . . . . . . . . . . . . . . . . 14
4.1.5. TreeHash . . . . . . . . . . . . . . . . . . . . . . 15
4.1.6. XMSS Public Key . . . . . . . . . . . . . . . . . . . 15
4.1.7. XMSS Signature . . . . . . . . . . . . . . . . . . . 16
4.1.8. XMSS Signature Generation . . . . . . . . . . . . . . 18
4.1.9. XMSS Signature Verification . . . . . . . . . . . . . 19
4.1.10. Pseudorandom Key Generation . . . . . . . . . . . . . 20
4.1.11. Free Index Handling and Partial Secret Keys . . . . . 21
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4.2. XMSS^MT: Multi-Tree XMSS . . . . . . . . . . . . . . . . 21
4.2.1. XMSS^MT Parameters . . . . . . . . . . . . . . . . . 21
4.2.2. XMSS Algorithms Without Message Hash . . . . . . . . 22
4.2.3. XMSS^MT Private Key . . . . . . . . . . . . . . . . . 22
4.2.4. XMSS^MT Public Key . . . . . . . . . . . . . . . . . 22
4.2.5. XMSS^MT Signature . . . . . . . . . . . . . . . . . . 23
4.2.6. XMSS^MT Signature Generation . . . . . . . . . . . . 24
4.2.7. XMSS^MT Signature Verification . . . . . . . . . . . 25
4.2.8. Pseudorandom Key Generation . . . . . . . . . . . . . 26
4.2.9. Free Index Handling and Partial Secret Keys . . . . . 26
5. Parameter Sets . . . . . . . . . . . . . . . . . . . . . . . 27
5.1. Zero Bitmasks . . . . . . . . . . . . . . . . . . . . . . 27
5.2. WOTS+ Parameters . . . . . . . . . . . . . . . . . . . . 28
5.3. XMSS Parameters . . . . . . . . . . . . . . . . . . . . . 29
5.3.1. XMSS Parameters . . . . . . . . . . . . . . . . . . . 29
5.3.1.1. XMSS Parameters with AES and SHA3 . . . . . . . . 29
5.3.1.2. XMSS Parameters with SHA3 . . . . . . . . . . . . 30
5.3.2. XMSS Parameters With Empty Bitmasks . . . . . . . . . 31
5.4. XMSS^MT Parameters . . . . . . . . . . . . . . . . . . . 32
5.4.1. XMSS^MT Parameters . . . . . . . . . . . . . . . . . 32
5.4.1.1. XMSS^MT Parameters with AES and SHA3 . . . . . . 32
5.4.1.2. XMSS^MT Parameters with SHA3 . . . . . . . . . . 33
5.4.2. XMSS^MT Parameters With Empty Bitmasks . . . . . . . 35
6. Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 38
8. Security Considerations . . . . . . . . . . . . . . . . . . . 49
8.1. Security Proofs . . . . . . . . . . . . . . . . . . . . . 50
8.2. Security Assumptions . . . . . . . . . . . . . . . . . . 51
8.3. Post-Quantum Security . . . . . . . . . . . . . . . . . . 51
9. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 51
10. References . . . . . . . . . . . . . . . . . . . . . . . . . 51
10.1. Normative References . . . . . . . . . . . . . . . . . . 51
10.2. Informative References . . . . . . . . . . . . . . . . . 52
Appendix A. WOTS+ XDR Formats . . . . . . . . . . . . . . . . . 53
Appendix B. XMSS XDR Formats . . . . . . . . . . . . . . . . . . 55
Appendix C. XMSS^MT XDR Formats . . . . . . . . . . . . . . . . 65
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 87
1. Introduction
A (cryptographic) digital signature scheme provides asymmetric
message authentication. The key generation algorithm produces a key
pair consisting of a private and a public key. A message is signed
using a private key to produce a signature. A message/signature pair
can be verified using a public key. A One-Time Signature (OTS)
scheme allows us to use a key pair to sign exactly one message
securely. A many-time signature system can be used to sign multiple
messages.
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One-Time Signature schemes, and Many-Time Signature (MTS) schemes
composed of them, were proposed by Merkle in 1979 [Merkle79]. They
were well-studied in the 1990s and have regained interest from 2006
onwards because of their resistance against quantum-computer-aided
attacks. These kinds of signature schemes are called hash-based
signature schemes as they are built out of a cryptographic hash
function. Hash-based signature schemes generally feature small
private and public keys as well as fast signature generation and
verification but large signatures and a relatively slow key
generation. In addition, they are suitable for compact
implementations that benefit various applications and are naturally
resistant to most kinds of side-channel attacks.
Some progress has already been made toward standardizing and
introducing hash signatures. McGrew and Curcio have published an
Internet-Draft [DC14] specifying the "textbook" Lamport-Diffie-
Winternitz-Merkle (LDWM) scheme based on early publications.
Independently, Buchmann, Dahmen and Huelsing have proposed XMSS
[BDH11], the "eXtended Merkle Signature Scheme," offering better
efficiency and a modern security proof. Very recently, SPHINCS, a
stateless hash-based signature scheme was introduced [BHH15], with
the intent of being easier to deploy in current applications. A
reasonable next step toward introducing hash signatures would seem to
complete the specifications of the basic algorithms - LDWM, XMSS,
SPHINCS and/or variants [Kaliski15].
The eXtended Merkle Signature Scheme (XMSS) [BDH11] is the latest
hash-based signature scheme. It has the smallest signatures out of
such schemes and comes with a multi-tree variant that solves the
problem of slow key generation. Moreover, it can be shown that XMSS
is secure, making only mild assumptions on the underlying hash
function. Especially, it is not required that the cryptographic hash
function is collision-resistant for the security of XMSS.
This note describes a single-tree and a multi-tree variant of the
eXtended Merkle Signature Scheme (XMSS) [BDH11]. It also describes
WOTS+, a variant of the Winternitz OTS scheme introduced in
[Huelsing13] that is used by XMSS. The schemes are described with
enough specificity to ensure interoperability between
implementations.
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This note is structured as follows. Notation is introduced in
Section 2. Section 3 describes the WOTS+ signature system. Many
time signature schemes are defined in Section 4: the eXtended Merkle
Signature Scheme (XMSS) in Section 4.1, and its Multi-Tree variant
(XMSS^MT) in Section 4.2. Parameter sets are described in Section 5.
Section 6 describes the rationale behind choices in this note. The
IANA registry for these signature systems is described in Section 7.
Finally, security considerations are presented in Section 8.
1.1. Conventions Used In This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
2. Notation
2.1. Data Types
Bytes and byte strings are the fundamental data types. A byte is a
sequence of eight bits. A single byte is denoted as a pair of
hexadecimal digits with a leading "0x". A byte string is an ordered
sequence of zero or more bytes and is denoted as an ordered sequence
of hexadecimal characters with a leading "0x". For example, 0xe534f0
is a byte string of length 3. An array of byte strings is an
ordered, indexed set starting with index 0 in which all byte strings
have identical length.
2.2. Operators
When a and b are integers, mathematical operators are defined as
follows:
^ : a ^ b denotes the result of a raised to the power of b.
* : a * b denotes the product of a and b. This operator is
sometimes used implicitly in the absence of ambiguity, as in usual
mathematical notation.
/ : a / b denotes the quotient of a by b.
% : a % b denotes the non-negative remainder of the integer
division of a by b.
+ : a + b denotes the sum of a and b.
- : a - b denotes the difference of a and b.
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The standard order of operations is used when evaluating arithmetic
expressions.
Arrays are used in the common way, where the i^th element of an array
A is denoted A[i]. Byte strings are treated as arrays of bytes where
necessary: If X is a byte string, then X[i] denotes its i^th byte,
where X[0] is the leftmost byte. In addition, bytes(X, i, j) with i
< j denotes the range of bytes from the i^th to the j^th byte in X,
inclusively. For example, if X = 0x01020304, then X[0] is 0x01 and
bytes(X, 1, 2) is 0x0203.
If A and B are byte strings of equal length, then:
A AND B denotes the bitwise logical conjunction operation.
A XOR B denotes the bitwise logical exclusive disjunction
operation.
When B is a byte and i is an integer, then B >> i denotes the logical
right-shift operation. Similarly, B << i denotes the logical left-
shift operation.
If X is a x-byte string and Y a y-byte string, then X || Y denotes
the concatenation of X and Y, with X || Y =
X[0]...X[x-1]Y[0]...Y[y-1].
2.3. Functions
If x is a non-negative real number, then we define the following
functions:
ceil(x) : returns the smallest integer greater or equal than x.
floor(x) : returns the largest integer less or equal than x.
lg(x) : returns the base-2 logarithm of x.
If x, y, and z are real numbers, then we define the functions max(x,
y) and max(x, y, z) which return the maximum value of the set {x, y}
and {x, y, z}, respectively.
2.4. Strings of Base-w Numbers
A byte string can be considered as a string of base-w numbers, i.e.
integers in the set {0, ... , w - 1}. The correspondence is defined
by the function base_w(X, w) as follows. If X is a m-byte string, w
is a member of the set {4, 8, 16}, then base_w(X, w) outputs a length
ceil(8m/lg(w)) array of integers between 0 and w - 1. In case lg(w)
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does not divide 8 * m without a remainder, X is virtually padded with
a sufficient amount of zero bits.
Algorithm 1: base_w(X, w)
i_byte = 0;
i_bit = 0;
for ( i=0; i < ceil(8m/lg(w)); i++ ){
if( i_bit + lg(w) <= 8 ){
basew[i] = ((X[i_byte] << i_bit) >> (8-lg(w))) AND (w-1);
i_bit += lg(w);
if ( i_bit == 8 ){
i_bit = 0;
i_byte = i_byte + 1;
}
} else {
basew[i] = ((X[i_byte] << i_bit) >> (8-lg(w))) AND (w-1);
i_byte = i_byte + 1;
if ( i_byte < m ){
basew[i] += (X[i_byte] >> (8-(i_bit + lg(w)-8))) AND (w-1);
i_bit = i_bit + lg(w)-8;
}
}
}
return basew;
For example, if X is 0x1234, then base_w(X, 8) returns the array {0,
4, 4, 3, 2, 0}.
X (represented as bits)
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 0| 1| 0| 0| 1| 0| 0| 0| 1| 1| 0| 1| 0| 0|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
X (padded with zeros)
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| 0| 0| 0| 1| 0| 0| 1| 0| 0| 0| 1| 1| 0| 1| 0| 0| 0| 0|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
X (represented as base-w numbers)
+--------+--------+--------+--------+--------+--------+
| 0 | 4 | 4 | 3 | 2 | 0 |
+--------+--------+--------+--------+--------+--------+
2.5. Member Functions
To simplify algorithm descriptions, we assume the existence of member
functions. If a complex data structure like a public key PK contains
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a value X then getX(PK) returns the value of X for this public key.
Accordingly, setX(PK, X, Y) sets value X in PK to the value hold by
Y.
3. Primitives
3.1. WOTS+ One-Time Signatures
This section describes the WOTS+ one-time signature system, as
defined in [Huelsing13]. WOTS+ is a one-time signature scheme; while
a private key can be used to sign any message, each private key MUST
be used only once to sign a single message. In particular, if a
secret key is used to sign two different messages, the scheme becomes
insecure.
The section starts with an explanation of parameters. Afterwards,
the so-called chaining function, which forms the main building block
of the WOTS+ scheme, is explained. It follows a description of the
algorithms for key generation, signing and verification. Finally,
pseudorandom key generation is discussed.
3.1.1. WOTS+ Parameters
WOTS+ uses the parameters m, n, and w; they all take positive integer
values. These parameters are summarized as follows:
m : the message length in bytes
n : the length, in bytes, of a secret key, public key, or
signature element
w : the Winternitz parameter; it is a member of the set {4, 8, 16}
The parameters are used to compute values l, l_1 and l_2:
l : the number of n-byte string elements in a WOTS+ secret key,
public key, and signature. It is computed as l = l_1 + l_2, with
l_1 = ceil(8m/lg(w)) and l_2 = floor(lg(l_1*(w-1))/lg(w)) + 1
The value of n is determined by the cryptographic hash function used
for WOTS+. The hash function is chosen to ensure an appropriate
level of security. The value of m is often the length of a message
digest. The parameter w can be chosen from the set {4,8,16}. A
larger value of w results in shorter signatures but slower overall
signing operations; it has little effect on security. Choices of w
are limited to the values 4, 8 and 16 since these values yield
optimal trade-offs.
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3.1.1.1. WOTS+ Hashing Functions
The WOTS+ algorithm uses a cryptographic hash function F. F accepts
and returns byte strings of length n. Security requirements on F are
discussed in Section 8.
3.1.2. WOTS+ Chaining Function
The chaining function (Algorithm 2) computes an iteration of F on an
n-byte input using a vector of n-byte strings called bitmasks. In
each iteration, a bitmask is first XORed to an intermediate result
before it is processed by F. In the following, bm is an array of at
least w-2 n-byte strings (that contains the bitmasks). The chaining
function takes as input an n-byte string X, a start index i, a number
of steps s, and the bitmasks bm. The chaining function returns as
output the value obtained by iterating F for s times on input X,
using the bitmasks from bm starting at index i.
Algorithm 2: Chaining Function
if s is equal to 0 then
return X;
end
if (i+s) > w-1 then
return NULL;
end
byte[n] tmp = chain(X, i, s-1, bm);
tmp = F(tmp XOR bm[i+s-1]);
return tmp;
3.1.3. WOTS+ Private Key
The private key in WOTS+, denoted by sk, is a length l array of
n-byte strings. This private key MUST be only used to sign exactly
one message. Each n-byte string MUST either be selected randomly
from the uniform distribution or using a cryptographically secure
pseudorandom procedure. In the latter case, the security of the used
procedure MUST at least match that of the WOTS+ parameters used. For
a further discussion on pseudorandom key generation see the end of
this section. The following pseudocode (Algorithm 3) describes an
algorithm for generating sk.
Algorithm 3: Generating a WOTS+ Private Key
for ( i = 0; i < l; i = i + 1 ) {
set sk[i] to a uniformly random n-byte string
}
return sk
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3.1.4. WOTS+ Public Key
A WOTS+ key pair defines a virtual structure that consists of l hash
chains of length w. The l n-byte strings in the secret key each
define the start node for one hash chain. The public key consists of
the end nodes of these hash chains. Therefore, like the secret key,
the public key is also a length l array of n-byte strings. To
compute the hash chain, the chaining function (Algorithm 2) is used.
The bitmasks have to be provided by the calling algorithm. The same
bitmasks are used for all chains. The following pseudocode
(Algorithm 4) describes an algorithm for generating the public key
pk, where sk is the private key.
Algorithm 4 (WOTS_genPK): Generating a WOTS+ Public Key From a
Private Key
for ( i = 0; i < l; i = i + 1 ) {
pk[i] = chain(sk[i], 0, w-1, bm);
}
return pk;
3.1.5. WOTS+ Signature Generation
A WOTS+ signature is a length l array of n-byte strings. The WOTS+
signature is generated by mapping a message to l integers between 0
and w - 1. To this end, the message is transformed into base w
numbers using the base_w function defined in Section 2.4. Next, a
checksum is computed and appended to the transformed message as base
w numbers using base_w(). Each of the base w integers is used to
select a node from a different hash chain. The signature is formed
by concatenating the selected nodes. The pseudocode for signature
generation is shown below (Algorithm 5), where M is the message and
sig is the resulting signature.
Algorithm 5 (WOTS_sign): Generating a signature from a private key
and a message
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csum = 0;
// convert message to base w
msg = base_w(M,w)
// compute checksum
for ( i = 0; i < l_1; i = i + 1 ) {
csum = csum + w - 1 - msg[i]
}
// Convert csum to base w
msg = msg || base_w(csum, w);
for ( i = 0; i < l; i = i + 1 ) {
sig[i] = chain(sk[i], 0, msg[i], bm)
}
return sig
The data format for a signature is given below.
WOTS+ Signature
+---------------------------------+
| algorithm OID |
+---------------------------------+
| |
| sig_ots[0] | n bytes
| |
+---------------------------------+
| |
~ .... ~
| |
+---------------------------------+
| |
| sig_ots[l-1] | n bytes
| |
+---------------------------------+
3.1.6. WOTS+ Signature Verification
In order to verify a signature sig on a message M, the verifier
computes a WOTS+ public key value from the signature. This can be
done by "completing" the chain computations starting from the
signature values, using the base-w values of the message hash and its
checksum. This step, called WOTS_pkFromSig, is described below in
Algorithm 6. The result of WOTS_pkFromSig is then compared to the
given public key. If the values are equal, the signature is
accepted. Otherwise, the signature is rejected.
Algorithm 6 (WOTS_pkFromSig): Computing a WOTS+ public key from a
message and its signature
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csum = 0;
// convert message to base w
msg = base_w(M,w)
// compute checksum
for ( i = 0; i < l_1; i = i + 1 ) {
csum = csum + w - 1 - msg[i]
}
// Convert csum to base w
msg = msg || base_w(csum, w);
for ( i = 0; i < l; i = i + 1 ) {
tmp_pk[i] = chain(sig[i], msg[i], w-1-msg[i], bm)
}
return tmp_pk
Note: XMSS uses WOTS_pkFromSig to compute a public key value and
delays the comparison to a later point.
3.1.7. Pseudorandom Key Generation
An implementation MAY use a cryptographically secure pseudorandom
method to generate the secret key from a single n-byte value. For
example, the method suggested in [BDH11] and explained below MAY be
used. Other methods MAY be used. The choice of a pseudorandom
method does not affect interoperability, but the cryptographic
strength MUST match that of the used WOTS+ parameters.
The advantage of generating the secret key elements from a random
n-byte string is that only this n-byte string needs to be stored
instead of the full secret key. The key can be regenerated when
needed. The suggested method from [BDH11] uses a pseudorandom
function G(K,M) that takes an n-byte key and an n-byte message.
During key generation a uniformly random n-byte string S is sampled
from a secure source of randomness. The secret key elements are
computed as sk[i] = G(S,i) whenever needed. The second parameter of
G is i, represented as n-byte string in the common way. To implement
G, an implementation MAY use the hash function F in PRF mode. When
WOTS+ is used within XMSS or XMSS^MT, an implementation SHOULD use
PRF_m, taking the first n bytes from the output.
4. Schemes
In this section, the extended Merkle signature scheme (XMSS) is
described using WOTS+. XMSS comes in two flavours: First, a single-
tree variant (XMSS) and second a multi-tree variant (XMSS^MT). Both
allow combining a large number of WOTS+ key pairs under a single
small public key. The main ingredient added is a binary hash tree
construction. XMSS uses a single hash tree while XMSS^MT uses a tree
of XMSS key pairs.
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4.1. XMSS: eXtended Merkle Signature Scheme
XMSS is a method for signing a potentially large but fixed number of
messages. It is based on the Merkle signature scheme. XMSS uses
four cryptographic components: WOTS+ as OTS method, two additional
cryptographic hash functions H and H_m, and a pseudorandom function
PRF_m. One of the main advantages of XMSS with WOTS+ is that it does
not rely on the collision resistance of the used hash functions but
on weaker properties. Each XMSS public/private key pair is
associated with a perfect binary tree, every node of which contains
an n-byte value. Each tree leaf contains a special tree hash of a
WOTS+ public key value. Each non-leaf tree node is computed by first
concatenating the values of its child nodes, computing the XOR with a
bitmask, and applying the hash function H to the result. The value
corresponding to the root of the XMSS tree forms the XMSS public key
together with the bitmasks.
To generate a key pair that can be used to sign 2^h messages, a tree
of height h is used. XMSS is a stateful signature scheme, meaning
that the secret key changes after every signature. To prevent one-
time secret keys from being used twice, the WOTS+ key pairs are
numbered from 0 to (2^h)-1 according to the related leaf, starting
from index 0 for the leftmost leaf. The secret key contains an index
that is updated after every signature, such that it contains the
index of the next unused WOTS+ key pair.
A signature consists of the index of the used WOTS+ key pair, the
WOTS+ signature on the message and the so-called authentication path.
The latter is a vector of tree nodes that allow a verifier to compute
a value for the root of the tree. A verifier computes the root value
and compares it to the respective value in the XMSS public key. If
they match, the signature is valid. The XMSS secret key consists of
all WOTS+ secret keys and the actual index. To reduce storage, a
pseudorandom key generation procedure, as described in [BDH11], MAY
be used. The security of the used method MUST at least match the
security of the XMSS instance.
