Internet DRAFT - draft-irtf-cfrg-re-keying
draft-irtf-cfrg-re-keying
CFRG S. Smyshlyaev, Ed.
Internet-Draft CryptoPro
Intended status: Informational May 31, 2019
Expires: December 2, 2019
Re-keying Mechanisms for Symmetric Keys
draft-irtf-cfrg-re-keying-17
Abstract
A certain maximum amount of data can be safely encrypted when
encryption is performed under a single key. This amount is called
"key lifetime". This specification describes a variety of methods to
increase the lifetime of symmetric keys. It provides two types of
re-keying mechanisms based on hash functions and on block ciphers,
that can be used with modes of operations such as CTR, GCM, CBC, CFB
and OMAC.
This document is a product of the Crypto Forum Research Group (CFRG)
in the IRTF.
Status of This Memo
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This Internet-Draft will expire on December 2, 2019.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Conventions Used in This Document . . . . . . . . . . . . . . 6
3. Basic Terms and Definitions . . . . . . . . . . . . . . . . . 6
4. Choosing Constructions and Security Parameters . . . . . . . 8
5. External Re-keying Mechanisms . . . . . . . . . . . . . . . . 10
5.1. Methods of Key Lifetime Control . . . . . . . . . . . . . 13
5.2. Parallel Constructions . . . . . . . . . . . . . . . . . 13
5.2.1. Parallel Construction Based on a KDF on a Block
Cipher . . . . . . . . . . . . . . . . . . . . . . . 14
5.2.2. Parallel Construction Based on a KDF on a Hash
Function . . . . . . . . . . . . . . . . . . . . . . 14
5.2.3. Tree-based Construction . . . . . . . . . . . . . . . 15
5.3. Serial Constructions . . . . . . . . . . . . . . . . . . 16
5.3.1. Serial Construction Based on a KDF on a Block Cipher 17
5.3.2. Serial Construction Based on a KDF on a Hash Function 18
5.4. Using Additional Entropy during Re-keying . . . . . . . . 18
6. Internal Re-keying Mechanisms . . . . . . . . . . . . . . . . 19
6.1. Methods of Key Lifetime Control . . . . . . . . . . . . . 21
6.2. Constructions that Do Not Require Master Key . . . . . . 22
6.2.1. ACPKM Re-keying Mechanisms . . . . . . . . . . . . . 22
6.2.2. CTR-ACPKM Encryption Mode . . . . . . . . . . . . . . 24
6.2.3. GCM-ACPKM Authenticated Encryption Mode . . . . . . . 26
6.3. Constructions that Require Master Key . . . . . . . . . . 28
6.3.1. ACPKM-Master Key Derivation from the Master Key . . . 29
6.3.2. CTR-ACPKM-Master Encryption Mode . . . . . . . . . . 31
6.3.3. GCM-ACPKM-Master Authenticated Encryption Mode . . . 33
6.3.4. CBC-ACPKM-Master Encryption Mode . . . . . . . . . . 35
6.3.5. CFB-ACPKM-Master Encryption Mode . . . . . . . . . . 38
6.3.6. OMAC-ACPKM-Master Authentication Mode . . . . . . . . 40
7. Joint Usage of External and Internal Re-keying . . . . . . . 41
8. Security Considerations . . . . . . . . . . . . . . . . . . . 42
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 43
10. References . . . . . . . . . . . . . . . . . . . . . . . . . 43
10.1. Normative References . . . . . . . . . . . . . . . . . . 43
10.2. Informative References . . . . . . . . . . . . . . . . . 44
Appendix A. Test Examples . . . . . . . . . . . . . . . . . . . 46
A.1. Test Examples for External Re-keying . . . . . . . . . . 46
A.1.1. External Re-keying with a Parallel Construction . . . 46
A.1.2. External Re-keying with a Serial Construction . . . . 48
A.2. Test Examples for Internal Re-keying . . . . . . . . . . 51
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A.2.1. Internal Re-keying Mechanisms that Do Not Require
Master Key . . . . . . . . . . . . . . . . . . . . . 51
A.2.2. Internal Re-keying Mechanisms with a Master Key . . . 55
Appendix B. Contributors . . . . . . . . . . . . . . . . . . . . 67
Appendix C. Acknowledgments . . . . . . . . . . . . . . . . . . 68
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 68
1. Introduction
A certain maximum amount of data can be safely encrypted when
encryption is performed under a single key. Hereinafter this amount
will be referred to as "key lifetime". The need for such a
limitation is dictated by the following methods of cryptanalysis:
1. Methods based on the combinatorial properties of the used block
cipher mode of operation
These methods do not depend on the underlying block cipher.
Common modes restrictions derived from such methods are of order
2^{n/2}, where n is a block size defined in Section 3. [Sweet32]
is an example of attack that is based on such methods.
2. Methods based on side-channel analysis issues
In most cases these methods do not depend on the used encryption
modes and weakly depend on the used block cipher features.
Limitations resulting from these considerations are usually the
most restrictive ones. [TEMPEST] is an example of attack that is
based on such methods.
3. Methods based on the properties of the used block cipher
The most common methods of this type are linear and differential
cryptanalysis [LDC]. In most cases these methods do not depend on
the used modes of operation. In case of secure block ciphers,
bounds resulting from such methods are roughly the same as the
natural bounds of 2^n, and are dominated by the other bounds
above. Therefore, they can be excluded from the considerations
here.
As a result, it is important to replace a key when the total size of
the processed plaintext under that key approaches the lifetime
limitation. A specific value of the key lifetime should be
determined in accordance with some safety margin for protocol
security and the methods outlined above.
Suppose L is a key lifetime limitation in some protocol P. For
simplicity, assume that all messages have the same length m. Hence,
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the number of messages q that can be processed with a single key K
should be such that m * q <= L. This can be depicted graphically as
a rectangle with sides m and q which is enclosed by area L (see
Figure 1).
+------------------------+
| L |
| +--------m---------+ |
| |==================| |
| |==================| |
| q==================| | m * q <= L
| |==================| |
| |==================| |
| +------------------+ |
+------------------------+
Figure 1: Graphic display of the key lifetime limitation
In practice, such amount of data that corresponds to limitation L may
not be enough. The simplest and obvious way in this situation is a
regular renegotiation of an initial key after processing this
threshold amount of data L. However, this reduces the total
performance, since it usually entails termination of application data
transmission, additional service messages, the use of random number
generator and many other additional calculations, including resource-
intensive public key cryptography.
For the protocols based on block ciphers or stream ciphers a more
efficient way to increasing the key lifetime is to use various re-
keying mechanisms. This specification considers only the case of re-
keying mechanisms for block ciphers, while re-keying mechanisms
typical for stream ciphers (e.g., [Pietrzak2009], [FPS2012]) case go
beyond the scope of this document.
Re-keying mechanisms can be applied on the different protocol levels:
on the block cipher level (this approach is known as fresh re-keying
and is described, for instance, in [FRESHREKEYING]), on the block
cipher mode of operation level (see Section 6), on the protocol level
above the block cipher mode of operation (see Section 5). The usage
of the first approach is highly inefficient due to the key changing
after processing each message block. Moreover, fresh re-keying
mechanisms can change the block cipher internal structure, and,
consequently, can require the additional security analysis for each
particular block cipher. As a result, this approach depends on
particular primitive properties and can not be applied to any
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arbitrary block cipher without additional security analysis,
therefore, fresh re-keying mechanisms go beyond the scope of this
document.
Thus, this document contains the list of recommended re-keying
mechanisms that can be used in the symmetric encryption schemes based
on the block ciphers. These mechanisms are independent from the
particular block cipher specification and their security properties
rely only on the standard block cipher security assumption.
This specification presents two basic approaches to extend the
lifetime of a key while avoiding renegotiation that were introduced
in [AAOS2017]:
1. External re-keying
External re-keying is performed by a protocol, and it is
independent of the underlying block cipher and the mode of
operation. External re-keying can use parallel and serial
constructions. In the parallel case, data processing keys K^1,
K^2, ... are generated directly from the initial key K
independently of each other. In the serial case, every data
processing key depends on the state that is updated after the
generation of each new data processing key.
As a generalization of external parallel re-keying an external
tree-based mechanism can be considered. It is specified in the
Section 5.2.3 and can be viewed as the [GGM] tree generalization.
Similar constructions are used in the one-way tree mechanism
([OWT]) and [AESDUKPT] standard.
2. Internal re-keying
Internal re-keying is built into the mode, and it depends heavily
on the properties of the mode of operation and the block size.
The re-keying approaches extend the key lifetime for a single initial
key by providing the possibility to limit the leakages (via side
channels) and by improving combinatorial properties of the used block
cipher mode of operation.