4.1.1. XMSS Parameters
XMSS has the following parameters:
h : the height (number of levels - 1) of the tree
n : the length in bytes of each node
m : the length of the message digest
w : the Winternitz parameter as defined for WOTS+ in Section 3.1
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There are N = 2^h leaves in the tree. XMSS uses num_bm = max{2 * (h
+ ceil(lg(l))), w - 2} bitmasks produced during key generation.
For XMSS and XMSS^MT, secret and public keys are denoted by SK and
PK. For WOTS+, secret and public keys are denoted by sk and pk,
respectively. XMSS and XMSS^MT signatures are denoted by Sig. WOTS+
signatures are denoted by sig.
4.1.2. XMSS Hash Functions
Besides the cryptographic hash function F required by WOTS+, XMSS
uses three more functions:
A cryptographic hash function H. H accepts byte strings of length
(2 * n) and returns an n-byte string.
A cryptographic hash function H_m. H_m accepts byte strings of
arbitrary length and returns an m-byte string.
A pseudorandom function PRF_m. PRF_m accepts byte strings of
arbitrary length and an m-byte key and returns an m-byte string.
4.1.3. XMSS Private Key
An XMSS private key contains N = 2^h WOTS+ private keys, the leaf
index idx of the next WOTS+ private key that has not yet been used
and SK_PRF, an m-byte key for the PRF. The leaf index idx is
initialized to zero when the XMSS private key is created. The PRF
key SK_PRF MUST be sampled from a secure source of randomness that
follows the uniform distribution. The WOTS+ secret keys MUST be
generated as described in Section 3.1. To reduce the secret key
size, a cryptographic pseudorandom method MAY be used as discussed at
the end of this section. For the following algorithm descriptions,
the existence of a method getWOTS_SK(SK,i) is assumed. This method
takes as inputs an XMSS secret key SK and an integer i and outputs
the i^th WOTS+ secret key of SK.
4.1.4. L-Trees
To compute the leaves of the binary hash tree, a so-called L-tree is
used. An L-tree is an unbalanced binary hash tree, distinct but
similar to the main XMSS binary hash tree. The algorithm ltree
(Algorithm 7) takes as input a WOTS+ public key pk and compresses it
to a single n-byte value pk[0]. The algorithm uses the first (2 *
ceil( log(l) )) of the num_bm n-byte bitmasks bm.
Algorithm 7: ltree
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unsigned int l' = l
unsigned int j = 0
while ( l' > 1 ) {
for ( i = 0; i < floor(l' / 2); i = i + 1 ) {
pk[i] = H((pk[2i] XOR bm[j]) || (pk[2i + 1] XOR bm[j + 1]))
}
if ( l' is equal to 1 % 2 ) {
pk[floor(l' / 2) + 1] = pk[l']
}
l' = ceil(l' / 2)
j = j + 2
}
return pk[0]
4.1.5. TreeHash
For the computation of the internal n-byte nodes of a Merkle tree,
the subroutine treeHash (Algorithm 8) accepts an XMSS secret key SK,
an unsigned integer s (the start index), an unsigned integer h (the
target node height) and the bitmasks bm. The treeHash algorithm
returns the root node of a tree of height h with the leftmost leaf
being the hash of the WOTS+ pk with index s. The treeHash algorithm
uses a stack holding up to (h-1) n-byte strings, with the usual stack
functions push() and pop().
Algorithm 8: treeHash
for ( i = 0; i < 2^h; i = i + 1 ) {
pk = WOTS_genPK (getWOTS_SK(SK, s+i), bm)
node = ltree(pk, bm)
while ( Top node on Stack has same height h' as node ) {
node = H((Stack.pop() XOR bm[2l + 2h']) ||
(node XOR bm[2l + 2h' + 1]))
}
Stack.push(node)
}
return Stack.pop()
4.1.6. XMSS Public Key
The XMSS public key is computed as described in XMSS_genPK (Algorithm
9). The algorithm takes the num_bm n-byte bitmasks bm, the XMSS
secret key SK, and the tree height h. The XMSS public key PK
consists of the root of the binary hash tree and the bitmasks bm.
Algorithm 9: XMSS_genPK - Generate an XMSS public key from an XMSS
private key
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for ( i = 0; i < num_bm; i = i + 1 ) {
set bm[i] to a uniformly random n-byte string
}
root = treeHash(SK, 0, h, bm)
PK = root || bm
return PK
Public and private key generation MAY be interleaved to save space.
Especially, when a pseudorandom method is used to generate the secret
key, generation MAY be done when the respective WOTS+ key pair is
needed by treeHash.
The format of an XMSS public key is given below.
XMSS Public Key
+---------------------------------+
| algorithm OID |
+---------------------------------+
| |
| root node | n bytes
| |
+---------------------------------+
| |
| bm[0] | n bytes
| |
+---------------------------------+
| |
~ .... ~
| |
+---------------------------------+
| |
| bm[num_bm-1] | n bytes
| |
+---------------------------------+
4.1.7. XMSS Signature
An XMSS signature is a (4 + m + (l + h) * n)-byte string consisting
of
the index idx_sig of the used WOTS+ key pair (4 bytes),
a byte string r used for randomized hashing (m bytes),
a WOTS+ signature sig_ots (l * n bytes),
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the so called authentication path 'auth' for the leaf associated
with the used WOTS+ key pair (h * n bytes).
The authentication path is an array of h n-byte strings. It contains
the siblings of the nodes on the path from the used leaf to the root.
It does not contain the nodes on the path itself. These nodes are
needed by a verifier to compute a root node for the tree from the
WOTS+ public key. A node Node is addressed by its position in the
tree. Node(x,y) denotes the x^th node on level y with x = 0 being
the leftmost node on a level. The leaves are on level 0, the root is
on level h. An authentication path contains exactly one node on
every layer 0 <= x <= h-1. For the i^th WOTS+ key pair, counting
from zero, the j^th authentication path node is
Node(j, floor(i / (2^j)) + 1) if floor(i / (2^j)) is even or
Node(j, floor(i / (2^j)) - 1) if floor(i / (2^j)) is odd.
Given an XMSS secret key SK and bitmasks bm, all nodes in a tree are
determined. Their value is defined in terms of treeHash (Algorithm
8):
Node(x,y) = treeHash(SK, x * 2^y, y, bm).
The data format for a signature is given below.
XMSS Signature
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+---------------------------------+
| algorithm OID |
+---------------------------------+
| |
| index idx_sig | 4 bytes
| |
+---------------------------------+
| |
| randomness r | m bytes
| |
+---------------------------------+
| |
| WOTS+ signature sig_ots | l * n bytes
| |
+---------------------------------+
| |
| auth[0] | n bytes
| |
+---------------------------------+
| |
~ .... ~
| |
+---------------------------------+
| |
| auth[h-1] | n bytes
| |
+---------------------------------+
4.1.8. XMSS Signature Generation
To compute the XMSS signature of a message M with an XMSS private
key, the signer first computes a randomized message digest. Then a
WOTS+ signature of the message is computed using the next unused
WOTS+ private key. Next, the authentication path is computed.
Finally, the secret key is updated, i.e. idx is incremented. An
implementation MUST NOT output the signature before the updated
private key.
The node values of the authentication path MAY be computed in any
way. This computation is assumed to be performed by the subroutine
buildAuth for the function XMSS_sign, as below. The fastest
alternative is to store all tree nodes and set the array in the
signature by copying them, respectively. The least storage-intensive
alternative is to recompute all nodes for each signature online.
There exist several algorithms in between, with different time/
storage trade-offs. For an overview see [BDS09]. Note that the
details of this procedure are not relevant to interoperability; it is
not necessary to know any of these details in order to perform the
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signature verification operation. As a consequence, buildAuth is not
specified here.
The algorithm XMSS_sign (Algorithm 10) described below calculates an
updated secret key SK and a signature on a message M. XMSS_sign
takes as inputs a message M of an arbitrary length, an XMSS secret
key SK and bitmasks bm. It returns the byte string containing the
concatenation of the updated secret key SK and the signature Sig.
Algorithm 10: XMSS_sign - Generate an XMSS signature and update the
XMSS secret key
idx_sig = getIdx(SK)
auth = buildAuth(SK, bm, idx_sig)
byte[m] r = PRF_m(getSK_PRF(SK), M)
byte[m] M' = H_m(r || M)
sig_ots = WOTS_sign(getWOTS_SK(SK, idx_sig), M', bm)
Sig = (idx_sig || r || sig_ots || auth)
setIdx(SK, idx_sig + 1)
return (SK || Sig)
4.1.9. XMSS Signature Verification
An XMSS signature is verified by first computing the message digest
using randomness r and a message M. Then the used WOTS+ public key
pk_ots is computed from the WOTS+ signature using WOTS_pkFromSig.
The WOTS+ public key in turn is used to compute the corresponding
leaf using an L-tree. The leaf, together with index idx_sig,
authentication path auth and bitmasks bm is used to compute an
alternative root value for the tree. These first steps are done by
XMSS_rootFromSig (Algorithm 11). The verification succeeds if and
only if the computed root value matches the one in the XMSS public
key. In any other case it MUST return fail.
The main part of XMSS signature verification is done by the function
XMSS_rootFromSig (Algorithm 11) described below. XMSS_rootFromSig
takes as inputs an XMSS signature Sig, a message M, and the bitmasks
bm. XMSS_rootFromSig returns an n-byte string holding the value of
the root of a tree defined by the input data.
Algorithm 11: XMSS_rootFromSig - Compute a root node using an XMSS
signature, a message, and bitmasks bm
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byte[m] M' = H_m(r || M)
pk_ots = WOTS_pkFromSig(sig_ots, M', bm)
byte[n][2] node
node[0] = ltree(pk_ots, bm)
for ( k = 1; k < h; k = k + 1 ) {
if ( floor(i / (2^k)) % 2 is equal to 0 ) {
node[1] = H((node[0] XOR bm[2l + 2k]) ||
(auth[k - 1] XOR bm[2l + 2k + 1]))
} else {
node[1] = H((auth[k - 1] XOR bm[2l + 2k]) ||
(node[0] XOR bm[2l + 2k + 1]))
}
node[0] = node[1]
}
return node[0]
The full XMSS signature verification is depicted below for
completeness. XMSS^MT uses only XMSS_rootFromSig and delegates the
comparison to a later comparison of data depending on its output.
Algorithm 12: XMSS_verify - Verify an XMSS signature using an XMSS
signature, the corresponding XMSS public key and a message
byte[n] node = XMSS_rootFromSig(Sig, M, getBM(PK))
if ( node is equal to root in PK ) {
return true
} else {
return false
}
4.1.10. Pseudorandom Key Generation
An implementation MAY use a cryptographically secure pseudorandom
method to generate the XMSS secret key from a single n-byte value.
For example, the method suggested in [BDH11] and explained below MAY
be used. Other methods MAY be used. The choice of a pseudorandom
method does not affect interoperability, but the cryptographic
strength MUST match that of the used XMSS parameters.
For XMSS a similar method than the one used for WOTS+ can be used.
The suggested method from [BDH11] uses a pseudorandom function G(K,M)
that takes an n-byte key and an n-byte message. During key
generation a uniformly random n-byte string S is sampled from a
secure source of randomness. This seed S is used to generate an
n-byte value S_ots for each WOTS+ key pair. This n-byte value can
then be used to compute the respective WOTS+ secret key using the
method described in Section 3.1.7. The seeds for the WOTS+ key pairs
are computed as S_ots[i] = G(S,i). The second parameter of G is the
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index i of the WOTS+ key pair, represented as n-byte string in the
common way. To implement G an implementation SHOULD use PRF_m,
taking the first n bytes from the output. An advantage of this
method is that a WOTS+ key can be computed using only l+1 evaluations
of G when S is given.
4.1.11. Free Index Handling and Partial Secret Keys
Some applications might require to work with partial secret keys or
copies of secret keys. Examples include delegation of signing rights
/ proxy signatures, and load balancing. Such applications MAY use
their own key format and MAY use a signing algorithm different from
the one described above. The index in partial secret keys or copies
of a secret key MAY be manipulated as required by the applications.
However, applications MUST establish means that guarantee that each
index and thereby each WOTS+ key pair is used to sign only a single
message.
4.2. XMSS^MT: Multi-Tree XMSS
XMSS^MT is a method for signing a large but fixed number of messages.
It was first described in [HRB13]. It builds on XMSS. XMSS^MT uses
a tree of several layers of XMSS trees. The trees on top and
intermediate layers are used to sign the root nodes of the trees on
the respective layer below. Trees on the lowest layer are used to
sign the actual messages. All XMSS trees have equal height.
Consider an XMSS^MT tree of total height h that has d layers of XMSS
trees of height h / d. Then layer d - 1 contains one XMSS tree,
layer d - 2 contains 2^(h / d) XMSS trees, and so on. Finally, layer
0 contains 2^(h - h / d) XMSS trees.
4.2.1. XMSS^MT Parameters
In addition to all XMSS parameters, an XMSS^MT system requires the
number of tree layers d, specified as an integer value that divides h
without remainder. The same tree height h / d and the same
Winternitz parameter w are used for all tree layers.
All the trees on higher layers sign root nodes of other trees which
are n-byte strings. Hence, no message compression is needed and
WOTS+ is used to sign the root nodes themselves instead of their hash
values. Hence the WOTS+ message length for these layers is n not m.
Accordingly, the values of l_1, l_2 and l change for these layers.
The parameters l_1_n, l_2_n, and l_n denote the respective values
computed using n as message length for WOTS+.
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4.2.2. XMSS Algorithms Without Message Hash
As all XMSS trees besides those on layer 0 are used to sign short
fixed length messages, the initial message hash can be omitted. In
the description below XMSS_sign_wo_hash and XMSS_rootFromSig_wo_hash
are versions of XMSS_sign and XMSS_rootFromSig, respectively, that
omit the initial message hash. They are obtained by setting M' = M
in the above algorithms. Accordingly, the evaluations of H_m and
PRF_m SHOULD be omitted. This also means that no randomization
element r for the message hash is required. XMSS signatures
generated by XMSS_sign_wo_hash and verified by
XMSS_rootFromSig_wo_hash MUST NOT contain a value r.
4.2.3. XMSS^MT Private Key
An XMSS^MT private key SK_MT consists of one reduced XMSS private key
for each XMSS tree. These reduced XMSS private keys contain no
pseudorandom function key and no index. Instead, SK_MT contains a
single m-byte pseudorandom function key SK_PRF and a single (ceil(h /
8))-byte index idx_MT. The index is a global index over all WOTS+
key pairs of all XMSS trees on layer 0. It is initialized with 0.
It stores the index of the last used WOTS+ key pair on the bottom
layer, i.e. a number between 0 and 2^h - 1.
The algorithm descriptions below uses a function getXMSS_SK(SK, x, y)
that outputs the reduced secret key of the x^th XMSS tree on the y^th
layer.
4.2.4. XMSS^MT Public Key
The XMSS^MT public key PK_MT contains the root of the single XMSS
tree on layer d-1 and the bitmasks. The same bitmasks are used for
all XMSS tress. Algorithm 13 shows pseudocode to generate PK_MT.
First, num_bm = max{ 2 * (h / d + ceil(lg(l))), 2 * (h / d +
ceil(lg(l_n))), w - 2 } n-byte bitmasks bm are chosen uniformly at
random. The n-byte root node of the top layer tree is computed using
treeHash. The algorithm XMSSMT_genPK takes the XMSS^MT secret key
SK_MT as an input and outputs an XMSS^MT public key PK_MT.
Algorithm 13: XMSSMT_genPK - Generate an XMSS^MT public key from an
XMSS^MT private key
for ( i = 0; i < num_bm; i = i + 1 ) {
set bm[i] to a uniformly random n-byte string
}
root = treeHash(getXMSS_SK(SK_MT, 0, d - 1), 0, h / d, bm)
PK_MT = root || bm
return PK_MT
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The format of an XMSS^MT public key is given below.
XMSS^MT Public Key
+---------------------------------+
| algorithm OID |
+---------------------------------+
| |
| root node | n bytes
| |
+---------------------------------+
| |
| bm[0] | n bytes
| |
+---------------------------------+
| |
~ .... ~
| |
+---------------------------------+
| |
| bm[num_bm-1] | n bytes
| |
+---------------------------------+
4.2.5. XMSS^MT Signature
An XMSS^MT signature Sig_MT is a byte string of length (ceil(h / 8) +
m + (h + l + (d - 1) * l_n) * n). It consists of
the index idx_sig of the used WOTS+ key pair on the bottom layer
(ceil(h / 8) bytes),
a byte string r used for randomized hashing (m bytes),
one reduced XMSS signature ((h + l) * n bytes),
d-1 reduced XMSS signatures with message length n ((h + l_n) * n
bytes).
The reduced XMSS signatures contain no index idx and no byte string
r. They only contain a WOTS+ signature sig_ots and an authentication
path auth. The first reduced XMSS signature contains a WOTS+
signature that consists of l n-byte elements. The remaining reduced
XMSS signatures contain a WOTS+ signature on an n-byte message and
hence consist of l_n n-byte elements.
The data format for a signature is given below.
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XMSS^MT signature
+---------------------------------+
| algorithm OID |
+---------------------------------+
| |
| index idx_sig | ceil(h / 8) bytes
| |
+---------------------------------+
| |
| randomness r | m bytes
| |
+---------------------------------+
| |
| (reduced) XMSS signature Sig | (h + l) * n bytes
| (bottom layer 0) |
| |
+---------------------------------+
| |
| (reduced) XMSS signature Sig | (h + l_n) * n bytes
| (layer 1) |
| |
+---------------------------------+
| |
~ .... ~
| |
+---------------------------------+
| |
| (reduced) XMSS signature Sig | (h + l_n) * n bytes
| (layer d-1) |
| |
+---------------------------------+
4.2.6. XMSS^MT Signature Generation
To compute the XMSS^MT signature Sig_MT of a message M using an
XMSS^MT private key SK_MT and bitmasks bm, XMSSMT_sign (Algorithm 14)
described below uses XMSS_sign and XMSS_sign_wo_hash as defined in
Section 4.2.2. First, the signature index is set to idx. Next,
PRF_m is used to compute a pseudorandom m-byte string r. This m-byte
string is then used to compute a randomized message digest of length
m. The message digest is signed using the WOTS+ key pair on the
bottom layer with absolute index idx. The authentication path for
the WOTS+ key pair is computed as well as the root of the containing
XMSS tree. The root is signed by the parent XMSS tree. This is
repeated until the top tree is reached.
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Algorithm 14: XMSSMT_sign - Generate an XMSS^MT signature and update
the XMSS^MT secret key
SK_PRF = getSK_PRF(SK_MT)
idx_sig = getIdx(SK_MT)
setIdx(SK_MT, idx_sig + 1)
Sig_MT = idx_sig
unsigned int idx_tree = (h - h / d) most significant bits of idx_sig
unsigned int idx_leaf = (h / d) least significant bits of idx_sig
SK = idx_leaf || SK_PRF || getXMSS_SK(SK_MT, idx_tree, 0)
Sig_tmp = XMSS_sign(M, SK, bm)
Sig_tmp = Sig_tmp without idx
Sig_MT = Sig_MT || Sig_tmp
for ( j = 1; j < d; j = j + 1 ) {
root = treeHash(SK, 0, h / d, bm)
idx_leaf = (h / d) least significant bits of idx_tree
idx_tree = (h - j * (h / d)) most significant bytes of idx_tree
SK = idx_leaf || SK_PRF || getXMSS_SK(SK_MT, idx_tree, j)
Sig_tmp = XMSS_sign_wo_hash(root, SK, bm) with idx removed
Sig_MT = Sig_MT || Sig_tmp
}
return SK_MT || Sig_MT
Algorithm 14 is only one method to compute XMSS^MT signatures.
Especially, there exist time-memory trade-offs that allow to reduce
the signing time to less than the signing time of an XMSS scheme with
tree height h / d. These trade-offs prevent certain values from being
recomputed several times by keeping a state and distribute all
computations over all signature generations. Details can be found in
[Huelsing13a].
4.2.7. XMSS^MT Signature Verification
XMSS^MT signature verification (Algorithm 15) can be summarized as d
XMSS signature verifications with small changes. First, only the
message is hashed. The remaining XMSS signatures are on the root
nodes of trees which have a fixed length. Second, instead of
comparing the computed root node to a given value, a signature on the
root is verified. Only the root node of the top tree is compared to
the value in the XMSS^MT public key. XMSSMT_verify uses
XMSS_rootFromSig and XMSS_rootFromSig_wo_hash. XMSSMT_verify takes
as inputs an XMSS^MT signature Sig^MT, a message M and a public key
PK_MT. It outputs a boolean.