In practical applications, re-keying can be useful for protocols that
need to operate in hostile environments or under restricted resource
conditions (e.g., that require lightweight cryptography, where
ciphers have a small block size, that imposes strict combinatorial
limitations). Moreover, mechanisms that use external or internal re-
keying may provide some protection against possible future attacks
(by limiting the number of plaintext-ciphertext pairs that an
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adversary can collect) and some properties of forward or backward
security (meaning that past or future data processing keys remain
secure even if the current key is compromised, see for more details
[AbBell]). External or internal re-keying can be used in network
protocols as well as in the systems for data-at-rest encryption.
Depending on the concrete protocol characteristics there might be
situations in which both external and internal re-keying mechanisms
(see Section 7) can be applied. For example, the similar approach
was used in the Taha's tree construction (see [TAHA]).
Note that there are key updating (key regression) algorithms (e.g.,
[FKK2005] and [KMNT2003]) which are called "re-keying" as well, but
they pursue the goal different from increasing key lifetime.
Therefore, key regression algorithms are excluded from the
considerations here.
This document represents the consensus of the Crypto Forum Research
Group (CFRG).
2. 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].
3. Basic Terms and Definitions
This document uses the following terms and definitions for the sets
and operations on the elements of these sets:
V* the set of all bit strings of a finite length (hereinafter
referred to as strings), including the empty string;
V_s the set of all bit strings of length s, where s is a non-
negative integer;
|X| the bit length of the bit string X;
A | B concatenation of strings A and B both belonging to V*, i.e.,
a string in V_{|A|+|B|}, where the left substring in V_|A| is
equal to A, and the right substring in V_|B| is equal to B;
(xor) exclusive-or of two bit strings of the same length;
Z_{2^n} ring of residues modulo 2^n;
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Int_s: V_s -> Z_{2^s} the transformation that maps a string a =
(a_s, ... , a_1) in V_s into the integer Int_s(a) = 2^{s-1} *
a_s + ... + 2 * a_2 + a_1 (the interpretation of the binary
string as an integer);
Vec_s: Z_{2^s} -> V_s the transformation inverse to the mapping
Int_s (the interpretation of an integer as a binary string);
MSB_i: V_s -> V_i the transformation that maps the string a = (a_s,
... , a_1) in V_s into the string MSB_i(a) = (a_s, ... ,
a_{s-i+1}) in V_i (most significant bits);
LSB_i: V_s -> V_i the transformation that maps the string a = (a_s,
... , a_1) in V_s into the string LSB_i(a) = (a_i, ... , a_1)
in V_i (least significant bits);
Inc_c: V_s -> V_s the transformation that maps the string a = (a_s,
... , a_1) in V_s into the string Inc_c(a) = MSB_{|a|-c}(a) |
Vec_c(Int_c(LSB_c(a)) + 1(mod 2^c)) in V_s (incrementing the
least significant c bits of the bit string, regarded as the
binary representation of an integer);
a^s the string in V_s that consists of s 'a' bits;
E_{K}: V_n -> V_n the block cipher permutation under the key K in
V_k;
ceil(x) the smallest integer that is greater than or equal to x;
floor(x) the biggest integer that is less than or equal to x;
k the bit-length of the K; k is assumed to be divisible by 8;
n the block size of the block cipher (in bits); n is assumed to
be divisible by 8;
b the number of data blocks in the plaintext P (b =
ceil(|P|/n));
N the section size (the number of bits that are processed with
one section key before this key is transformed).
A plaintext message P and the corresponding ciphertext C are divided
into b = ceil(|P|/n) blocks, denoted P = P_1 | P_2 | ... | P_b and C
= C_1 | C_2 | ... | C_b, respectively. The first b-1 blocks P_i and
C_i are in V_n, for i = 1, 2, ... , b-1. The b-th blocks P_b, C_b
may be an incomplete blocks, i.e., in V_r, where r <= n if not
otherwise specified.
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4. Choosing Constructions and Security Parameters
External re-keying is an approach assuming that a key is transformed
after encrypting a limited number of entire messages. External re-
keying method is chosen at the protocol level, regardless of the
underlying block cipher or the encryption mode. External re-keying
is recommended for protocols that process relatively short messages
or for protocols that have a way to divide a long message into
manageable pieces. Through external re-keying the number of messages
that can be securely processed with a single initial key K is
substantially increased without loss in message length.