Algorithm 15: XMSSMT_verify - Verify an XMSS^MT signature Sig_MT on a
message M using an XMSS^MT public key PK_MT
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idx = getIdx(Sig_MT)
unsigned int idx_leaf = (h / d) least significant bits of idx
unsigned int idx_tree = (h - h / d) most significant bits of idx
Sig' = leaf || setR(Sig_MT) || getXMSSSignature(Sig, 0)
byte[n] node = XMSS_rootFromSig(Sig', M, getBm(PK_MT))
for ( j = 1; j < d; j = j + 1 ) {
idx_leaf = (h / d) least significant bytes of idx_tree
idx_tree = (h - j * h / d) most significant bytes of idx_tree
Sig' = idx_leaf || getXMSSSignature(Sig, j)
node = XMSS_rootFromSig_wo_hash(Sig', node, getBm(PK_MT))
}
if ( node is equal to getRoot(PK_MT) ) {
return true
} else {
return false
}
4.2.8. Pseudorandom Key Generation
Like for XMSS, an implementation MAY use a cryptographically secure
pseudorandom method to generate the XMSS^MT secret key from a single
n-byte value. For example, the method explained below MAY be used.
Other methods MAY be used. The choice of a pseudorandom method does
not affect interoperability, but the cryptographic strength MUST
match that of the used XMSS parameters.
For XMSS^MT a method similar to that for XMSS and WOTS+ can be used.
The method uses a pseudorandom function G(K,M) that takes an n-byte
key and an n-byte message. During key generation a uniformly random
n-byte string S_MT is sampled from a secure source of randomness.
This seed S_MT is used to generate one n-byte value S for each XMSS
key pair. This n-byte value can be used to compute the respective
XMSS secret key using the method described in Section 4.1.10. Let
S[x][y] be the seed for the x^th XMSS secret key on layer y. The
seeds are computed as S[x][y] = G(G(S, y), x). The second parameter
of G is the index x (resp. level y), represented as n-byte string in
the common way. To implement G an implementation SHOULD use PRF_m,
taking the first n bytes from the output.
4.2.9. Free Index Handling and Partial Secret Keys
The content of Section 4.1.11 also applies to XMSS^MT.
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5. Parameter Sets
This note provides a first basic set of parameter sets which are
assumed to cover most relevant applicants. Parameter sets for three
classical security levels are defined: 128, 256 and 512 bits.
Function output sizes are n = 16, 32 and 64 bytes and m = 32, 64,
respectively. While m = n is used for n = 32 and n = 64, m = 32 is
used for the n = 16 case. Considering quantum-computer-aided
attacks, these output sizes yield post-quantum security of 64, 128
and 256 bits, respectively. The n = 16 parameter sets are included
to encourage adoption in the pre-quantum era as they lead to smaller
signatures and faster runtimes than other parameter sets. The n = 64
parameter sets are provided to support post-quantum scenarios.
For the n = 16 setting, this note only defines parameter sets with
AES-based hash functions. The reason is that they benefit from
hardware acceleration on many modern platforms. Let AES(K,M) denote
evaluation of AES-128 with 128 bit key K and 128 bit message M.
Define the 16-byte string IV = 0x0001020304050607080910111213141516.
Then F and H are implemented as
F(X) = AES(IV,X) XOR X
H(X) = AES( AES(IV, X1) XOR X1, X2) XOR X2
where X = X1 || X2, i.e. X1 denotes the most significant 16 bytes of
X and X2 the least significant 16 bytes. For these parameter sets
H_m is implemented as SHA3-256 and PRF_m as SHA3-256 in PRF/MAC mode.
For the n = m = 32 and n = m = 64 settings, all functions are
implemented using SHA3-256 and SHA3-512, respectively.
5.1. Zero Bitmasks
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For applications that require a very small public key this note
additionally defines zero bitmasks parameter sets. For these
parameter sets the bitmasks are set to an all-zero string. The XMSS
and XMSS^MT public keys for these parameter sets contain no bitmasks.
Instead, they only contain the single n-byte value holding the root
node. When handling zero bitmasks parameter sets, implementations
MAY internally use an all-zero string as bitmasks and stick to the
same algorithms as for the other parameter sets. Implementations MAY
omit the XOR with an all-zero bitmask. Zero bitmasks parameter sets
are only defined for n = 32 and n = 64, as formal security reductions
require the used hash functions to be collision-resistant in this
case. Hence, the estimated classical security levels are 128 and 256
bits for n = 32 and n = 64 with zero bitmasks, respectively. The
corresponding post-quantum security levels are approximately 85 and
170 bits, respectively.
5.2. WOTS+ Parameters
To fully describe a WOTS+ signature method, the parameters m, n, and
w, as well as the function F MUST be specified. This section defines
several WOTS+ signature systems, each of which is identified by a
name. Values for l are provided for convenience.
+------------------------+--------+----+----+----+-----+
| Name | F | m | n | w | l |
+------------------------+--------+----+----+----+-----+
| WOTSP_AES128_M32_W4 | AES128 | 32 | 16 | 4 | 133 |
| | | | | | |
| WOTSP_AES128_M32_W8 | AES128 | 32 | 16 | 8 | 90 |
| | | | | | |
| WOTSP_AES128_M32_W16 | AES128 | 32 | 16 | 16 | 67 |
| | | | | | |
| WOTSP_SHA3-256_M32_W4 | SHA3 | 32 | 32 | 4 | 133 |
| | | | | | |
| WOTSP_SHA3-256_M32_W8 | SHA3 | 32 | 32 | 8 | 90 |
| | | | | | |
| WOTSP_SHA3-256_M32_W16 | SHA3 | 32 | 32 | 16 | 67 |
| | | | | | |
| WOTSP_SHA3-512_M64_W4 | SHA3 | 64 | 64 | 4 | 261 |
| | | | | | |
| WOTSP_SHA3-512_M64_W8 | SHA3 | 64 | 64 | 8 | 175 |
| | | | | | |
| WOTSP_SHA3-512_M64_W16 | SHA3 | 64 | 64 | 16 | 131 |
+------------------------+--------+----+----+----+-----+
Table 1
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Here SHA3 denotes the NIST standard hash function, also known as
Keccak [DRAFTFIPS202]. XDR formats for WOTS+ are listed in
Appendix A.
5.3. XMSS Parameters
To fully describe an XMSS signature method, the parameters m, n, w,
and h, as well as the functions F, H, H_m and PRF_m MUST be
specified. This section defines several XMSS signature systems, each
of which is identified by a name.
The XDR formats for XMSS are listed in Appendix B.
5.3.1. XMSS Parameters
We first define XMSS signature methods as described in Section 4.1.
We define parameter sets that implement the functions using AES and
SHA3 as described above as well as pure SHA3 parameter sets.
5.3.1.1. XMSS Parameters with AES and SHA3
The following XMSS signature methods implement the functions F, H,
H_m and PRF_m using AES and SHA3 as described above.
+--------------------------+----+----+----+-----+----+
| Name | m | n | w | l | h |
+--------------------------+----+----+----+-----+----+
| XMSS_AES128_M32_W4_H10 | 32 | 16 | 4 | 133 | 10 |
| | | | | | |
| XMSS_AES128_M32_W4_H16 | 32 | 16 | 4 | 133 | 16 |
| | | | | | |
| XMSS_AES128_M32_W4_H20 | 32 | 16 | 4 | 133 | 20 |
| | | | | | |
| XMSS_AES128_M32_W8_H10 | 32 | 16 | 8 | 90 | 10 |
| | | | | | |
| XMSS_AES128_M32_W8_H16 | 32 | 16 | 8 | 90 | 16 |
| | | | | | |
| XMSS_AES128_M32_W8_H20 | 32 | 16 | 8 | 90 | 20 |
| | | | | | |
| XMSS_AES128_M32_W16_H10 | 32 | 16 | 16 | 67 | 10 |
| | | | | | |
| XMSS_AES128_M32_W16_H16 | 32 | 16 | 16 | 67 | 16 |
| | | | | | |
| XMSS_AES128_M32_W16_H20 | 32 | 16 | 16 | 67 | 20 |
+--------------------------+----+----+----+-----+----+
Table 2
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5.3.1.2. XMSS Parameters with SHA3
The following XMSS signature methods implement the functions F, H,
H_m and PRF_m solely using SHA3 as described above.
+----------------------------+----+----+----+-----+----+
| Name | m | n | w | l | h |
+----------------------------+----+----+----+-----+----+
| XMSS_SHA3-256_M32_W4_H10 | 32 | 32 | 4 | 133 | 10 |
| | | | | | |
| XMSS_SHA3-256_M32_W4_H16 | 32 | 32 | 4 | 133 | 16 |
| | | | | | |
| XMSS_SHA3-256_M32_W4_H20 | 32 | 32 | 4 | 133 | 20 |
| | | | | | |
| XMSS_SHA3-256_M32_W8_H10 | 32 | 32 | 8 | 90 | 10 |
| | | | | | |
| XMSS_SHA3-256_M32_W8_H16 | 32 | 32 | 8 | 90 | 16 |
| | | | | | |
| XMSS_SHA3-256_M32_W8_H20 | 32 | 32 | 8 | 90 | 20 |
| | | | | | |
| XMSS_SHA3-256_M32_W16_H10 | 32 | 32 | 16 | 67 | 10 |
| | | | | | |
| XMSS_SHA3-256_M32_W16_H16 | 32 | 32 | 16 | 67 | 16 |
| | | | | | |
| XMSS_SHA3-256_M32_W16_H20 | 32 | 32 | 16 | 67 | 20 |
| | | | | | |
| XMSS_SHA3-512_M64_W4_H10 | 64 | 64 | 4 | 261 | 10 |
| | | | | | |
| XMSS_SHA3-512_M64_W4_H16 | 64 | 64 | 4 | 261 | 16 |
| | | | | | |
| XMSS_SHA3-512_M64_W4_H20 | 64 | 64 | 4 | 261 | 20 |
| | | | | | |
| XMSS_SHA3-512_M64_W8_H10 | 64 | 64 | 8 | 175 | 10 |
| | | | | | |
| XMSS_SHA3-512_M64_W8_H16 | 64 | 64 | 8 | 175 | 16 |
| | | | | | |
| XMSS_SHA3-512_M64_W8_H20 | 64 | 64 | 8 | 175 | 20 |
| | | | | | |
| XMSS_SHA3-512_M64_W16_H10 | 64 | 64 | 16 | 131 | 10 |
| | | | | | |
| XMSS_SHA3-512_M64_W16_H16 | 64 | 64 | 16 | 131 | 16 |
| | | | | | |
| XMSS_SHA3-512_M64_W16_H20 | 64 | 64 | 16 | 131 | 20 |
+----------------------------+----+----+----+-----+----+
Table 3
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5.3.2. XMSS Parameters With Empty Bitmasks
We now define XMSS signature methods for the zero bitmasks special
case described in Section 5.1. For this setting all signature
methods implement the functions F, H, H_m and PRF_m solely using SHA3
as described above.
+------------------------------+----+----+----+-----+----+
| Name | m | n | w | l | h |
+------------------------------+----+----+----+-----+----+
| XMSS_SHA3-256_M32_W4_H10_z | 32 | 32 | 4 | 133 | 10 |
| | | | | | |
| XMSS_SHA3-256_M32_W4_H16_z | 32 | 32 | 4 | 133 | 16 |
| | | | | | |
| XMSS_SHA3-256_M32_W4_H20_z | 32 | 32 | 4 | 133 | 20 |
| | | | | | |
| XMSS_SHA3-256_M32_W8_H10_z | 32 | 32 | 8 | 90 | 10 |
| | | | | | |
| XMSS_SHA3-256_M32_W8_H16_z | 32 | 32 | 8 | 90 | 16 |
| | | | | | |
| XMSS_SHA3-256_M32_W8_H20_z | 32 | 32 | 8 | 90 | 20 |
| | | | | | |
| XMSS_SHA3-256_M32_W16_H10_z | 32 | 32 | 16 | 67 | 10 |
| | | | | | |
| XMSS_SHA3-256_M32_W16_H16_z | 32 | 32 | 16 | 67 | 16 |
| | | | | | |
| XMSS_SHA3-256_M32_W16_H20_z | 32 | 32 | 16 | 67 | 20 |
| | | | | | |
| XMSS_SHA3-512_M64_W4_H10_z | 64 | 64 | 4 | 261 | 10 |
| | | | | | |
| XMSS_SHA3-512_M64_W4_H16_z | 64 | 64 | 4 | 261 | 16 |
| | | | | | |
| XMSS_SHA3-512_M64_W4_H20_z | 64 | 64 | 4 | 261 | 20 |
| | | | | | |
| XMSS_SHA3-512_M64_W8_H10_z | 64 | 64 | 8 | 175 | 10 |
| | | | | | |
| XMSS_SHA3-512_M64_W8_H16_z | 64 | 64 | 8 | 175 | 16 |
| | | | | | |
| XMSS_SHA3-512_M64_W8_H20_z | 64 | 64 | 8 | 175 | 20 |
| | | | | | |
| XMSS_SHA3-512_M64_W16_H10_z | 64 | 64 | 16 | 131 | 10 |
| | | | | | |
| XMSS_SHA3-512_M64_W16_H16_z | 64 | 64 | 16 | 131 | 16 |
| | | | | | |
| XMSS_SHA3-512_M64_W16_H20_z | 64 | 64 | 16 | 131 | 20 |
+------------------------------+----+----+----+-----+----+
Table 4
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5.4. XMSS^MT Parameters
To fully describe an XMSS^MT signature method, the parameters m, n,
w, h, and d, as well as the functions F, H, H_m and PRF_m MUST be
specified. This section defines several XMSS^MT signature systems,
each of which is identified by a name.
XDR formats for XMSS^MT are listed in Appendix C.
5.4.1. XMSS^MT Parameters
We first define XMSS^MT signature methods as described in
Section 4.2. We define parameter sets that implement the functions
using AES and SHA3 as described above as well as pure SHA3 parameter
sets.
5.4.1.1. XMSS^MT Parameters with AES and SHA3
The following XMSS^MT signature methods implement the functions F, H,
H_m and PRF_m using AES and SHA3 as described above.
+-------------------------------+----+----+----+-----+----+----+
| Name | m | n | w | l | h | d |
+-------------------------------+----+----+----+-----+----+----+
| XMSSMT_AES128_M32_W4_H20_D2 | 32 | 16 | 4 | 133 | 20 | 2 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H20_D4 | 32 | 16 | 4 | 133 | 20 | 4 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H40_D2 | 32 | 16 | 4 | 133 | 40 | 2 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H40_D4 | 32 | 16 | 4 | 133 | 40 | 4 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H40_D8 | 32 | 16 | 4 | 133 | 40 | 8 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H60_D3 | 32 | 16 | 4 | 133 | 60 | 3 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H60_D6 | 32 | 16 | 4 | 133 | 60 | 6 |
| | | | | | | |
| XMSSMT_AES128_M32_W4_H60_D12 | 32 | 16 | 4 | 133 | 60 | 12 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H20_D2 | 32 | 16 | 8 | 90 | 20 | 2 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H20_D4 | 32 | 16 | 8 | 90 | 20 | 4 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H40_D2 | 32 | 16 | 8 | 90 | 40 | 2 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H40_D4 | 32 | 16 | 8 | 90 | 40 | 4 |
| | | | | | | |
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| XMSSMT_AES128_M32_W8_H40_D8 | 32 | 16 | 8 | 90 | 40 | 8 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H60_D3 | 32 | 16 | 8 | 90 | 60 | 3 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H60_D6 | 32 | 16 | 8 | 90 | 60 | 6 |
| | | | | | | |
| XMSSMT_AES128_M32_W8_H60_D12 | 32 | 16 | 8 | 90 | 60 | 12 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H20_D2 | 32 | 16 | 16 | 67 | 20 | 2 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H20_D4 | 32 | 16 | 16 | 67 | 20 | 4 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H40_D2 | 32 | 16 | 16 | 67 | 40 | 2 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H40_D4 | 32 | 16 | 16 | 67 | 40 | 4 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H40_D8 | 32 | 16 | 16 | 67 | 40 | 8 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H60_D3 | 32 | 16 | 16 | 67 | 60 | 3 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H60_D6 | 32 | 16 | 16 | 67 | 60 | 6 |
| | | | | | | |
| XMSSMT_AES128_M32_W16_H60_D12 | 32 | 16 | 16 | 67 | 60 | 12 |
+-------------------------------+----+----+----+-----+----+----+
Table 5
5.4.1.2. XMSS^MT Parameters with SHA3
The following XMSS^MT signature methods implement the functions F, H,
H_m and PRF_m solely using SHA3 as described above.
+----------------------------------+----+----+----+-----+----+----+
| Name | m | n | w | l | h | d |
+----------------------------------+----+----+----+-----+----+----+
| XMSSMT_SHA3-256_M32_W4_H20_D2 | 32 | 32 | 4 | 133 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H20_D4 | 32 | 32 | 4 | 133 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H40_D2 | 32 | 32 | 4 | 133 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H40_D4 | 32 | 32 | 4 | 133 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H40_D8 | 32 | 32 | 4 | 133 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H60_D3 | 32 | 32 | 4 | 133 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H60_D6 | 32 | 32 | 4 | 133 | 60 | 6 |
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| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H60_D12 | 32 | 32 | 4 | 133 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H20_D2 | 32 | 32 | 8 | 90 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H20_D4 | 32 | 32 | 8 | 90 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H40_D2 | 32 | 32 | 8 | 90 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H40_D4 | 32 | 32 | 8 | 90 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H40_D8 | 32 | 32 | 8 | 90 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H60_D3 | 32 | 32 | 8 | 90 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H60_D6 | 32 | 32 | 8 | 90 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H60_D12 | 32 | 32 | 8 | 90 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H20_D2 | 32 | 32 | 16 | 67 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H20_D4 | 32 | 32 | 16 | 67 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H40_D2 | 32 | 32 | 16 | 67 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H40_D4 | 32 | 32 | 16 | 67 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H40_D8 | 32 | 32 | 16 | 67 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H60_D3 | 32 | 32 | 16 | 67 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H60_D6 | 32 | 32 | 16 | 67 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H60_D12 | 32 | 32 | 16 | 67 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H20_D2 | 64 | 64 | 4 | 261 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H20_D4 | 64 | 64 | 4 | 261 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H40_D2 | 64 | 64 | 4 | 261 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H40_D4 | 64 | 64 | 4 | 261 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H40_D8 | 64 | 64 | 4 | 261 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H60_D3 | 64 | 64 | 4 | 261 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H60_D6 | 64 | 64 | 4 | 261 | 60 | 6 |
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| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H60_D12 | 64 | 64 | 4 | 261 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H20_D2 | 64 | 64 | 8 | 175 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H20_D4 | 64 | 64 | 8 | 175 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H40_D2 | 64 | 64 | 8 | 175 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H40_D4 | 64 | 64 | 8 | 175 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H40_D8 | 64 | 64 | 8 | 175 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H60_D3 | 64 | 64 | 8 | 175 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H60_D6 | 64 | 64 | 8 | 175 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H60_D12 | 64 | 64 | 8 | 175 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H20_D2 | 64 | 64 | 16 | 131 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H20_D4 | 64 | 64 | 16 | 131 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H40_D2 | 64 | 64 | 16 | 131 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H40_D4 | 64 | 64 | 16 | 131 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H40_D8 | 64 | 64 | 16 | 131 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H60_D3 | 64 | 64 | 16 | 131 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H60_D6 | 64 | 64 | 16 | 131 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H60_D12 | 64 | 64 | 16 | 131 | 60 | 12 |
+----------------------------------+----+----+----+-----+----+----+
Table 6
5.4.2. XMSS^MT Parameters With Empty Bitmasks
We now define XMSS^MT signature methods for the zero bitmasks special
case described in Section 5.1. For this setting all signature
methods implement the functions F, H, H_m and PRF_m solely using SHA3
as described above.
+-----------------------------------+----+----+----+-----+----+----+
| Name | m | n | w | l | h | d |
+-----------------------------------+----+----+----+-----+----+----+
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| XMSSMT_SHA3-256_M32_W4_H20_D2_z | 32 | 32 | 4 | 133 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H20_D4_z | 32 | 32 | 4 | 133 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H40_D2_z | 32 | 32 | 4 | 133 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H40_D4_z | 32 | 32 | 4 | 133 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H40_D8_z | 32 | 32 | 4 | 133 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H60_D3_z | 32 | 32 | 4 | 133 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H60_D6_z | 32 | 32 | 4 | 133 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W4_H60_D12_z | 32 | 32 | 4 | 133 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H20_D2_z | 32 | 32 | 8 | 90 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H20_D4_z | 32 | 32 | 8 | 90 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H40_D2_z | 32 | 32 | 8 | 90 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H40_D4_z | 32 | 32 | 8 | 90 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H40_D8_z | 32 | 32 | 8 | 90 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H60_D3_z | 32 | 32 | 8 | 90 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H60_D6_z | 32 | 32 | 8 | 90 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W8_H60_D12_z | 32 | 32 | 16 | 67 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H20_D2_z | 32 | 32 | 16 | 67 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H20_D4_z | 32 | 32 | 16 | 67 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H40_D2_z | 32 | 32 | 16 | 67 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H40_D4_z | 32 | 32 | 16 | 67 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H40_D8_z | 32 | 32 | 16 | 67 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H60_D3_z | 32 | 32 | 16 | 67 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H60_D6_z | 32 | 32 | 16 | 67 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-256_M32_W16_H60_D12_z | 32 | 32 | 16 | 67 | 60 | 12 |
| | | | | | | |
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| XMSSMT_SHA3-512_M64_W4_H20_D2_z | 64 | 64 | 4 | 261 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H20_D4_z | 64 | 64 | 4 | 261 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H40_D2_z | 64 | 64 | 4 | 261 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H40_D4_z | 64 | 64 | 4 | 261 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H40_D8_z | 64 | 64 | 4 | 261 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H60_D3_z | 64 | 64 | 4 | 261 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H60_D6_z | 64 | 64 | 4 | 261 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W4_H60_D12_z | 64 | 64 | 4 | 261 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H20_D2_z | 64 | 64 | 8 | 175 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H20_D4_z | 64 | 64 | 8 | 175 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H40_D2_z | 64 | 64 | 8 | 175 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H40_D4_z | 64 | 64 | 8 | 175 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H40_D8_z | 64 | 64 | 8 | 175 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H60_D3_z | 64 | 64 | 8 | 175 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H60_D6_z | 64 | 64 | 8 | 175 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W8_H60_D12_z | 64 | 64 | 8 | 175 | 60 | 12 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H20_D2_z | 64 | 64 | 16 | 131 | 20 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H20_D4_z | 64 | 64 | 16 | 131 | 20 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H40_D2_z | 64 | 64 | 16 | 131 | 40 | 2 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H40_D4_z | 64 | 64 | 16 | 131 | 40 | 4 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H40_D8_z | 64 | 64 | 16 | 131 | 40 | 8 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H60_D3_z | 64 | 64 | 16 | 131 | 60 | 3 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H60_D6_z | 64 | 64 | 16 | 131 | 60 | 6 |
| | | | | | | |
| XMSSMT_SHA3-512_M64_W16_H60_D12_z | 64 | 64 | 16 | 131 | 60 | 12 |
+-----------------------------------+----+----+----+-----+----+----+
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Table 7
6. Rationale
The goal of this note is to describe the WOTS+, XMSS and XMSS^MT
algorithms following the scientific literature. Other signature
methods are out of scope and may be an interesting follow-on work.
The description is done in a modular way that allows to base a
description of stateless hash-based signature algorithms like SPHINCS
[BHH15] on it.
The parameter w is constrained to powers of 2 to support simpler and
more efficient implementations. Furthermore, w is restricted to the
set {4, 8, 16}. No bigger values are included since the decrease in
signature size then becomes less significant. The value w = 2 was
not included since w = 4 leads to similar runtimes but a halved
signature size. This is the case because while chains get twice as
long, thereby increasing runtime, the number of chains is roughly
halved. For instance, assuming m = n = 32, one obtains l = 38 for w
= 2 and l = 19 for w = 4.
The signature and public key formats are designed so that they are
easy to parse. Each format starts with a 32-bit enumeration value
that indicates all of the details of the signature algorithm and
hence defines all of the information that is needed in order to parse
the format.
The enumeration values used in this note are palindromes, which have
the same byte representation in either host order or network order.
This fact allows an implementation to omit the conversion between
byte order for those enumerations. Note however that the idx field
used in XMSS and XMSS^MT signatures and secret keys must be properly
converted to and from network byte order; this is the only field that
requires such conversion. There are 2^32 XDR enumeration values,
2^16 of which are palindromes, which is adequate for the foreseeable
future. If there is a need for more assignments, non-palindromes can
be assigned.
7. IANA Considerations
The Internet Assigned Numbers Authority (IANA) is requested to create
three registries: one for WOTS+ signatures as defined in Section 3,
one for XMSS signatures and one for XMSS^MT signatures; the latter
two being defined in Section 4. For the sake of clarity and
convenience, the first sets of WOTS+, XMSS, and XMSS^MT parameter
sets are defined in Section 5. Additions to these registries require
that a specification be documented in an RFC or another permanent and
readily available reference in sufficient details to make
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interoperability between independent implementations possible. Each
entry in the registry contains the following elements:
a short name, such as "XMSS_SHA3-512_M64_W16_H20",
a positive number, and
a reference to a specification that completely defines the
signature method test cases that can be used to verify the
correctness of an implementation.
Requests to add an entry to the registry MUST include the name and
the reference. The number is assigned by IANA. These number
assignments SHOULD use the smallest available palindromic number.
Submitters SHOULD have their requests reviewed by the IRTF Crypto
Forum Research Group (CFRG) at cfrg@ietf.org. Interested applicants
that are unfamiliar with IANA processes should visit http://
www.iana.org.
The numbers between 0xDDDDDDDD (decimal 3,722,304,989) and 0xFFFFFFFF
(decimal 4,294,967,295) inclusive, will not be assigned by IANA, and
are reserved for private use; no attempt will be made to prevent
multiple sites from using the same value in different (and
incompatible) ways [RFC2434].
The WOTS+ registry is as follows.
+-------------------------+-------------+--------------------+
| Name | Reference | Numeric Identifier |
+-------------------------+-------------+--------------------+
| WOTSP_AES128_M32_W4 | Section 5.2 | 0x01000001 |
| | | |
| WOTSP_AES128_M32_W8 | Section 5.2 | 0x02000002 |
| | | |
| WOTSP_AES128_M32_W16 | Section 5.2 | 0x03000003 |
| | | |
| WOTSP_SHA3-256_M32_W4 | Section 5.2 | 0x04000004 |
| | | |
| WOTSP_SHA3-256_M32_W8 | Section 5.2 | 0x05000005 |
| | | |
| WOTSP_SHA3-256_M32_W16 | Section 5.2 | 0x06000006 |
| | | |
| WOTSP_SHA3-512_M64_W4 | Section 5.2 | 0x07000007 |
| | | |
| WOTSP_SHA3-512_M64_W8 | Section 5.2 | 0x08000008 |
| | | |
| WOTSP_SHA3-512_M64_W16 | Section 5.2 | 0x09000009 |
+-------------------------+-------------+--------------------+
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Table 8
The XMSS registry is as follows.
+------------------------------+-------------+--------------------+
| Name | Reference | Numeric Identifier |
+------------------------------+-------------+--------------------+
| XMSS_SHA3-256_M32_W4_H10_Z | Section 5.3 | 0x01000001 |
| | | |
| XMSS_SHA3-256_M32_W4_H16_Z | Section 5.3 | 0x02000002 |
| | | |
| XMSS_SHA3-256_M32_W4_H20_Z | Section 5.3 | 0x03000003 |
| | | |
| XMSS_SHA3-256_M32_W8_H10_Z | Section 5.3 | 0x04000004 |
| | | |
| XMSS_SHA3-256_M32_W8_H16_Z | Section 5.3 | 0x05000005 |
| | | |
| XMSS_SHA3-256_M32_W8_H20_Z | Section 5.3 | 0x06000006 |
| | | |
| XMSS_SHA3-256_M32_W16_H10_Z | Section 5.3 | 0x07000007 |
| | | |
| XMSS_SHA3-256_M32_W16_H16_Z | Section 5.3 | 0x08000008 |
| | | |
| XMSS_SHA3-256_M32_W16_H20_Z | Section 5.3 | 0x09000009 |
| | | |
| XMSS_SHA3-512_M64_W4_H10_Z | Section 5.3 | 0x0a00000a |
| | | |
| XMSS_SHA3-512_M64_W4_H16_Z | Section 5.3 | 0x0b00000b |
| | | |
| XMSS_SHA3-512_M64_W4_H20_Z | Section 5.3 | 0x0c00000c |
| | | |
| XMSS_SHA3-512_M64_W8_H10_Z | Section 5.3 | 0x0d00000d |
| | | |
| XMSS_SHA3-512_M64_W8_H16_Z | Section 5.3 | 0x0e00000e |
| | | |
| XMSS_SHA3-512_M64_W8_H20_Z | Section 5.3 | 0x0f00000f |
| | | |
| XMSS_SHA3-512_M64_W16_H10_Z | Section 5.3 | 0x01010101 |
| | | |
| XMSS_SHA3-512_M64_W16_H16_Z | Section 5.3 | 0x02010102 |
| | | |
| XMSS_SHA3-512_M64_W16_H20_Z | Section 5.3 | 0x03010103 |
| | | |
| XMSS_AES128_M32_W4_H10 | Section 5.3 | 0x04010104 |
| | | |
| XMSS_AES128_M32_W4_H16 | Section 5.3 | 0x05010105 |
| | | |
| XMSS_AES128_M32_W4_H20 | Section 5.3 | 0x06010106 |
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| | | |
| XMSS_AES128_M32_W8_H10 | Section 5.3 | 0x07010107 |
| | | |
| XMSS_AES128_M32_W8_H16 | Section 5.3 | 0x08010108 |
| | | |
| XMSS_AES128_M32_W8_H20 | Section 5.3 | 0x09010109 |
| | | |
| XMSS_AES128_M32_W16_H10 | Section 5.3 | 0x0a01010a |
| | | |
| XMSS_AES128_M32_W16_H16 | Section 5.3 | 0x0b01010b |
| | | |
| XMSS_AES128_M32_W16_H20 | Section 5.3 | 0x0c01010c |
| | | |
| XMSS_SHA3-256_M32_W4_H10 | Section 5.3 | 0x0d01010d |
| | | |
| XMSS_SHA3-256_M32_W4_H16 | Section 5.3 | 0x0e01010e |
| | | |
| XMSS_SHA3-256_M32_W4_H20 | Section 5.3 | 0x0f01010f |
| | | |
| XMSS_SHA3-256_M32_W8_H10 | Section 5.3 | 0x01020201 |
| | | |
| XMSS_SHA3-256_M32_W8_H16 | Section 5.3 | 0x02020202 |
| | | |
| XMSS_SHA3-256_M32_W8_H20 | Section 5.3 | 0x03020203 |
| | | |
| XMSS_SHA3-256_M32_W16_H10 | Section 5.3 | 0x04020204 |
| | | |
| XMSS_SHA3-256_M32_W16_H16 | Section 5.3 | 0x05020205 |
| | | |
| XMSS_SHA3-256_M32_W16_H20 | Section 5.3 | 0x06020206 |
| | | |
| XMSS_SHA3-512_M64_W4_H10 | Section 5.3 | 0x07020207 |
| | | |
| XMSS_SHA3-512_M64_W4_H16 | Section 5.3 | 0x08020208 |
| | | |
| XMSS_SHA3-512_M64_W4_H20 | Section 5.3 | 0x09020209 |
| | | |
| XMSS_SHA3-512_M64_W8_H10 | Section 5.3 | 0x0a02020a |
| | | |
| XMSS_SHA3-512_M64_W8_H16 | Section 5.3 | 0x0b02020b |
| | | |
| XMSS_SHA3-512_M64_W8_H20 | Section 5.3 | 0x0c02020c |
| | | |
| XMSS_SHA3-512_M64_W16_H10 | Section 5.3 | 0x0d02020d |
| | | |
| XMSS_SHA3-512_M64_W16_H16 | Section 5.3 | 0x0e02020e |
| | | |
| XMSS_SHA3-512_M64_W16_H20 | Section 5.3 | 0x0f02020f |
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+------------------------------+-------------+--------------------+
Table 9
The XMSS^MT registry is as follows.
+---------------------------------------+------------+--------------+
| Name | Reference | Numeric |
| | | Identifier |
+---------------------------------------+------------+--------------+
| XMSSMT_SHA3-256_M32_W4_H20_D2_Z | Section | 0x01000001 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H20_D4_Z | Section | 0x02000002 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H40_D2_Z | Section | 0x03000003 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H40_D4_Z | Section | 0x04000004 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H40_D8_Z | Section | 0x05000005 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H60_D3_Z | Section | 0x06000006 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H60_D6_Z | Section | 0x07000007 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H60_D12_Z | Section | 0x08000008 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H20_D2_Z | Section | 0x09000009 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H20_D4_Z | Section | 0x0a00000a |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H40_D2_Z | Section | 0x0b00000b |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H40_D4_Z | Section | 0x0c00000c |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H40_D8_Z | Section | 0x0d00000d |
| | 5.4 | |
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| | | |
| XMSSMT_SHA3-256_M32_W8_H60_D3_Z | Section | 0x0e00000e |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H60_D6_Z | Section | 0x0f00000f |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H60_D12_Z | Section | 0x00010100 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H20_D2_Z | Section | 0x01010101 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H20_D4_Z | Section | 0x02010102 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H40_D2_Z | Section | 0x03010103 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H40_D4_Z | Section | 0x04010104 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H40_D8_Z | Section | 0x05010105 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H60_D3_Z | Section | 0x06010106 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H60_D6_Z | Section | 0x07010107 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H60_D12_Z | Section | 0x08010108 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H20_D2_Z | Section | 0x09010109 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H20_D4_Z | Section | 0x0a01010a |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H40_D2_Z | Section | 0x0b01010b |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H40_D4_Z | Section | 0x0c01010c |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H40_D8_Z | Section | 0x0d01010d |
| | 5.4 | |
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| | | |
| XMSSMT_SHA3-512_M64_W4_H60_D3_Z | Section | 0x0e01010e |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H60_D6_Z | Section | 0x0f01010f |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H60_D12_Z | Section | 0x00020200 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H20_D2_Z | Section | 0x01020201 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H20_D4_Z | Section | 0x02020202 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H40_D2_Z | Section | 0x03020203 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H40_D4_Z | Section | 0x04020204 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H40_D8_Z | Section | 0x05020205 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H60_D3_Z | Section | 0x06020206 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H60_D6_Z | Section | 0x07020207 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H60_D12_Z | Section | 0x08020208 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H20_D2_Z | Section | 0x09020209 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H20_D4_Z | Section | 0x0a02020a |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H40_D2_Z | Section | 0x0b02020b |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H40_D4_Z | Section | 0x0c02020c |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H40_D8_Z | Section | 0x0d02020d |
| | 5.4 | |
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| | | |
| XMSSMT_SHA3-512_M64_W16_H60_D3_Z | Section | 0x0e02020e |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H60_D6_Z | Section | 0x0f02020f |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H60_D12_Z | Section | 0x00030300 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H20_D2 | Section | 0x01030301 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H20_D4 | Section | 0x02030302 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H40_D2 | Section | 0x03030303 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H40_D4 | Section | 0x04030304 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H40_D8 | Section | 0x05030305 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H60_D3 | Section | 0x06030306 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H60_D6 | Section | 0x07030307 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W4_H60_D12 | Section | 0x08030308 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H20_D2 | Section | 0x09030309 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H20_D4 | Section | 0x0a03030a |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H40_D2 | Section | 0x0b03030b |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H40_D4 | Section | 0x0c03030c |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H40_D8 | Section | 0x0d03030d |
| | 5.4 | |
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| | | |
| XMSSMT_AES128_M32_W8_H60_D3 | Section | 0x0e03030e |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H60_D6 | Section | 0x0f03030f |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W8_H60_D12 | Section | 0x00040400 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H20_D2 | Section | 0x01040401 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H20_D4 | Section | 0x02040402 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H40_D2 | Section | 0x03040403 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H40_D4 | Section | 0x04040404 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H40_D8 | Section | 0x05040405 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H60_D3 | Section | 0x06040406 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H60_D6 | Section | 0x07040407 |
| | 5.4 | |
| | | |
| XMSSMT_AES128_M32_W16_H60_D12 | Section | 0x08040408 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H20_D2 | Section | 0x09040409 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H20_D4 | Section | 0x0a04040a |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H40_D2 | Section | 0x0b04040b |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H40_D4 | Section | 0x0c04040c |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H40_D8 | Section | 0x0d04040d |
| | 5.4 | |
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| XMSSMT_SHA3-256_M32_W4_H60_D3 | Section | 0x0e04040e |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H60_D6 | Section | 0x0f04040f |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W4_H60_D12 | Section | 0x00050500 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H20_D2 | Section | 0x01050501 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H20_D4 | Section | 0x02050502 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H40_D2 | Section | 0x03050503 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H40_D4 | Section | 0x04050504 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H40_D8 | Section | 0x05050505 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H60_D3 | Section | 0x06050506 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H60_D6 | Section | 0x07050507 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W8_H60_D12 | Section | 0x08050508 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H20_D2 | Section | 0x09050509 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H20_D4 | Section | 0x0a05050a |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H40_D2 | Section | 0x0b05050b |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H40_D4 | Section | 0x0c05050c |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H40_D8 | Section | 0x0d05050d |
| | 5.4 | |
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| | | |
| XMSSMT_SHA3-256_M32_W16_H60_D3 | Section | 0x0e05050e |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H60_D6 | Section | 0x0f05050f |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-256_M32_W16_H60_D12 | Section | 0x00060600 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H20_D2 | Section | 0x01060601 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H20_D4 | Section | 0x02060602 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H40_D2 | Section | 0x03060603 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H40_D4 | Section | 0x04060604 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H40_D8 | Section | 0x05060605 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H60_D3 | Section | 0x06060606 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H60_D6 | Section | 0x07060607 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W4_H60_D12 | Section | 0x08060608 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H20_D2 | Section | 0x09060609 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H20_D4 | Section | 0x0a06060a |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H40_D2 | Section | 0x0b06060b |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H40_D4 | Section | 0x0c06060c |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H40_D8 | Section | 0x0d06060d |
| | 5.4 | |
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| | | |
| XMSSMT_SHA3-512_M64_W8_H60_D3 | Section | 0x0e06060e |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H60_D6 | Section | 0x0f06060f |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W8_H60_D12 | Section | 0x00070700 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H20_D2 | Section | 0x01070701 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H20_D4 | Section | 0x02070702 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H40_D2 | Section | 0x03070703 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H40_D4 | Section | 0x04070704 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H40_D8 | Section | 0x05070705 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H60_D3 | Section | 0x06070706 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H60_D6 | Section | 0x07070707 |
| | 5.4 | |
| | | |
| XMSSMT_SHA3-512_M64_W16_H60_D12 | Section | 0x08070708 |
| | 5.4 | |
+---------------------------------------+------------+--------------+
Table 10
An IANA registration of a signature system does not constitute an
endorsement of that system or its security.
8. Security Considerations
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A signature system is considered secure if it prevents an attacker
from forging a valid signature. More specifically, consider a
setting in which an attacker gets a public key and can learn
signatures on arbitrary messages of his choice. A signature system
is secure if, even in this setting, the attacker can not produce a
message signature pair of his choosing such that the verification
algorithm accepts.
Preventing an attacker from mounting an attack means that the attack
is computationally too expensive to be carried out. There exist
various estimates when a computation is too expensive to be done.
For that reason, this note only describes how expensive it is for an
attacker to generate a forgery. Parameters are accompanied by a bit
security value. The meaning of bit security is as follows. A
parameter set grants b bits of security if the best attack takes at
least 2^(b-1) bit operations to achieve a success probability of 1/2.
Hence, to mount a successful attack, an attacker needs to perform 2^b
bit operations on average. How the given values for bit security
were estimated is described below.
8.1. Security Proofs
There exist formal security proofs for the schemes described here in
the literature [Huelsing13a]. These proofs show that an attacker has
to break at least one out of certain security properties of the used
hash functions and PRFs to forge a signature. The proofs in
[Huelsing13a] do not consider the initial message compression. For
the scheme without initial message compression, these proofs show
that an attacker has to break certain minimal security properties.
In particular, it is not sufficient to break the collision resistance
of the hash functions to generate a forgery.
It is a folklore that one can securely combine a secure signature
scheme for fixed length messages with an initial message digest. It
is easy to proof that an attacker either must break the security of
the fixed-input-length signature scheme or the collision resistance
of the used hash function. XMSS and XMSS^MT use a known trick to
prevent the applicability of collision attacks. Namely, the schemes
use a randomized message hash. For technical reasons, it is not
possible to formally prove that the resulting scheme is secure if the
hash function is not collision-resistant but fulfills some weaker
security properties.
The given bit security values were estimated based on the complexity
of the best known generic attacks against the required security
properties of the used hash functions and PRFs.