External re-keying has the following advantages:
1. it increases the lifetime of an initial key by increasing the
number of messages processed with this key;
2. it has minimal impact on performance, when the number of messages
processed under one initial key is sufficiently large;
3. it provides forward and backward security of data processing
keys.
However, the use of external re-keying has the following
disadvantage: in case of restrictive key lifetime limitations the
message sizes can become inconvenient due to impossibility of
processing sufficiently large messages, so it could be necessary to
perform additional fragmentation at the protocol level. E.g. if the
key lifetime L is 1 GB and the message length m = 3 GB, then this
message cannot be processed as a whole and it should be divided into
three fragments that will be processed separately.
Internal re-keying is an approach assuming that a key is transformed
during each separate message processing. Such procedures are
integrated into the base modes of operations, so every internal re-
keying mechanism is defined for the particular operation mode and the
block size of the used cipher. Internal re-keying is recommended for
protocols that process long messages: the size of each single message
can be substantially increased without loss in number of messages
that can be securely processed with a single initial key.
Internal re-keying has the following advantages:
1. it increases the lifetime of an initial key by increasing the
size of the messages processed with one initial key;
2. it has minimal impact on performance;
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3. internal re-keying mechanisms without a master key does not
affect short messages transformation at all;
4. it is transparent (works like any mode of operation): does not
require changes of IV's and restarting MACing.
However, the use of internal re-keying has the following
disadvantages:
1. a specific method must not be chosen independently of a mode of
operation;
2. internal re-keying mechanisms without a master key do not provide
backward security of data processing keys.
Any block cipher modes of operations with internal re-keying can be
jointly used with any external re-keying mechanisms. Such joint
usage increases both the number of messages processed with one
initial key and their maximum possible size.
If the adversary has access to the data processing interface the use
of the same cryptographic primitives both for data processing and re-
keying transformation decreases the code size but can lead to some
possible vulnerabilities (the possibility of mounting a chosen-
plaintext attack may lead to the compromise of the following keys).
This vulnerability can be eliminated by using different primitives
for data processing and re-keying, e.g., block cipher for data
processing and hash for re-keying (see Section 5.2.2 and
Section 5.3.2). However, in this case the security of the whole
scheme cannot be reduced to standard notions like PRF or PRP, so
security estimations become more difficult and unclear.
Summing up the above-mentioned issues briefly:
1. If a protocol assumes processing long records (e.g., [CMS]),
internal re-keying should be used. If a protocol assumes
processing a significant amount of ordered records, which can be
considered as a single data stream (e.g., [TLS], [SSH]), internal
re-keying may also be used.
2. For protocols which allow out-of-order delivery and lost records
(e.g., [DTLS], [ESP]) external re-keying should be used as in
this case records cannot be considered as a single data stream.
If at the same time records are long enough, internal re-keying
should be additionally used during each separate message
processing.
For external re-keying:
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1. If it is desirable to separate transformations used for data
processing and for key update, hash function based re-keying
should be used.
2. If parallel data processing is required, then parallel external
re-keying should be used.
3. In case of restrictive key lifetime limitations external tree-
based re-keying should be used.
For internal re-keying:
1. If the property of forward and backward security is desirable for
data processing keys and if additional key material can be easily
obtained for the data processing stage, internal re-keying with a
master key should be used.
5. External Re-keying Mechanisms
This section presents an approach to increase the initial key
lifetime by using a transformation of a data processing key (frame
key) after processing a limited number of entire messages (frame).
It provides external parallel and serial re-keying mechanisms (see
[AbBell]). These mechanisms use initial key K only for frame keys
generation and never use it directly for data processing. Such
mechanisms operate outside of the base modes of operations and do not
change them at all, therefore they are called "external re-keying"
mechanisms in this document.
External re-keying mechanisms are recommended for usage in protocols
that process quite small messages, since the maximum gain in
increasing the initial key lifetime is achieved by increasing the
number of messages.
External re-keying increases the initial key lifetime through the
following approach. Suppose there is a protocol P with some mode of
operation (base encryption or authentication mode). Let L1 be a key
lifetime limitation induced by side-channel analysis methods (side-
channel limitation), let L2 be a key lifetime limitation induced by
methods based on the combinatorial properties of a used mode of
operation (combinatorial limitation) and let q1, q2 be the total
numbers of messages of length m, that can be safely processed with an
initial key K according to these limitations.