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8.2. Security Assumptions
The security assumptions made to argue for the security of the
described schemes are minimal. Any signature algorithm that allows
arbitrary size messages relies on the security of a cryptographic
hash function. For the schemes described here this is already
sufficient to be secure. In contrast, common signature schemes like
RSA, DSA, and ECDSA additionally rely on the conjectured hardness of
certain mathematical problems.
8.3. Post-Quantum Security
A post-quantum cryptosystem is a system that is secure against
attackers with access to a reasonably sized quantum computer. At the
time of writing this note, whether or not it is feasible to build
such machine is an open conjecture. However, significant progress
was made over the last few years in this regard.
In contrast to RSA, DSA, and ECDSA, the described signature systems
are post-quantum-secure if they are used with an appropriate
cryptographic hash function. In particular, for post-quantum
security, the size of m and n must be twice the size required for
classical security. This is in order to protect against quantum
square root attacks due to Grover's algorithm. It has been shown
that Grover's algorithm is optimal for finding preimages and
collisions.
9. Acknowledgements
We would like to thank Burt Kaliski, and David McGrew for their help.
10. References
10.1. Normative References
[DRAFTFIPS202]
National Institute of Standards and Technology, "SHA-3
Standard: Permutation-Based Hash and Extendable-Output
Functions", Draft FIPS 202, 2014.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2434] Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", BCP 26, RFC 2434,
October 1998.
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[RFC4506] Eisler, M., "XDR: External Data Representation Standard",
STD 67, RFC 4506, May 2006.
10.2. Informative References
[BDH11] Buchmann, J., Dahmen, E., and A. Huelsing, "XMSS - A
Practical Forward Secure Signature Scheme Based on Minimal
Security Assumptions", Lecture Notes in Computer Science
volume 7071. Post-Quantum Cryptography, 2011.
[BDS09] Buchmann, J., Dahmen, E., and M. Szydlo, "Hash-based
Digital Signature Schemes", Book chapter Post-Quantum
Cryptography, Springer, 2009.
[BHH15] Bernstein, D., Hopwood, D., Huelsing, A., Lange, T.,
Niederhagen, R., Papachristodoulou, L., Schneider, M.,
Schwabe, P., and Z. Wilcox-O'Hearn, "SPHINCS: practical
stateless hash-based signatures", To appear. Advances in
Cryptology - EUROCRYPT, 2015.
[DC14] McGrew, D. and M. Curcio, "Hash-based signatures", draft-
mcgrew-hash-sigs-02 (work in progress), July 2014.
[HRB13] Huelsing, A., Rausch, L., and J. Buchmann, "Optimal
Parameters for XMSS^MT", Lecture Notes in Computer Science
volume 8128. CD-ARES, 2013.
[Huelsing13]
Huelsing, A., "W-OTS+ - Shorter Signatures for Hash-Based
Signature Schemes", Lecture Notes in Computer Science
volume 7918. Progress in Cryptology - AFRICACRYPT, 2013.
[Huelsing13a]
Huelsing, A., "Practical Forward Secure Signatures using
Minimal Security Assumptions", PhD thesis TU Darmstadt,
2013.
[Kaliski15]
Kaliski, B., "Shoring up the Infrastructure: A Strategy
for Standardizing Hash Signatures", Post Quantum NIST
Workshop on Cybersecurity in a Post-Quantum World, 2015.
[Merkle79]
Merkle, R., "Secrecy, Authentication, and Public Key
Systems", Stanford University Information Systems
Laboratory Technical Report 1979-1, 1979.
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Appendix A. WOTS+ XDR Formats
The WOTS+ signature and public key formats are formally defined using
XDR [RFC4506] in order to provide an unambiguous, machine readable
definition. Though XDR is used, these formats are simple and easy to
parse without any special tools. To avoid the need to convert to and
from network / host byte order, the enumeration values are all
palindromes.
WOTS+ parameter sets are defined using XDR syntax as follows:
/* ots_algorithm_type identifies a particular
signature algorithm */
enum ots_algorithm_type {
wotsp_reserved = 0x00000000,
wotsp_aes128_m32_w4 = 0x01000001,
wotsp_aes128_m32_w8 = 0x02000002,
wotsp_aes128_m32_w16 = 0x03000003,
wotsp_sha3-256_m32_w4 = 0x04000004,
wotsp_sha3-256_m32_w8 = 0x05000005,
wotsp_sha3-256_m32_w16 = 0x06000006,
wotsp_sha3-512_m64_w4 = 0x07000007,
wotsp_sha3-512_m64_w8 = 0x08000008,
wotsp_sha3-512_m64_w16 = 0x09000009,
};
WOTS+ signatures are defined using XDR syntax as follows:
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/* Byte strings */
typedef opaque bytestring32[32];
typedef opaque bytestring64[64];
union ots_signature switch (ots_algorithm_type type) {
case wotsp_aes128_m32_w4:
case wotsp_sha3-256_m32_w4:
bytestring32 ots_sig_m32_l133[133];
case wotsp_aes128_m32_w8:
case wotsp_sha3-256_m32_w8:
bytestring32 ots_sig_m32_l90[90];
case wotsp_aes128_m32_w16:
case wotsp_sha3-256_m32_w16:
bytestring32 ots_sig_m32_l67[67];
case wotsp_sha3-512_m64_w4:
bytestring64 ots_sig_m64_l261[261];
case wotsp_sha3-512_m64_w8:
bytestring64 ots_sig_m64_l75[175];
case wotsp_sha3-512_m64_w16:
bytestring64 ots_sig_m64_l18[131];
default:
void; /* error condition */
};
WOTS+ public keys are defined using XDR syntax as follows:
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union ots_pubkey switch (ots_algorithm_type type) {
case wotsp_aes128_m32_w4:
case wotsp_sha3-256_m32_w4:
bytestring32 ots_pubk_m32_l133[133];
case wotsp_aes128_m32_w8:
case wotsp_sha3-256_m32_w8:
bytestring32 ots_pubk_m32_l90[90];
case wotsp_aes128_m32_w16:
case wotsp_sha3-256_m32_w16:
bytestring32 ots_pubk_m32_l67[67];
case wotsp_sha3-512_m64_w4:
bytestring64 ots_pubk_m64_l261[261];
case wotsp_sha3-512_m64_w8:
bytestring64 ots_pubk_m64_l75[175];
case wotsp_sha3-512_m64_w16:
bytestring64 ots_pubk_m64_l18[131];
default:
void; /* error condition */
};
Appendix B. XMSS XDR Formats
XMSS parameter sets are defined using XDR syntax as follows:
/* Byte strings */
typedef opaque bytestring4[4];
typedef opaque bytestring16[16];
/* Definition of parameter sets */
enum xmss_algorithm_type {
xmss_reserved = 0x00000000,
/* Empty bitmasks */
/* 128 bit classical security, 85 bit post-quantum security */
xmss_sha3-256_m32_w4_h10_z = 0x01000001,
xmss_sha3-256_m32_w4_h16_z = 0x02000002,
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xmss_sha3-256_m32_w4_h20_z = 0x03000003,
xmss_sha3-256_m32_w8_h10_z = 0x04000004,
xmss_sha3-256_m32_w8_h16_z = 0x05000005,
xmss_sha3-256_m32_w8_h20_z = 0x06000006,
xmss_sha3-256_m32_w16_h10_z = 0x07000007,
xmss_sha3-256_m32_w16_h16_z = 0x08000008,
xmss_sha3-256_m32_w16_h20_z = 0x09000009,
/* 256 bit classical security, 170 bit post-quantum security */
xmss_sha3-512_m64_w4_h10_z = 0x0a00000a,
xmss_sha3-512_m64_w4_h16_z = 0x0b00000b,
xmss_sha3-512_m64_w4_h20_z = 0x0c00000c,
xmss_sha3-512_m64_w8_h10_z = 0x0d00000d,
xmss_sha3-512_m64_w8_h16_z = 0x0e00000e,
xmss_sha3-512_m64_w8_h20_z = 0x0f00000f,
xmss_sha3-512_m64_w16_h10_z = 0x01010101,
xmss_sha3-512_m64_w16_h16_z = 0x02010102,
xmss_sha3-512_m64_w16_h20_z = 0x03010103,
/* Non-empty bitmasks */
/* 128 bit classical security, 64 bit post-quantum security */
xmss_aes128_m32_w4_h10 = 0x04010104,
xmss_aes128_m32_w4_h16 = 0x05010105,
xmss_aes128_m32_w4_h20 = 0x06010106,
xmss_aes128_m32_w8_h10 = 0x07010107,
xmss_aes128_m32_w8_h16 = 0x08010108,
xmss_aes128_m32_w8_h20 = 0x09010109,
xmss_aes128_m32_w16_h10 = 0x0a01010a,
xmss_aes128_m32_w16_h16 = 0x0b01010b,
xmss_aes128_m32_w16_h20 = 0x0c01010c,
/* 256 bit classical security, 128 bit post-quantum security */
xmss_sha3-256_m32_w4_h10 = 0x0d01010d,
xmss_sha3-256_m32_w4_h16 = 0x0e01010e,
xmss_sha3-256_m32_w4_h20 = 0x0f01010f,
xmss_sha3-256_m32_w8_h10 = 0x01020201,
xmss_sha3-256_m32_w8_h16 = 0x02020202,
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xmss_sha3-256_m32_w8_h20 = 0x03020203,
xmss_sha3-256_m32_w16_h10 = 0x04020204,
xmss_sha3-256_m32_w16_h16 = 0x05020205,
xmss_sha3-256_m32_w16_h20 = 0x06020206,
/* 512 bit classical security, 256 bit post-quantum security */
xmss_sha3-512_m64_w4_h10 = 0x07020207,
xmss_sha3-512_m64_w4_h16 = 0x08020208,
xmss_sha3-512_m64_w4_h20 = 0x09020209,
xmss_sha3-512_m64_w8_h10 = 0x0a02020a,
xmss_sha3-512_m64_w8_h16 = 0x0b02020b,
xmss_sha3-512_m64_w8_h20 = 0x0c02020c,
xmss_sha3-512_m64_w16_h10 = 0x0d02020d,
xmss_sha3-512_m64_w16_h16 = 0x0e02020e,
xmss_sha3-512_m64_w16_h20 = 0x0f02020f,
};
XMSS signatures are defined using XDR syntax as follows:
/* Authentication path types */
union xmss_path switch (xmss_algorithm_type type) {
case xmss_sha3-256_m32_w4_h10_z:
case xmss_sha3-256_m32_w8_h10_z:
case xmss_sha3-256_m32_w16_h10_z:
case xmss_sha3-256_m32_w4_h10:
case xmss_sha3-256_m32_w8_h10:
case xmss_sha3-256_m32_w16_h10:
bytestring32 path_n32_t10[10];
case xmss_sha3-256_m32_w4_h16_z:
case xmss_sha3-256_m32_w8_h16_z:
case xmss_sha3-256_m32_w16_h16_z:
case xmss_sha3-256_m32_w4_h16:
case xmss_sha3-256_m32_w8_h16:
case xmss_sha3-256_m32_w16_h16:
bytestring32 path_n32_t16[16];
case xmss_sha3-256_m32_w4_h20_z:
case xmss_sha3-256_m32_w8_h20_z:
case xmss_sha3-256_m32_w16_h20_z:
case xmss_sha3-256_m32_w4_h20:
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case xmss_sha3-256_m32_w8_h20:
case xmss_sha3-256_m32_w16_h20:
bytestring32 path_n32_t20[20];
case xmss_sha3-512_m64_w4_h10_z:
case xmss_sha3-512_m64_w8_h10_z:
case xmss_sha3-512_m64_w16_h10_z:
case xmss_sha3-512_m64_w4_h10:
case xmss_sha3-512_m64_w8_h10:
case xmss_sha3-512_m64_w16_h10:
bytestring64 path_n64_t10[10];
case xmss_sha3-512_m64_w4_h16_z:
case xmss_sha3-512_m64_w8_h16_z:
case xmss_sha3-512_m64_w16_h16_z:
case xmss_sha3-512_m64_w4_h16:
case xmss_sha3-512_m64_w8_h16:
case xmss_sha3-512_m64_w16_h16:
bytestring64 path_n64_t16[16];
case xmss_sha3-512_m64_w4_h20_z:
case xmss_sha3-512_m64_w8_h20_z:
case xmss_sha3-512_m64_w16_h20_z:
case xmss_sha3-512_m64_w4_h20:
case xmss_sha3-512_m64_w8_h20:
case xmss_sha3-512_m64_w16_h20:
bytestring64 path_n64_t20[20];
case xmss_aes128_m32_w4_h10:
case xmss_aes128_m32_w8_h10:
case xmss_aes128_m32_w16_h10:
bytestring16 path_n16_t10[10];
case xmss_aes128_m32_w4_h16:
case xmss_aes128_m32_w8_h16:
case xmss_aes128_m32_w16_h16:
bytestring16 path_n16_t16[16];
case xmss_aes128_m32_w4_h20:
case xmss_aes128_m32_w8_h20:
case xmss_aes128_m32_w16_h20:
bytestring16 path_n16_t20[20];
default:
void; /* error condition */
};
/* Types for XMSS random strings */
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union random_string_xmss switch (xmss_algorithm_type type) {
case xmss_sha3-256_m32_w4_h10_z:
case xmss_sha3-256_m32_w4_h16_z:
case xmss_sha3-256_m32_w4_h20_z:
case xmss_sha3-256_m32_w8_h10_z:
case xmss_sha3-256_m32_w8_h16_z:
case xmss_sha3-256_m32_w8_h20_z:
case xmss_sha3-256_m32_w16_h10_z:
case xmss_sha3-256_m32_w16_h16_z:
case xmss_sha3-256_m32_w16_h20_z:
case xmss_sha3-256_m32_w4_h10:
case xmss_sha3-256_m32_w4_h16:
case xmss_sha3-256_m32_w4_h20:
case xmss_sha3-256_m32_w8_h10:
case xmss_sha3-256_m32_w8_h16:
case xmss_sha3-256_m32_w8_h20:
case xmss_sha3-256_m32_w16_h10:
case xmss_sha3-256_m32_w16_h16:
case xmss_sha3-256_m32_w16_h20:
case xmss_aes128_m32_w4_h10:
case xmss_aes128_m32_w4_h16:
case xmss_aes128_m32_w4_h20:
case xmss_aes128_m32_w8_h10:
case xmss_aes128_m32_w8_h16:
case xmss_aes128_m32_w8_h20:
case xmss_aes128_m32_w16_h10:
case xmss_aes128_m32_w16_h16:
case xmss_aes128_m32_w16_h20:
bytestring32 rand_m32;
case xmss_sha3-512_m64_w4_h10_z:
case xmss_sha3-512_m64_w4_h16_z:
case xmss_sha3-512_m64_w4_h20_z:
case xmss_sha3-512_m64_w8_h10_z:
case xmss_sha3-512_m64_w8_h16_z:
case xmss_sha3-512_m64_w8_h20_z:
case xmss_sha3-512_m64_w16_h10_z:
case xmss_sha3-512_m64_w16_h16_z:
case xmss_sha3-512_m64_w16_h20_z:
case xmss_sha3-512_m64_w4_h10:
case xmss_sha3-512_m64_w4_h16:
case xmss_sha3-512_m64_w4_h20:
case xmss_sha3-512_m64_w8_h10:
case xmss_sha3-512_m64_w8_h16:
case xmss_sha3-512_m64_w8_h20:
case xmss_sha3-512_m64_w16_h10:
case xmss_sha3-512_m64_w16_h16:
case xmss_sha3-512_m64_w16_h20:
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bytestring64 rand_m64;
default:
void; /* error condition */
};
/* Corresponding WOTS+ type for given XMSS type */
union xmss_ots_signature switch (xmss_algorithm_type type) {
case xmss_sha3-256_m32_w4_h10_z:
case xmss_sha3-256_m32_w4_h16_z:
case xmss_sha3-256_m32_w4_h20_z:
wotsp_sha3-256_m32_w4;
case xmss_sha3-256_m32_w8_h10_z:
case xmss_sha3-256_m32_w8_h16_z:
case xmss_sha3-256_m32_w8_h20_z:
wotsp_sha3-256_m32_w8;
case xmss_sha3-256_m32_w16_h10_z:
case xmss_sha3-256_m32_w16_h16_z:
case xmss_sha3-256_m32_w16_h20_z:
wotsp_sha3-256_m32_w16
case xmss_sha3-512_m64_w4_h10_z:
case xmss_sha3-512_m64_w4_h16_z:
case xmss_sha3-512_m64_w4_h20_z:
wotsp_sha3-512_m64_w4;
case xmss_sha3-512_m64_w8_h10_z:
case xmss_sha3-512_m64_w8_h16_z:
case xmss_sha3-512_m64_w8_h20_z:
wotsp_sha3-512_m64_w8;
case xmss_sha3-512_m64_w16_h10_z:
case xmss_sha3-512_m64_w16_h16_z:
case xmss_sha3-512_m64_w16_h20_z:
wotsp_sha3-512_m64_w16;
case xmss_aes128_m32_w4_h10:
case xmss_aes128_m32_w4_h16:
case xmss_aes128_m32_w4_h20:
wotsp_aes128_m32_w4;
case xmss_aes128_m32_w8_h10:
case xmss_aes128_m32_w8_h16:
case xmss_aes128_m32_w8_h20:
wotsp_aes128_m32_w8;
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case xmss_aes128_m32_w16_h10:
case xmss_aes128_m32_w16_h16:
case xmss_aes128_m32_w16_h20:
wotsp_aes128_m32_w16;
case xmss_sha3-256_m32_w4_h10:
case xmss_sha3-256_m32_w4_h16:
case xmss_sha3-256_m32_w4_h20:
wotsp_sha3-256_m32_w4;
case xmss_sha3-256_m32_w8_h10:
case xmss_sha3-256_m32_w8_h16:
case xmss_sha3-256_m32_w8_h20:
wotsp_sha3-256_m32_w8;
case xmss_sha3-256_m32_w16_h10:
case xmss_sha3-256_m32_w16_h16:
case xmss_sha3-256_m32_w16_h20:
wotsp_sha3-256_m32_w16;
case xmss_sha3-512_m64_w4_h10:
case xmss_sha3-512_m64_w4_h16:
case xmss_sha3-512_m64_w4_h20:
wotsp_sha3-512_m64_w4;
case xmss_sha3-512_m64_w8_h10:
case xmss_sha3-512_m64_w8_h16:
case xmss_sha3-512_m64_w8_h20:
wotsp_sha3-512_m64_w8;
case xmss_sha3-512_m64_w16_h10:
case xmss_sha3-512_m64_w16_h16:
case xmss_sha3-512_m64_w16_h20:
wotsp_sha3-512_m64_w16;
default:
void; /* error condition */
};
/* XMSS signature structure */
struct xmss_signature {
/* WOTS+ key pair index */
bytestring4 idx_sig;
/* Random string for randomized hashing */
random_string_xmss rand_string;
/* WOTS+ signature */
xmss_ots_signature sig_ots;
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/* authentication path */
xmss_path nodes;
};
When no bitmasks are used, XMSS public keys are defined using XDR
syntax as follows:
/* Types for XMSS root node */
union xmss_root switch (xmss_algorithm_type type) {
case xmss_sha3-256_m32_w4_h10_z:
case xmss_sha3-256_m32_w4_h16_z:
case xmss_sha3-256_m32_w4_h20_z:
case xmss_sha3-256_m32_w8_h10_z:
case xmss_sha3-256_m32_w16_h10_z:
case xmss_sha3-256_m32_w8_h16_z:
case xmss_sha3-256_m32_w16_h16_z:
case xmss_sha3-256_m32_w8_h20_z:
case xmss_sha3-256_m32_w16_h20_z:
bytestring32 root_n32;
case xmss_sha3-512_m64_w4_h10_z:
case xmss_sha3-512_m64_w4_h16_z:
case xmss_sha3-512_m64_w4_h20_z:
case xmss_sha3-512_m64_w8_h10_z:
case xmss_sha3-512_m64_w16_h10_z:
case xmss_sha3-512_m64_w8_h16_z:
case xmss_sha3-512_m64_w16_h16_z:
case xmss_sha3-512_m64_w8_h20_z:
case xmss_sha3-512_m64_w16_h20_z:
bytestring64 root_n64;
default:
void; /* error condition */
};
/* XMSS public key structure */
struct xmss_public_key {
xmss_root root; /* Root node */
};
When bitmasks are used, XMSS public keys are defined using XDR syntax
as follows:
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/* Types for XMSS bitmasks */
union xmss_bm switch (xmss_algorithm_type type) {
case xmss_aes128_m32_w4_h10:
bytestring16 bm_n16_bm36[36];
case xmss_aes128_m32_w4_h16:
bytestring16 bm_n16_bm48[48];
case xmss_aes128_m32_w4_h20:
bytestring16 bm_n16_bm56[56];
case xmss_aes128_m32_w8_h10:
case xmss_aes128_m32_w16_h10:
bytestring16 bm_n16_bm34[34];
case xmss_aes128_m32_w8_h16:
case xmss_aes128_m32_w16_h16:
bytestring16 bm_n16_bm46[46];
case xmss_aes128_m32_w8_h20:
case xmss_aes128_m32_w16_h20:
bytestring16 bm_n16_bm54[54];
case xmss_sha3-256_m32_w4_h10:
bytestring32 bm_n32_bm36[36];
case xmss_sha3-256_m32_w4_h16:
bytestring32 bm_n32_bm48[48];
case xmss_sha3-256_m32_w4_h20:
bytestring32 bm_n32_bm56[56];
case xmss_sha3-256_m32_w8_h10:
case xmss_sha3-256_m32_w16_h10:
bytestring32 bm_n32_bm34[34];
case xmss_sha3-256_m32_w8_h16:
case xmss_sha3-256_m32_w16_h16:
bytestring32 bm_n32_bm46[46];
case xmss_sha3-256_m32_w8_h20:
case xmss_sha3-256_m32_w16_h20:
bytestring32 bm_n32_bm54[54];
case xmss_sha3-512_m64_w4_h10:
bytestring64 bm_n64_bm38[38];
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case xmss_sha3-512_m64_w4_h16:
bytestring64 bm_n64_bm50[50];
case xmss_sha3-512_m64_w4_h20:
bytestring64 bm_n64_bm58[58];
case xmss_sha3-512_m64_w8_h10:
case xmss_sha3-512_m64_w16_h10:
bytestring64 bm_n64_bm36[36];
case xmss_sha3-512_m64_w8_h16:
case xmss_sha3-512_m64_w16_h16:
bytestring64 bm_n64_bm48[48];
case xmss_sha3-512_m64_w8_h20:
case xmss_sha3-512_m64_w16_h20:
bytestring64 bm_n64_bm56[56];
default:
void; /* error condition */
};
/* Types for XMSS root node */
union xmss_root switch (xmss_algorithm_type type) {
case xmss_aes128_m32_w4_h10:
case xmss_aes128_m32_w4_h16:
case xmss_aes128_m32_w4_h20:
case xmss_aes128_m32_w8_h10:
case xmss_aes128_m32_w16_h10:
case xmss_aes128_m32_w8_h16:
case xmss_aes128_m32_w16_h16:
case xmss_aes128_m32_w8_h20:
case xmss_aes128_m32_w16_h20:
bytestring16 root_n16;
case xmss_sha3-256_m32_w4_h10:
case xmss_sha3-256_m32_w4_h16:
case xmss_sha3-256_m32_w4_h20:
case xmss_sha3-256_m32_w8_h10:
case xmss_sha3-256_m32_w16_h10:
case xmss_sha3-256_m32_w8_h16:
case xmss_sha3-256_m32_w16_h16:
case xmss_sha3-256_m32_w8_h20:
case xmss_sha3-256_m32_w16_h20:
bytestring32 root_n32;
case xmss_sha3-512_m64_w4_h10:
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case xmss_sha3-512_m64_w4_h16:
case xmss_sha3-512_m64_w4_h20:
case xmss_sha3-512_m64_w8_h10:
case xmss_sha3-512_m64_w16_h10:
case xmss_sha3-512_m64_w8_h16:
case xmss_sha3-512_m64_w16_h16:
case xmss_sha3-512_m64_w8_h20:
case xmss_sha3-512_m64_w16_h20:
bytestring64 root_n64;
default:
void; /* error condition */
};
/* XMSS public key structure */
struct xmss_public_key {
xmss_bm bm; /* Bitmasks */
xmss_root root; /* Root node */
};
Appendix C. XMSS^MT XDR Formats
XMSS^MT parameter sets are defined using XDR syntax as follows:
/* Byte strings */
typedef opaque bytestring3[3];
typedef opaque bytestring5[5];
typedef opaque bytestring8[8];
/* Definition of parameter sets */
enum xmssmt_algorithm_type {
xmssmt_reserved = 0x00000000,
/* Empty bitmasks */
/* 128 bit classical security, 85 bit post-quantum security */
xmssmt_sha3-256_m32_w4_h20_d2_z = 0x01000001,
xmssmt_sha3-256_m32_w4_h20_d4_z = 0x02000002,
xmssmt_sha3-256_m32_w4_h40_d2_z = 0x03000003,
xmssmt_sha3-256_m32_w4_h40_d4_z = 0x04000004,
xmssmt_sha3-256_m32_w4_h40_d8_z = 0x05000005,
xmssmt_sha3-256_m32_w4_h60_d3_z = 0x06000006,
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xmssmt_sha3-256_m32_w4_h60_d6_z = 0x07000007,
xmssmt_sha3-256_m32_w4_h60_d12_z = 0x08000008,
xmssmt_sha3-256_m32_w8_h20_d2_z = 0x09000009,
xmssmt_sha3-256_m32_w8_h20_d4_z = 0x0a00000a,
xmssmt_sha3-256_m32_w8_h40_d2_z = 0x0b00000b,
xmssmt_sha3-256_m32_w8_h40_d4_z = 0x0c00000c,
xmssmt_sha3-256_m32_w8_h40_d8_z = 0x0d00000d,
xmssmt_sha3-256_m32_w8_h60_d3_z = 0x0e00000e,
xmssmt_sha3-256_m32_w8_h60_d6_z = 0x0f00000f,
xmssmt_sha3-256_m32_w8_h60_d12_z = 0x00010100,
xmssmt_sha3-256_m32_w16_h20_d2_z = 0x01010101,
xmssmt_sha3-256_m32_w16_h20_d4_z = 0x02010102,
xmssmt_sha3-256_m32_w16_h40_d2_z = 0x03010103,
xmssmt_sha3-256_m32_w16_h40_d4_z = 0x04010104,
xmssmt_sha3-256_m32_w16_h40_d8_z = 0x05010105,
xmssmt_sha3-256_m32_w16_h60_d3_z = 0x06010106,
xmssmt_sha3-256_m32_w16_h60_d6_z = 0x07010107,
xmssmt_sha3-256_m32_w16_h60_d12_z = 0x08010108,
/* 256 bit classical security, 170 bit post-quantum security */
xmssmt_sha3-512_m64_w4_h20_d2_z = 0x09010109,
xmssmt_sha3-512_m64_w4_h20_d4_z = 0x0a01010a,
xmssmt_sha3-512_m64_w4_h40_d2_z = 0x0b01010b,
xmssmt_sha3-512_m64_w4_h40_d4_z = 0x0c01010c,
xmssmt_sha3-512_m64_w4_h40_d8_z = 0x0d01010d,
xmssmt_sha3-512_m64_w4_h60_d3_z = 0x0e01010e,
xmssmt_sha3-512_m64_w4_h60_d6_z = 0x0f01010f,
xmssmt_sha3-512_m64_w4_h60_d12_z = 0x00020200,
xmssmt_sha3-512_m64_w8_h20_d2_z = 0x01020201,
xmssmt_sha3-512_m64_w8_h20_d4_z = 0x02020202,
xmssmt_sha3-512_m64_w8_h40_d2_z = 0x03020203,
xmssmt_sha3-512_m64_w8_h40_d4_z = 0x04020204,
xmssmt_sha3-512_m64_w8_h40_d8_z = 0x05020205,
xmssmt_sha3-512_m64_w8_h60_d3_z = 0x06020206,
xmssmt_sha3-512_m64_w8_h60_d6_z = 0x07020207,
xmssmt_sha3-512_m64_w8_h60_d12_z = 0x08020208,
xmssmt_sha3-512_m64_w16_h20_d2_z = 0x09020209,
xmssmt_sha3-512_m64_w16_h20_d4_z = 0x0a02020a,
xmssmt_sha3-512_m64_w16_h40_d2_z = 0x0b02020b,
xmssmt_sha3-512_m64_w16_h40_d4_z = 0x0c02020c,
xmssmt_sha3-512_m64_w16_h40_d8_z = 0x0d02020d,
xmssmt_sha3-512_m64_w16_h60_d3_z = 0x0e02020e,
xmssmt_sha3-512_m64_w16_h60_d6_z = 0x0f02020f,
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xmssmt_sha3-512_m64_w16_h60_d12_z = 0x00030300,
/* Non-empty bitmasks */
/* 128 bit classical security, 64 bit post-quantum security */
xmssmt_aes128_m32_w4_h20_d2 = 0x01030301,
xmssmt_aes128_m32_w4_h20_d4 = 0x02030302,
xmssmt_aes128_m32_w4_h40_d2 = 0x03030303,
xmssmt_aes128_m32_w4_h40_d4 = 0x04030304,
xmssmt_aes128_m32_w4_h40_d8 = 0x05030305,
xmssmt_aes128_m32_w4_h60_d3 = 0x06030306,
xmssmt_aes128_m32_w4_h60_d6 = 0x07030307,
xmssmt_aes128_m32_w4_h60_d12 = 0x08030308,
xmssmt_aes128_m32_w8_h20_d2 = 0x09030309,
xmssmt_aes128_m32_w8_h20_d4 = 0x0a03030a,
xmssmt_aes128_m32_w8_h40_d2 = 0x0b03030b,
xmssmt_aes128_m32_w8_h40_d4 = 0x0c03030c,
xmssmt_aes128_m32_w8_h40_d8 = 0x0d03030d,
xmssmt_aes128_m32_w8_h60_d3 = 0x0e03030e,
xmssmt_aes128_m32_w8_h60_d6 = 0x0f03030f,
xmssmt_aes128_m32_w8_h60_d12 = 0x00040400,
xmssmt_aes128_m32_w16_h20_d2 = 0x01040401,
xmssmt_aes128_m32_w16_h20_d4 = 0x02040402,
xmssmt_aes128_m32_w16_h40_d2 = 0x03040403,
xmssmt_aes128_m32_w16_h40_d4 = 0x04040404,
xmssmt_aes128_m32_w16_h40_d8 = 0x05040405,
xmssmt_aes128_m32_w16_h60_d3 = 0x06040406,
xmssmt_aes128_m32_w16_h60_d6 = 0x07040407,
xmssmt_aes128_m32_w16_h60_d12 = 0x08040408,
/* 256 bit classical security, 128 bit post-quantum security */
xmssmt_sha3-256_m32_w4_h20_d2 = 0x09040409,
xmssmt_sha3-256_m32_w4_h20_d4 = 0x0a04040a,
xmssmt_sha3-256_m32_w4_h40_d2 = 0x0b04040b,
xmssmt_sha3-256_m32_w4_h40_d4 = 0x0c04040c,
xmssmt_sha3-256_m32_w4_h40_d8 = 0x0d04040d,
xmssmt_sha3-256_m32_w4_h60_d3 = 0x0e04040e,
xmssmt_sha3-256_m32_w4_h60_d6 = 0x0f04040f,
xmssmt_sha3-256_m32_w4_h60_d12 = 0x00050500,
xmssmt_sha3-256_m32_w8_h20_d2 = 0x01050501,
xmssmt_sha3-256_m32_w8_h20_d4 = 0x02050502,
xmssmt_sha3-256_m32_w8_h40_d2 = 0x03050503,
xmssmt_sha3-256_m32_w8_h40_d4 = 0x04050504,
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xmssmt_sha3-256_m32_w8_h40_d8 = 0x05050505,
xmssmt_sha3-256_m32_w8_h60_d3 = 0x06050506,
xmssmt_sha3-256_m32_w8_h60_d6 = 0x07050507,
xmssmt_sha3-256_m32_w8_h60_d12 = 0x08050508,
xmssmt_sha3-256_m32_w16_h20_d2 = 0x09050509,
xmssmt_sha3-256_m32_w16_h20_d4 = 0x0a05050a,
xmssmt_sha3-256_m32_w16_h40_d2 = 0x0b05050b,
xmssmt_sha3-256_m32_w16_h40_d4 = 0x0c05050c,
xmssmt_sha3-256_m32_w16_h40_d8 = 0x0d05050d,
xmssmt_sha3-256_m32_w16_h60_d3 = 0x0e05050e,
xmssmt_sha3-256_m32_w16_h60_d6 = 0x0f05050f,
xmssmt_sha3-256_m32_w16_h60_d12 = 0x00060600,
/* 512 bit classical security, 256 bit post-quantum security */
xmssmt_sha3-512_m64_w4_h20_d2 = 0x01060601,
xmssmt_sha3-512_m64_w4_h20_d4 = 0x02060602,
xmssmt_sha3-512_m64_w4_h40_d2 = 0x03060603,
xmssmt_sha3-512_m64_w4_h40_d4 = 0x04060604,
xmssmt_sha3-512_m64_w4_h40_d8 = 0x05060605,
xmssmt_sha3-512_m64_w4_h60_d3 = 0x06060606,
xmssmt_sha3-512_m64_w4_h60_d6 = 0x07060607,
xmssmt_sha3-512_m64_w4_h60_d12 = 0x08060608,
xmssmt_sha3-512_m64_w8_h20_d2 = 0x09060609,
xmssmt_sha3-512_m64_w8_h20_d4 = 0x0a06060a,
xmssmt_sha3-512_m64_w8_h40_d2 = 0x0b06060b,
xmssmt_sha3-512_m64_w8_h40_d4 = 0x0c06060c,
xmssmt_sha3-512_m64_w8_h40_d8 = 0x0d06060d,
xmssmt_sha3-512_m64_w8_h60_d3 = 0x0e06060e,
xmssmt_sha3-512_m64_w8_h60_d6 = 0x0f06060f,
xmssmt_sha3-512_m64_w8_h60_d12 = 0x00070700,
xmssmt_sha3-512_m64_w16_h20_d2 = 0x01070701,
xmssmt_sha3-512_m64_w16_h20_d4 = 0x02070702,
xmssmt_sha3-512_m64_w16_h40_d2 = 0x03070703,
xmssmt_sha3-512_m64_w16_h40_d4 = 0x04070704,
xmssmt_sha3-512_m64_w16_h40_d8 = 0x05070705,
xmssmt_sha3-512_m64_w16_h60_d3 = 0x06070706,
xmssmt_sha3-512_m64_w16_h60_d6 = 0x07070707,
xmssmt_sha3-512_m64_w16_h60_d12 = 0x08070708,
};
XMSS^MT signatures are defined using XDR syntax as follows:
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/* Type for XMSS^MT key pair index */
/* Depends solely on h */
union idx_sig_xmssmt switch (xmss_algorithm_type type) {
case xmssmt_sha3-256_m32_w4_h20_d2_z:
case xmssmt_sha3-256_m32_w4_h20_d4_z:
case xmssmt_sha3-256_m32_w8_h20_d2_z:
case xmssmt_sha3-256_m32_w8_h20_d4_z:
case xmssmt_sha3-256_m32_w16_h20_d2_z:
case xmssmt_sha3-256_m32_w16_h20_d4_z:
case xmssmt_sha3-512_m64_w4_h20_d2_z:
case xmssmt_sha3-512_m64_w4_h20_d4_z:
case xmssmt_sha3-512_m64_w8_h20_d2_z:
case xmssmt_sha3-512_m64_w8_h20_d4_z:
case xmssmt_sha3-512_m64_w16_h20_d2_z:
case xmssmt_sha3-512_m64_w16_h20_d4_z:
case xmssmt_aes128_m32_w4_h20_d2:
case xmssmt_aes128_m32_w4_h20_d4:
case xmssmt_aes128_m32_w8_h20_d2:
case xmssmt_aes128_m32_w8_h20_d4:
case xmssmt_aes128_m32_w16_h20_d2:
case xmssmt_aes128_m32_w16_h20_d4:
case xmssmt_sha3-256_m32_w4_h20_d2:
case xmssmt_sha3-256_m32_w4_h20_d4:
case xmssmt_sha3-256_m32_w8_h20_d2:
case xmssmt_sha3-256_m32_w8_h20_d4:
case xmssmt_sha3-256_m32_w16_h20_d2:
case xmssmt_sha3-256_m32_w16_h20_d4:
case xmssmt_sha3-512_m64_w4_h20_d2:
case xmssmt_sha3-512_m64_w4_h20_d4:
case xmssmt_sha3-512_m64_w8_h20_d2:
case xmssmt_sha3-512_m64_w8_h20_d4:
case xmssmt_sha3-512_m64_w16_h20_d2:
case xmssmt_sha3-512_m64_w16_h20_d4:
bytestring3 idx3;
case xmssmt_sha3-256_m32_w4_h40_d2_z:
case xmssmt_sha3-256_m32_w4_h40_d4_z:
case xmssmt_sha3-256_m32_w4_h40_d8_z:
case xmssmt_sha3-256_m32_w8_h40_d2_z:
case xmssmt_sha3-256_m32_w8_h40_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d8_z:
case xmssmt_sha3-256_m32_w16_h40_d2_z:
case xmssmt_sha3-256_m32_w16_h40_d4_z:
case xmssmt_sha3-256_m32_w16_h40_d8_z:
case xmssmt_sha3-512_m64_w4_h40_d2_z:
case xmssmt_sha3-512_m64_w4_h40_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d8_z:
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case xmssmt_sha3-512_m64_w8_h40_d2_z:
case xmssmt_sha3-512_m64_w8_h40_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d8_z:
case xmssmt_sha3-512_m64_w16_h40_d2_z:
case xmssmt_sha3-512_m64_w16_h40_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d8_z:
case xmssmt_aes128_m32_w4_h40_d2:
case xmssmt_aes128_m32_w4_h40_d4:
case xmssmt_aes128_m32_w4_h40_d8:
case xmssmt_aes128_m32_w8_h40_d2:
case xmssmt_aes128_m32_w8_h40_d4:
case xmssmt_aes128_m32_w8_h40_d8:
case xmssmt_aes128_m32_w16_h40_d2:
case xmssmt_aes128_m32_w16_h40_d4:
case xmssmt_aes128_m32_w16_h40_d8:
case xmssmt_sha3-256_m32_w4_h40_d2:
case xmssmt_sha3-256_m32_w4_h40_d4:
case xmssmt_sha3-256_m32_w4_h40_d8:
case xmssmt_sha3-256_m32_w8_h40_d2:
case xmssmt_sha3-256_m32_w8_h40_d4:
case xmssmt_sha3-256_m32_w8_h40_d8:
case xmssmt_sha3-512_m64_w4_h40_d2:
case xmssmt_sha3-512_m64_w4_h40_d4:
case xmssmt_sha3-512_m64_w4_h40_d8:
case xmssmt_sha3-256_m32_w16_h40_d2:
case xmssmt_sha3-256_m32_w16_h40_d4:
case xmssmt_sha3-256_m32_w16_h40_d8:
case xmssmt_sha3-512_m64_w8_h40_d2:
case xmssmt_sha3-512_m64_w8_h40_d4:
case xmssmt_sha3-512_m64_w8_h40_d8:
case xmssmt_sha3-512_m64_w16_h40_d2:
case xmssmt_sha3-512_m64_w16_h40_d4:
case xmssmt_sha3-512_m64_w16_h40_d8:
bytestring5 idx5;
case xmssmt_sha3-256_m32_w4_h60_d3_z:
case xmssmt_sha3-256_m32_w4_h60_d6_z:
case xmssmt_sha3-256_m32_w4_h60_d12_z:
case xmssmt_sha3-256_m32_w8_h60_d3_z:
case xmssmt_sha3-256_m32_w8_h60_d6_z:
case xmssmt_sha3-256_m32_w8_h60_d12_z:
case xmssmt_sha3-256_m32_w16_h60_d3_z:
case xmssmt_sha3-256_m32_w16_h60_d6_z:
case xmssmt_sha3-256_m32_w16_h60_d12_z:
case xmssmt_sha3-512_m64_w4_h60_d3_z:
case xmssmt_sha3-512_m64_w4_h60_d6_z:
case xmssmt_sha3-512_m64_w4_h60_d12_z:
case xmssmt_sha3-512_m64_w8_h60_d3_z:
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case xmssmt_sha3-512_m64_w8_h60_d6_z:
case xmssmt_sha3-512_m64_w8_h60_d12_z:
case xmssmt_sha3-512_m64_w16_h60_d3_z:
case xmssmt_sha3-512_m64_w16_h60_d6_z:
case xmssmt_sha3-512_m64_w16_h60_d12_z:
case xmssmt_aes128_m32_w4_h60_d3:
case xmssmt_aes128_m32_w4_h60_d6:
case xmssmt_aes128_m32_w4_h60_d12:
case xmssmt_aes128_m32_w8_h60_d3:
case xmssmt_aes128_m32_w8_h60_d6:
case xmssmt_aes128_m32_w8_h60_d12:
case xmssmt_aes128_m32_w16_h60_d3:
case xmssmt_aes128_m32_w16_h60_d6:
case xmssmt_aes128_m32_w16_h60_d12:
case xmssmt_sha3-256_m32_w4_h60_d3:
case xmssmt_sha3-256_m32_w4_h60_d6:
case xmssmt_sha3-256_m32_w4_h60_d12:
case xmssmt_sha3-256_m32_w8_h60_d3:
case xmssmt_sha3-256_m32_w8_h60_d6:
case xmssmt_sha3-256_m32_w8_h60_d12:
case xmssmt_sha3-256_m32_w16_h60_d3:
case xmssmt_sha3-256_m32_w16_h60_d6:
case xmssmt_sha3-256_m32_w16_h60_d12:
case xmssmt_sha3-512_m64_w4_h60_d3:
case xmssmt_sha3-512_m64_w4_h60_d6:
case xmssmt_sha3-512_m64_w4_h60_d12:
case xmssmt_sha3-512_m64_w8_h60_d3:
case xmssmt_sha3-512_m64_w8_h60_d6:
case xmssmt_sha3-512_m64_w8_h60_d12:
case xmssmt_sha3-512_m64_w16_h60_d3:
case xmssmt_sha3-512_m64_w16_h60_d6:
case xmssmt_sha3-512_m64_w16_h60_d12:
bytestring8 idx8;
default:
void; /* error condition */
};
union random_string_xmssmt switch (xmssmt_algorithm_type type) {
case xmssmt_aes128_m32_w4_h20_d2:
case xmssmt_aes128_m32_w4_h20_d4:
case xmssmt_aes128_m32_w4_h40_d2:
case xmssmt_aes128_m32_w4_h40_d4:
case xmssmt_aes128_m32_w4_h40_d8:
case xmssmt_aes128_m32_w4_h60_d3:
case xmssmt_aes128_m32_w4_h60_d6:
case xmssmt_aes128_m32_w4_h60_d12:
case xmssmt_aes128_m32_w8_h20_d2:
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case xmssmt_aes128_m32_w8_h20_d4:
case xmssmt_aes128_m32_w8_h40_d2:
case xmssmt_aes128_m32_w8_h40_d4:
case xmssmt_aes128_m32_w8_h40_d8:
case xmssmt_aes128_m32_w8_h60_d3:
case xmssmt_aes128_m32_w8_h60_d6:
case xmssmt_aes128_m32_w8_h60_d12:
case xmssmt_aes128_m32_w16_h20_d2:
case xmssmt_aes128_m32_w16_h20_d4:
case xmssmt_aes128_m32_w16_h40_d2:
case xmssmt_aes128_m32_w16_h40_d4:
case xmssmt_aes128_m32_w16_h40_d8:
case xmssmt_aes128_m32_w16_h60_d3:
case xmssmt_aes128_m32_w16_h60_d6:
case xmssmt_aes128_m32_w16_h60_d12:
case xmssmt_sha3-256_m32_w4_h20_d2_z:
case xmssmt_sha3-256_m32_w4_h20_d4_z:
case xmssmt_sha3-256_m32_w4_h40_d2_z:
case xmssmt_sha3-256_m32_w4_h40_d4_z:
case xmssmt_sha3-256_m32_w4_h40_d8_z:
case xmssmt_sha3-256_m32_w4_h60_d3_z:
case xmssmt_sha3-256_m32_w4_h60_d6_z:
case xmssmt_sha3-256_m32_w4_h60_d12_z:
case xmssmt_sha3-256_m32_w8_h20_d2_z:
case xmssmt_sha3-256_m32_w8_h20_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d2_z:
case xmssmt_sha3-256_m32_w8_h40_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d8_z:
case xmssmt_sha3-256_m32_w8_h60_d3_z:
case xmssmt_sha3-256_m32_w8_h60_d6_z:
case xmssmt_sha3-256_m32_w8_h60_d12_z:
case xmssmt_sha3-256_m32_w16_h20_d2_z:
case xmssmt_sha3-256_m32_w16_h20_d4_z:
case xmssmt_sha3-256_m32_w16_h40_d2_z:
case xmssmt_sha3-256_m32_w16_h40_d4_z:
case xmssmt_sha3-256_m32_w16_h40_d8_z:
case xmssmt_sha3-256_m32_w16_h60_d3_z:
case xmssmt_sha3-256_m32_w16_h60_d6_z:
case xmssmt_sha3-256_m32_w16_h60_d12_z:
case xmssmt_sha3-256_m32_w4_h20_d2:
case xmssmt_sha3-256_m32_w4_h20_d4:
case xmssmt_sha3-256_m32_w4_h40_d2:
case xmssmt_sha3-256_m32_w4_h40_d4:
case xmssmt_sha3-256_m32_w4_h40_d8:
case xmssmt_sha3-256_m32_w4_h60_d3:
case xmssmt_sha3-256_m32_w4_h60_d6:
case xmssmt_sha3-256_m32_w4_h60_d12:
case xmssmt_sha3-256_m32_w8_h20_d2:
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case xmssmt_sha3-256_m32_w8_h20_d4:
case xmssmt_sha3-256_m32_w8_h40_d2:
case xmssmt_sha3-256_m32_w8_h40_d4:
case xmssmt_sha3-256_m32_w8_h40_d8:
case xmssmt_sha3-256_m32_w8_h60_d3:
case xmssmt_sha3-256_m32_w8_h60_d6:
case xmssmt_sha3-256_m32_w8_h60_d12:
case xmssmt_sha3-256_m32_w16_h20_d2:
case xmssmt_sha3-256_m32_w16_h20_d4:
case xmssmt_sha3-256_m32_w16_h40_d2:
case xmssmt_sha3-256_m32_w16_h40_d4:
case xmssmt_sha3-256_m32_w16_h40_d8:
case xmssmt_sha3-256_m32_w16_h60_d3:
case xmssmt_sha3-256_m32_w16_h60_d6:
case xmssmt_sha3-256_m32_w16_h60_d12:
bytestring32 rand_m32;
case xmssmt_sha3-512_m64_w4_h20_d2_z:
case xmssmt_sha3-512_m64_w4_h20_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d2_z:
case xmssmt_sha3-512_m64_w4_h40_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d8_z:
case xmssmt_sha3-512_m64_w4_h60_d3_z:
case xmssmt_sha3-512_m64_w4_h60_d6_z:
case xmssmt_sha3-512_m64_w4_h60_d12_z:
case xmssmt_sha3-512_m64_w8_h20_d2_z:
case xmssmt_sha3-512_m64_w8_h20_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d2_z:
case xmssmt_sha3-512_m64_w8_h40_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d8_z:
case xmssmt_sha3-512_m64_w8_h60_d3_z:
case xmssmt_sha3-512_m64_w8_h60_d6_z:
case xmssmt_sha3-512_m64_w8_h60_d12_z:
case xmssmt_sha3-512_m64_w16_h20_d2_z:
case xmssmt_sha3-512_m64_w16_h20_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d2_z:
case xmssmt_sha3-512_m64_w16_h40_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d8_z:
case xmssmt_sha3-512_m64_w16_h60_d3_z:
case xmssmt_sha3-512_m64_w16_h60_d6_z:
case xmssmt_sha3-512_m64_w16_h60_d12_z:
case xmssmt_sha3-512_m64_w4_h20_d2:
case xmssmt_sha3-512_m64_w4_h20_d4:
case xmssmt_sha3-512_m64_w4_h40_d2:
case xmssmt_sha3-512_m64_w4_h40_d4:
case xmssmt_sha3-512_m64_w4_h40_d8:
case xmssmt_sha3-512_m64_w4_h60_d3:
case xmssmt_sha3-512_m64_w4_h60_d6:
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case xmssmt_sha3-512_m64_w4_h60_d12:
case xmssmt_sha3-512_m64_w8_h20_d2:
case xmssmt_sha3-512_m64_w8_h20_d4:
case xmssmt_sha3-512_m64_w8_h40_d2:
case xmssmt_sha3-512_m64_w8_h40_d4:
case xmssmt_sha3-512_m64_w8_h40_d8:
case xmssmt_sha3-512_m64_w8_h60_d3:
case xmssmt_sha3-512_m64_w8_h60_d6:
case xmssmt_sha3-512_m64_w8_h60_d12:
case xmssmt_sha3-512_m64_w16_h20_d2:
case xmssmt_sha3-512_m64_w16_h20_d4:
case xmssmt_sha3-512_m64_w16_h40_d2:
case xmssmt_sha3-512_m64_w16_h40_d4:
case xmssmt_sha3-512_m64_w16_h40_d8:
case xmssmt_sha3-512_m64_w16_h60_d3:
case xmssmt_sha3-512_m64_w16_h60_d6:
case xmssmt_sha3-512_m64_w16_h60_d12:
bytestring64 rand_m64;
default:
void; /* error condition */
};
struct xmss_reduced_bottom {
xmss_ots_signature sig_ots; /* WOTS+ signature */
xmss_path nodes; /* authentication path */
};
/* Type for individual reduced XMSS signatures on higher layers */
union xmss_reduced_others (xmss_algorithm_type type) {
case xmssmt_aes128_m32_w4_h20_d2:
case xmssmt_aes128_m32_w4_h20_d4:
bytestring16 xmss_reduced_n16_t88[88];
case xmssmt_aes128_m32_w4_h40_d2:
case xmssmt_aes128_m32_w4_h40_d4:
case xmssmt_aes128_m32_w4_h40_d8:
bytestring16 xmss_reduced_n16_t108[108];
case xmssmt_aes128_m32_w4_h60_d3:
case xmssmt_aes128_m32_w4_h60_d6:
case xmssmt_aes128_m32_w4_h60_d12:
bytestring16 xmss_reduced_n16_t128[128];
case xmssmt_aes128_m32_w8_h20_d2:
case xmssmt_aes128_m32_w8_h20_d4:
bytestring16 xmss_reduced_n16_t66[66];
Huelsing, et al. Expires September 24, 2015 [Page 74]
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case xmssmt_aes128_m32_w8_h40_d2:
case xmssmt_aes128_m32_w8_h40_d4:
case xmssmt_aes128_m32_w8_h40_d8:
bytestring16 xmss_reduced_n16_t86[86];
case xmssmt_aes128_m32_w8_h60_d3:
case xmssmt_aes128_m32_w8_h60_d6:
case xmssmt_aes128_m32_w8_h60_d12:
bytestring16 xmss_reduced_n16_t106[106];
case xmssmt_aes128_m32_w16_h20_d2:
case xmssmt_aes128_m32_w16_h20_d4:
bytestring16 xmss_reduced_n16_t55[55];
case xmssmt_aes128_m32_w16_h40_d2:
case xmssmt_aes128_m32_w16_h40_d4:
case xmssmt_aes128_m32_w16_h40_d8:
bytestring16 xmss_reduced_n16_t75[75];
case xmssmt_aes128_m32_w16_h60_d3:
case xmssmt_aes128_m32_w16_h60_d6:
case xmssmt_aes128_m32_w16_h60_d12:
bytestring16 xmss_reduced_n16_t95[95];
case xmssmt_sha3-256_m32_w4_h20_d2_z:
case xmssmt_sha3-256_m32_w4_h20_d4_z:
case xmssmt_sha3-256_m32_w4_h20_d2:
case xmssmt_sha3-256_m32_w4_h20_d4:
bytestring32 xmss_reduced_n32_t153[153];
case xmssmt_sha3-256_m32_w4_h40_d2_z:
case xmssmt_sha3-256_m32_w4_h40_d4_z:
case xmssmt_sha3-256_m32_w4_h40_d8_z:
case xmssmt_sha3-256_m32_w4_h40_d2:
case xmssmt_sha3-256_m32_w4_h40_d4:
case xmssmt_sha3-256_m32_w4_h40_d8:
bytestring32 xmss_reduced_n32_t173[173];
case xmssmt_sha3-256_m32_w4_h60_d3_z:
case xmssmt_sha3-256_m32_w4_h60_d6_z:
case xmssmt_sha3-256_m32_w4_h60_d12_z:
case xmssmt_sha3-256_m32_w4_h60_d3:
case xmssmt_sha3-256_m32_w4_h60_d6:
case xmssmt_sha3-256_m32_w4_h60_d12:
bytestring32 xmss_reduced_n32_t193[193];
case xmssmt_sha3-256_m32_w8_h20_d2_z:
case xmssmt_sha3-256_m32_w8_h20_d4_z:
Huelsing, et al. Expires September 24, 2015 [Page 75]
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case xmssmt_sha3-256_m32_w8_h20_d2:
case xmssmt_sha3-256_m32_w8_h20_d4:
bytestring32 xmss_reduced_n32_t110[110];
case xmssmt_sha3-256_m32_w8_h40_d2_z:
case xmssmt_sha3-256_m32_w8_h40_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d8_z:
case xmssmt_sha3-256_m32_w8_h40_d2:
case xmssmt_sha3-256_m32_w8_h40_d4:
case xmssmt_sha3-256_m32_w8_h40_d8:
bytestring32 xmss_reduced_n32_t130[130];
case xmssmt_sha3-256_m32_w8_h60_d3_z:
case xmssmt_sha3-256_m32_w8_h60_d6_z:
case xmssmt_sha3-256_m32_w8_h60_d12_z:
case xmssmt_sha3-256_m32_w8_h60_d3:
case xmssmt_sha3-256_m32_w8_h60_d6:
case xmssmt_sha3-256_m32_w8_h60_d12:
bytestring32 xmss_reduced_n32_t150[150];
case xmssmt_sha3-256_m32_w16_h20_d2_z:
case xmssmt_sha3-256_m32_w16_h20_d4_z:
case xmssmt_sha3-256_m32_w16_h20_d2:
case xmssmt_sha3-256_m32_w16_h20_d4:
bytestring32 xmss_reduced_n32_t87[87];
case xmssmt_sha3-256_m32_w16_h40_d2_z:
case xmssmt_sha3-256_m32_w16_h40_d4_z:
case xmssmt_sha3-256_m32_w16_h40_d8_z:
case xmssmt_sha3-256_m32_w16_h40_d2:
case xmssmt_sha3-256_m32_w16_h40_d4:
case xmssmt_sha3-256_m32_w16_h40_d8:
bytestring32 xmss_reduced_n32_t107[107];
case xmssmt_sha3-256_m32_w16_h60_d3_z:
case xmssmt_sha3-256_m32_w16_h60_d6_z:
case xmssmt_sha3-256_m32_w16_h60_d12_z:
case xmssmt_sha3-256_m32_w16_h60_d3:
case xmssmt_sha3-256_m32_w16_h60_d6:
case xmssmt_sha3-256_m32_w16_h60_d12:
bytestring32 xmss_reduced_n32_t127[127];
case xmssmt_sha3-512_m64_w4_h20_d2_z:
case xmssmt_sha3-512_m64_w4_h20_d4_z:
case xmssmt_sha3-512_m64_w4_h20_d2:
case xmssmt_sha3-512_m64_w4_h20_d4:
bytestring64 xmss_reduced_n64_t281[281];
Huelsing, et al. Expires September 24, 2015 [Page 76]
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case xmssmt_sha3-512_m64_w4_h40_d2_z:
case xmssmt_sha3-512_m64_w4_h40_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d8_z:
case xmssmt_sha3-512_m64_w4_h40_d2:
case xmssmt_sha3-512_m64_w4_h40_d4:
case xmssmt_sha3-512_m64_w4_h40_d8:
bytestring64 xmss_reduced_n64_t301[301];
case xmssmt_sha3-512_m64_w4_h60_d3_z:
case xmssmt_sha3-512_m64_w4_h60_d6_z:
case xmssmt_sha3-512_m64_w4_h60_d12_z:
case xmssmt_sha3-512_m64_w4_h60_d3:
case xmssmt_sha3-512_m64_w4_h60_d6:
case xmssmt_sha3-512_m64_w4_h60_d12:
bytestring64 xmss_reduced_n64_t321[321];
case xmssmt_sha3-512_m64_w8_h20_d2_z:
case xmssmt_sha3-512_m64_w8_h20_d4_z:
bytestring64 xmss_reduced_n64_t195[195];
case xmssmt_sha3-512_m64_w8_h40_d2_z:
case xmssmt_sha3-512_m64_w8_h40_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d8_z:
case xmssmt_sha3-512_m64_w8_h40_d2:
case xmssmt_sha3-512_m64_w8_h40_d4:
case xmssmt_sha3-512_m64_w8_h40_d8:
bytestring64 xmss_reduced_n64_t215[215];
case xmssmt_sha3-512_m64_w8_h60_d3_z:
case xmssmt_sha3-512_m64_w8_h60_d6_z:
case xmssmt_sha3-512_m64_w8_h60_d12_z:
case xmssmt_sha3-512_m64_w8_h60_d3:
case xmssmt_sha3-512_m64_w8_h60_d6:
case xmssmt_sha3-512_m64_w8_h60_d12:
bytestring64 xmss_reduced_n64_t235[235];
case xmssmt_sha3-512_m64_w16_h20_d2_z:
case xmssmt_sha3-512_m64_w16_h20_d4_z:
case xmssmt_sha3-512_m64_w16_h20_d2:
case xmssmt_sha3-512_m64_w16_h20_d4:
bytestring64 xmss_reduced_n64_t151[151];
case xmssmt_sha3-512_m64_w16_h40_d2_z:
case xmssmt_sha3-512_m64_w16_h40_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d8_z:
case xmssmt_sha3-512_m64_w16_h40_d2:
case xmssmt_sha3-512_m64_w16_h40_d4:
case xmssmt_sha3-512_m64_w16_h40_d8:
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bytestring64 xmss_reduced_n64_t171[171];
case xmssmt_sha3-512_m64_w16_h60_d3_z:
case xmssmt_sha3-512_m64_w16_h60_d6_z:
case xmssmt_sha3-512_m64_w16_h60_d12_z:
case xmssmt_sha3-512_m64_w16_h60_d3:
case xmssmt_sha3-512_m64_w16_h60_d6:
case xmssmt_sha3-512_m64_w16_h60_d12:
bytestring64 xmss_reduced_n64_t191[191];
default:
void; /* error condition */
};
/* xmss_reduced_array depends on d */
union xmss_reduced_array (xmss_algorithm_type type) {
case xmssmt_sha3-256_m32_w4_h20_d2_z:
case xmssmt_sha3-256_m32_w8_h20_d2_z:
case xmssmt_sha3-256_m32_w16_h20_d2_z:
case xmssmt_sha3-512_m64_w4_h20_d2_z:
case xmssmt_sha3-512_m64_w8_h20_d2_z:
case xmssmt_sha3-512_m64_w16_h20_d2_z:
case xmssmt_aes128_m32_w4_h20_d2:
case xmssmt_aes128_m32_w8_h20_d2:
case xmssmt_aes128_m32_w16_h20_d2:
case xmssmt_sha3-256_m32_w4_h20_d2:
case xmssmt_sha3-256_m32_w8_h20_d2:
case xmssmt_sha3-256_m32_w16_h20_d2:
case xmssmt_sha3-512_m64_w4_h20_d2:
case xmssmt_sha3-512_m64_w8_h20_d2:
case xmssmt_sha3-512_m64_w16_h20_d2:
case xmssmt_sha3-256_m32_w4_h40_d2_z:
case xmssmt_sha3-256_m32_w8_h40_d2_z:
case xmssmt_sha3-256_m32_w16_h40_d2_z:
case xmssmt_sha3-512_m64_w4_h40_d2_z:
case xmssmt_sha3-512_m64_w8_h40_d2_z:
case xmssmt_sha3-512_m64_w16_h40_d2_z:
case xmssmt_aes128_m32_w4_h40_d2:
case xmssmt_aes128_m32_w8_h40_d2:
case xmssmt_aes128_m32_w16_h40_d2:
case xmssmt_sha3-256_m32_w4_h40_d2:
case xmssmt_sha3-256_m32_w8_h40_d2:
case xmssmt_sha3-512_m64_w4_h40_d2:
case xmssmt_sha3-256_m32_w16_h40_d2:
case xmssmt_sha3-512_m64_w8_h40_d2:
case xmssmt_sha3-512_m64_w16_h40_d2:
xmss_reduced_others xmss_red_arr_d2[1];
Huelsing, et al. Expires September 24, 2015 [Page 78]
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case xmssmt_sha3-256_m32_w4_h60_d3_z:
case xmssmt_sha3-256_m32_w8_h60_d3_z:
case xmssmt_sha3-256_m32_w16_h60_d3_z:
case xmssmt_sha3-512_m64_w4_h60_d3_z:
case xmssmt_sha3-512_m64_w8_h60_d3_z:
case xmssmt_sha3-512_m64_w16_h60_d3_z:
case xmssmt_aes128_m32_w4_h60_d3:
case xmssmt_aes128_m32_w8_h60_d3:
case xmssmt_aes128_m32_w16_h60_d3:
case xmssmt_sha3-256_m32_w4_h60_d3:
case xmssmt_sha3-256_m32_w8_h60_d3:
case xmssmt_sha3-256_m32_w16_h60_d3:
case xmssmt_sha3-512_m64_w4_h60_d3:
case xmssmt_sha3-512_m64_w8_h60_d3:
case xmssmt_sha3-512_m64_w16_h60_d3:
xmss_reduced_others xmss_red_arr_d3[2];
case xmssmt_sha3-256_m32_w4_h20_d4_z:
case xmssmt_sha3-256_m32_w8_h20_d4_z:
case xmssmt_sha3-256_m32_w16_h20_d4_z:
case xmssmt_sha3-512_m64_w4_h20_d4_z:
case xmssmt_sha3-512_m64_w8_h20_d4_z:
case xmssmt_sha3-512_m64_w16_h20_d4_z:
case xmssmt_aes128_m32_w4_h20_d4:
case xmssmt_aes128_m32_w8_h20_d4:
case xmssmt_aes128_m32_w16_h20_d4:
case xmssmt_sha3-256_m32_w4_h20_d4:
case xmssmt_sha3-256_m32_w8_h20_d4:
case xmssmt_sha3-256_m32_w16_h20_d4:
case xmssmt_sha3-512_m64_w4_h20_d4:
case xmssmt_sha3-512_m64_w8_h20_d4:
case xmssmt_sha3-512_m64_w16_h20_d4:
case xmssmt_sha3-256_m32_w4_h40_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d4_z:
case xmssmt_sha3-256_m32_w16_h40_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d4_z:
case xmssmt_aes128_m32_w4_h40_d4:
case xmssmt_aes128_m32_w8_h40_d4:
case xmssmt_aes128_m32_w16_h40_d4:
case xmssmt_sha3-256_m32_w4_h40_d4:
case xmssmt_sha3-256_m32_w8_h40_d4:
case xmssmt_sha3-512_m64_w4_h40_d4:
case xmssmt_sha3-256_m32_w16_h40_d4:
case xmssmt_sha3-512_m64_w8_h40_d4:
case xmssmt_sha3-512_m64_w16_h40_d4:
xmss_reduced_others xmss_red_arr_d4[3];
Huelsing, et al. Expires September 24, 2015 [Page 79]
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case xmssmt_sha3-256_m32_w4_h60_d6_z:
case xmssmt_sha3-256_m32_w8_h60_d6_z:
case xmssmt_sha3-256_m32_w16_h60_d6_z:
case xmssmt_sha3-512_m64_w4_h60_d6_z:
case xmssmt_sha3-512_m64_w8_h60_d6_z:
case xmssmt_sha3-512_m64_w16_h60_d6_z:
case xmssmt_aes128_m32_w4_h60_d6:
case xmssmt_aes128_m32_w8_h60_d6:
case xmssmt_aes128_m32_w16_h60_d6:
case xmssmt_sha3-256_m32_w4_h60_d6:
case xmssmt_sha3-256_m32_w8_h60_d6:
case xmssmt_sha3-256_m32_w16_h60_d6:
case xmssmt_sha3-512_m64_w4_h60_d6:
case xmssmt_sha3-512_m64_w8_h60_d6:
case xmssmt_sha3-512_m64_w16_h60_d6:
xmss_reduced_others xmss_red_arr_d6[5];
case xmssmt_sha3-256_m32_w4_h40_d8_z:
case xmssmt_sha3-256_m32_w8_h40_d8_z:
case xmssmt_sha3-256_m32_w16_h40_d8_z:
case xmssmt_sha3-512_m64_w4_h40_d8_z:
case xmssmt_sha3-512_m64_w8_h40_d8_z:
case xmssmt_sha3-512_m64_w16_h40_d8_z:
case xmssmt_aes128_m32_w4_h40_d8:
case xmssmt_aes128_m32_w8_h40_d8:
case xmssmt_aes128_m32_w16_h40_d8:
case xmssmt_sha3-256_m32_w4_h40_d8:
case xmssmt_sha3-256_m32_w8_h40_d8:
case xmssmt_sha3-512_m64_w4_h40_d8:
case xmssmt_sha3-256_m32_w16_h40_d8:
case xmssmt_sha3-512_m64_w8_h40_d8:
case xmssmt_sha3-512_m64_w16_h40_d8:
xmss_reduced_others xmss_red_arr_d8[7];
case xmssmt_sha3-256_m32_w4_h60_d12_z:
case xmssmt_sha3-256_m32_w8_h60_d12_z:
case xmssmt_sha3-256_m32_w16_h60_d12_z:
case xmssmt_sha3-512_m64_w4_h60_d12_z:
case xmssmt_sha3-512_m64_w8_h60_d12_z:
case xmssmt_sha3-512_m64_w16_h60_d12_z:
case xmssmt_aes128_m32_w4_h60_d12:
case xmssmt_aes128_m32_w8_h60_d12:
case xmssmt_aes128_m32_w16_h60_d12:
case xmssmt_sha3-256_m32_w4_h60_d12:
case xmssmt_sha3-256_m32_w8_h60_d12:
case xmssmt_sha3-256_m32_w16_h60_d12:
case xmssmt_sha3-512_m64_w4_h60_d12:
case xmssmt_sha3-512_m64_w8_h60_d12:
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case xmssmt_sha3-512_m64_w16_h60_d12:
xmss_reduced_others xmss_red_arr_d12[11];
default:
void; /* error condition */
};
/* XMSS^MT signature structure */
struct xmssmt_signature {
/* WOTS+ key pair index */
idx_sig_xmssmt idx_sig;
/* Random string for randomized hashing */
random_string_xmssmt randomness;
/* Reduced bottom layer XMSS signature */
xmss_reduced_bottom;
/* Array of reduced XMSS signatures with message length n */
xmss_reduced_array;
};
When no bitmasks are used, XMSS^MT public keys are defined using XDR
syntax as follows:
/* Types for XMSS^MT root node */
union xmssmt_root switch (xmssmt_algorithm_type type) {
case xmssmt_sha3-256_m32_w4_h20_d2_z:
case xmssmt_sha3-256_m32_w4_h20_d4_z:
case xmssmt_sha3-256_m32_w4_h40_d2_z:
case xmssmt_sha3-256_m32_w4_h40_d4_z:
case xmssmt_sha3-256_m32_w4_h40_d8_z:
case xmssmt_sha3-256_m32_w4_h60_d3_z:
case xmssmt_sha3-256_m32_w4_h60_d6_z:
case xmssmt_sha3-256_m32_w4_h60_d12_z:
case xmssmt_sha3-256_m32_w8_h20_d2_z:
case xmssmt_sha3-256_m32_w8_h20_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d2_z:
case xmssmt_sha3-256_m32_w8_h40_d4_z:
case xmssmt_sha3-256_m32_w8_h40_d8_z:
case xmssmt_sha3-256_m32_w8_h60_d3_z:
case xmssmt_sha3-256_m32_w8_h60_d6_z:
case xmssmt_sha3-256_m32_w8_h60_d12_z:
case xmssmt_sha3-256_m32_w16_h20_d2_z:
case xmssmt_sha3-256_m32_w16_h20_d4_z:
case xmssmt_sha3-256_m32_w16_h40_d2_z:
case xmssmt_sha3-256_m32_w16_h40_d4_z:
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case xmssmt_sha3-256_m32_w16_h40_d8_z:
case xmssmt_sha3-256_m32_w16_h60_d3_z:
case xmssmt_sha3-256_m32_w16_h60_d6_z:
case xmssmt_sha3-256_m32_w16_h60_d12_z:
bytestring32 root_n32;
case xmssmt_sha3-512_m64_w4_h20_d2_z:
case xmssmt_sha3-512_m64_w4_h20_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d2_z:
case xmssmt_sha3-512_m64_w4_h40_d4_z:
case xmssmt_sha3-512_m64_w4_h40_d8_z:
case xmssmt_sha3-512_m64_w4_h60_d3_z:
case xmssmt_sha3-512_m64_w4_h60_d6_z:
case xmssmt_sha3-512_m64_w4_h60_d12_z:
case xmssmt_sha3-512_m64_w8_h20_d2_z:
case xmssmt_sha3-512_m64_w8_h20_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d2_z:
case xmssmt_sha3-512_m64_w8_h40_d4_z:
case xmssmt_sha3-512_m64_w8_h40_d8_z:
case xmssmt_sha3-512_m64_w8_h60_d3_z:
case xmssmt_sha3-512_m64_w8_h60_d6_z:
case xmssmt_sha3-512_m64_w8_h60_d12_z:
case xmssmt_sha3-512_m64_w16_h20_d2_z:
case xmssmt_sha3-512_m64_w16_h20_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d2_z:
case xmssmt_sha3-512_m64_w16_h40_d4_z:
case xmssmt_sha3-512_m64_w16_h40_d8_z:
case xmssmt_sha3-512_m64_w16_h60_d3_z:
case xmssmt_sha3-512_m64_w16_h60_d6_z:
case xmssmt_sha3-512_m64_w16_h60_d12_z:
bytestring64 root_n64;
default:
void; /* error condition */
};
/* XMSS^MT public key structure */
struct xmssmt_public_key {
xmssmt_root root; /* Root node */
};
When bitmasks are used, XMSS^MT public keys are defined using XDR
syntax as follows:
/* Types for XMSS^MT bitmasks */
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union xmssmt_bm switch (xmssmt_algorithm_type type) {
case xmssmt_aes128_m32_w4_h20_d2:
case xmssmt_aes128_m32_w4_h40_d4:
case xmssmt_aes128_m32_w4_h60_d6:
bytestring16 bm_n16_t36[36];
case xmssmt_aes128_m32_w4_h60_d3:
case xmssmt_aes128_m32_w4_h40_d2:
bytestring16 bm_n16_t36[56];
case xmssmt_aes128_m32_w4_h20_d4:
case xmssmt_aes128_m32_w4_h40_d8:
case xmssmt_aes128_m32_w4_h60_d12:
bytestring16 bm_n16_t26[26];
case xmssmt_aes128_m32_w8_h20_d2:
case xmssmt_aes128_m32_w8_h40_d4:
case xmssmt_aes128_m32_w8_h60_d6:
case xmssmt_aes128_m32_w16_h20_d2:
case xmssmt_aes128_m32_w16_h40_d4:
case xmssmt_aes128_m32_w16_h60_d6:
bytestring16 bm_n16_t34[34];
case xmssmt_aes128_m32_w8_h20_d4:
case xmssmt_aes128_m32_w8_h40_d8:
case xmssmt_aes128_m32_w8_h60_d12:
case xmssmt_aes128_m32_w16_h20_d4:
case xmssmt_aes128_m32_w16_h40_d8:
case xmssmt_aes128_m32_w16_h60_d12:
bytestring16 bm_n16_t24[24];
case xmssmt_aes128_m32_w8_h40_d2:
case xmssmt_aes128_m32_w8_h60_d3:
case xmssmt_aes128_m32_w16_h40_d2:
case xmssmt_aes128_m32_w16_h60_d3:
bytestring16 bm_n16_t54[54];
case xmssmt_sha3-256_m32_w4_h20_d2:
case xmssmt_sha3-256_m32_w4_h40_d4:
case xmssmt_sha3-256_m32_w4_h60_d6:
bytestring32 bm_n32_t36[36];
case xmssmt_sha3-256_m32_w4_h20_d4:
case xmssmt_sha3-256_m32_w4_h40_d8:
case xmssmt_sha3-256_m32_w4_h60_d12:
bytestring32 bm_n32_t26[26];
case xmssmt_sha3-256_m32_w4_h40_d2:
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case xmssmt_sha3-256_m32_w4_h60_d3:
bytestring32 bm_n32_t56[56];
case xmssmt_sha3-256_m32_w8_h20_d2:
case xmssmt_sha3-256_m32_w8_h40_d4:
case xmssmt_sha3-256_m32_w8_h60_d6:
case xmssmt_sha3-256_m32_w16_h20_d2:
case xmssmt_sha3-256_m32_w16_h40_d4:
case xmssmt_sha3-256_m32_w16_h60_d6:
bytestring32 bm_n32_t34[34];
case xmssmt_sha3-256_m32_w8_h20_d4:
case xmssmt_sha3-256_m32_w8_h40_d8:
case xmssmt_sha3-256_m32_w8_h60_d12:
case xmssmt_sha3-256_m32_w16_h20_d4:
case xmssmt_sha3-256_m32_w16_h40_d8:
case xmssmt_sha3-256_m32_w16_h60_d12:
bytestring32 bm_n32_t24[24];
case xmssmt_sha3-256_m32_w8_h40_d2:
case xmssmt_sha3-256_m32_w8_h60_d3:
case xmssmt_sha3-256_m32_w16_h40_d2:
case xmssmt_sha3-256_m32_w16_h60_d3:
bytestring32 bm_n32_t54[54];
case xmssmt_sha3-512_m64_w4_h20_d2:
case xmssmt_sha3-512_m64_w4_h40_d4:
case xmssmt_sha3-512_m64_w4_h60_d6:
bytestring64 bm_n64_t38[38];
case xmssmt_sha3-512_m64_w4_h20_d4:
case xmssmt_sha3-512_m64_w4_h40_d8:
case xmssmt_sha3-512_m64_w4_h60_d12:
bytestring64 bm_n64_t28[28];
case xmssmt_sha3-512_m64_w4_h40_d2:
case xmssmt_sha3-512_m64_w4_h60_d3:
bytestring64 bm_n64_t58[58];
case xmssmt_sha3-512_m64_w8_h20_d2:
case xmssmt_sha3-512_m64_w8_h40_d4:
case xmssmt_sha3-512_m64_w8_h60_d6:
case xmssmt_sha3-512_m64_w16_h20_d2:
case xmssmt_sha3-512_m64_w16_h40_d4:
case xmssmt_sha3-512_m64_w16_h60_d6:
bytestring64 bm_n64_t36[36];
case xmssmt_sha3-512_m64_w8_h20_d4:
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case xmssmt_sha3-512_m64_w8_h40_d8:
case xmssmt_sha3-512_m64_w8_h60_d12:
case xmssmt_sha3-512_m64_w16_h20_d4:
case xmssmt_sha3-512_m64_w16_h40_d8:
case xmssmt_sha3-512_m64_w16_h60_d12:
bytestring64 bm_n64_t26[26];
case xmssmt_sha3-512_m64_w8_h40_d2:
case xmssmt_sha3-512_m64_w8_h60_d3:
case xmssmt_sha3-512_m64_w16_h40_d2:
case xmssmt_sha3-512_m64_w16_h60_d3:
bytestring64 bm_n64_t56[56];
default:
void; /* error condition */
};
/* Types for XMSS^MT root node */
union xmssmt_root switch (xmssmt_algorithm_type type) {
case xmssmt_aes128_m32_w4_h20_d2:
case xmssmt_aes128_m32_w4_h20_d4:
case xmssmt_aes128_m32_w4_h40_d2:
case xmssmt_aes128_m32_w4_h40_d4:
case xmssmt_aes128_m32_w4_h40_d8:
case xmssmt_aes128_m32_w4_h60_d3:
case xmssmt_aes128_m32_w4_h60_d6:
case xmssmt_aes128_m32_w4_h60_d12:
case xmssmt_aes128_m32_w8_h20_d2:
case xmssmt_aes128_m32_w8_h20_d4:
case xmssmt_aes128_m32_w8_h40_d2:
case xmssmt_aes128_m32_w8_h40_d4:
case xmssmt_aes128_m32_w8_h40_d8:
case xmssmt_aes128_m32_w8_h60_d3:
case xmssmt_aes128_m32_w8_h60_d6:
case xmssmt_aes128_m32_w8_h60_d12:
case xmssmt_aes128_m32_w16_h20_d2:
case xmssmt_aes128_m32_w16_h20_d4:
case xmssmt_aes128_m32_w16_h40_d2:
case xmssmt_aes128_m32_w16_h40_d4:
case xmssmt_aes128_m32_w16_h40_d8:
case xmssmt_aes128_m32_w16_h60_d3:
case xmssmt_aes128_m32_w16_h60_d6:
case xmssmt_aes128_m32_w16_h60_d12:
bytestring16 root_n16;
case xmssmt_sha3-256_m32_w4_h20_d2:
case xmssmt_sha3-256_m32_w4_h20_d4:
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case xmssmt_sha3-256_m32_w4_h40_d2:
case xmssmt_sha3-256_m32_w4_h40_d4:
case xmssmt_sha3-256_m32_w4_h40_d8:
case xmssmt_sha3-256_m32_w4_h60_d3:
case xmssmt_sha3-256_m32_w4_h60_d6:
case xmssmt_sha3-256_m32_w4_h60_d12:
case xmssmt_sha3-256_m32_w8_h20_d2:
case xmssmt_sha3-256_m32_w8_h20_d4:
case xmssmt_sha3-256_m32_w8_h40_d2:
case xmssmt_sha3-256_m32_w8_h40_d4:
case xmssmt_sha3-256_m32_w8_h40_d8:
case xmssmt_sha3-256_m32_w8_h60_d3:
case xmssmt_sha3-256_m32_w8_h60_d6:
case xmssmt_sha3-256_m32_w8_h60_d12:
case xmssmt_sha3-256_m32_w16_h20_d2:
case xmssmt_sha3-256_m32_w16_h20_d4:
case xmssmt_sha3-256_m32_w16_h40_d2:
case xmssmt_sha3-256_m32_w16_h40_d4:
case xmssmt_sha3-256_m32_w16_h40_d8:
case xmssmt_sha3-256_m32_w16_h60_d3:
case xmssmt_sha3-256_m32_w16_h60_d6:
case xmssmt_sha3-256_m32_w16_h60_d12:
bytestring32 root_n32;
case xmssmt_sha3-512_m64_w4_h20_d2:
case xmssmt_sha3-512_m64_w4_h20_d4:
case xmssmt_sha3-512_m64_w4_h40_d2:
case xmssmt_sha3-512_m64_w4_h40_d4:
case xmssmt_sha3-512_m64_w4_h40_d8:
case xmssmt_sha3-512_m64_w4_h60_d3:
case xmssmt_sha3-512_m64_w4_h60_d6:
case xmssmt_sha3-512_m64_w4_h60_d12:
case xmssmt_sha3-512_m64_w8_h20_d2:
case xmssmt_sha3-512_m64_w8_h20_d4:
case xmssmt_sha3-512_m64_w8_h40_d2:
case xmssmt_sha3-512_m64_w8_h40_d4:
case xmssmt_sha3-512_m64_w8_h40_d8:
case xmssmt_sha3-512_m64_w8_h60_d3:
case xmssmt_sha3-512_m64_w8_h60_d6:
case xmssmt_sha3-512_m64_w8_h60_d12:
case xmssmt_sha3-512_m64_w16_h20_d2:
case xmssmt_sha3-512_m64_w16_h20_d4:
case xmssmt_sha3-512_m64_w16_h40_d2:
case xmssmt_sha3-512_m64_w16_h40_d4:
case xmssmt_sha3-512_m64_w16_h40_d8:
case xmssmt_sha3-512_m64_w16_h60_d3:
case xmssmt_sha3-512_m64_w16_h60_d6:
case xmssmt_sha3-512_m64_w16_h60_d12:
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bytestring64 root_n64;
default:
void; /* error condition */
};
/* XMSS^MT public key structure */
struct xmssmt_public_key {
xmssmt_bm bm; /* Bitmasks */
xmssmt_root root; /* Root node */
};
Authors' Addresses
Andreas Huelsing
TU Eindhoven
P.O. Box 513
Eindhoven 5600 MB
The Netherlands
Email: a.t.huelsing@tue.nl
Denis Butin
TU Darmstadt
Hochschulstrasse 10
Darmstadt 64289
Germany
Email: dbutin@cdc.informatik.tu-darmstadt.de
Stefan-Lukas Gazdag
genua mbH
Domagkstrasse 7
Kirchheim bei Muenchen 85551
Germany
Email: stefan-lukas_gazdag@genua.eu
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Aziz Mohaisen
Verisign Labs
12061 Bluemont Way
Reston, VA 20190
Phone: +1 703 948-3200
Email: amohaisen@verisign.com
Huelsing, et al. Expires September 24, 2015 [Page 88]