Let L = min(L1, L2), q = min (q1, q2), q * m <= L. As L1 limitation
is usually much stronger than L2 limitation (L1 < L2), the final key
lifetime restriction is equal to the most restrictive limitation L1.
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Thus, as displayed in Figure 2, without re-keying only q1 (q1 * m <=
L1) messages can be safely processed.
<--------m------->
+----------------+ ^ ^
|================| | |
|================| | |
K-->|================| q1|
|================| | |
|==============L1| | |
+----------------+ v |
| | |
| | |
| | q2
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| L2| |
+----------------+ v
Figure 2: Basic principles of message processing without
external re-keying
Suppose that the safety margin for the protocol P is fixed and the
external re-keying approach is applied to the initial key K to
generate the sequence of frame keys. The frame keys are generated in
such a way that the leakage of a previous frame key does not have any
impact on the following one, so the side channel limitation L1 goes
off. Thus, the resulting key lifetime limitation of the initial key
K can be calculated on the basis of a new combinatorial limitation
L2'. It is proven (see [AbBell]) that the security of the mode of
operation that uses external re-keying leads to an increase when
compared to base mode without re-keying (thus, L2 < L2'). Hence, as
displayed in Figure 3, the resulting key lifetime limitation in case
of using external re-keying can be increased up to L2'.
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<--------m------->
K +----------------+
| |================|
v |================|
K^1--> |================|
| |================|
| |==============L1|
| +----------------+
| |================|
v |================|
K^2--> |================|
| |================|
| |==============L1|
| +----------------+
| |================|
v |================|
... | . . . |
| |
| |
| L2|
+----------------+
| |
... ...
| L2'|
+----------------+
Figure 3: Basic principles of message processing
with external re-keying
Note: the key transformation process is depicted in a simplified
form. A specific approach (parallel and serial) is described below.
Consider an example. Let the message size in a protocol P be equal
to 1 KB. Suppose L1 = 128 MB and L2 = 1 TB. Thus, if an external
re-keying mechanism is not used, the initial key K must be
renegotiated after processing 128 MB / 1 KB = 131072 messages.
If an external re-keying mechanism is used, the key lifetime
limitation L1 goes off. Hence the resulting key lifetime limitation
L2' can be set to more then 1 TB. Thus if an external re-keying
mechanism is used, more then 1 TB / 1 KB = 2^30 messages can be
processed before the initial key K is renegotiated. This is 8192
times greater than the number of messages that can be processed, when
external re-keying mechanism is not used.
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5.1. Methods of Key Lifetime Control
Suppose L is an amount of data that can be safely processed with one
frame key. For i in {1, 2, ... , t} the frame key K^i (see Figure 4
and Figure 6) should be transformed after processing q_i messages,
where q_i can be calculated in accordance with one of the following
approaches:
Explicit approach:
q_i is such that |M^{i,1}| + ... + |M^{i,q_i}| <= L, |M^{i,1}| +
... + |M^{i,q_i+1}| > L.
This approach allows to use the frame key K^i in almost optimal
way but it can be applied only in case when messages cannot be
lost or reordered (e.g., TLS records).
Implicit approach:
q_i = L / m_max, i = 1, ... , t.
The amount of data processed with one frame key K^i is calculated
under the assumption that every message has the maximum length
m_max. Hence this amount can be considerably less than the key
lifetime limitation L. On the other hand, this approach can be
applied in case when messages may be lost or reordered (e.g., DTLS
records).
Dynamic key changes:
We can organize the key change using the Protected Point to Point
([P3]) solution by building a protected tunnel between the
endpoints in which the information about frame key updating can be
safely passed across. This can be useful, for example, when we
wish the adversary not to detect the key change during the
protocol evaluation.
5.2. Parallel Constructions
External parallel re-keying mechanisms generate frame keys K^1, K^2,
... directly from the initial key K independently of each other.
The main idea behind external re-keying with a parallel construction
is presented in Figure 4:
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Maximum message size = m_max.
_____________________________________________________________
m_max
<---------------->
M^{1,1} |=== |
M^{1,2} |=============== |
+->K^1--> ... ...
| M^{1,q_1} |======== |
|
|
| M^{2,1} |================|
| M^{2,2} |===== |
K-----|->K^2--> ... ...
| M^{2,q_2} |========== |
|
...
| M^{t,1} |============ |
| M^{t,2} |============= |
+->K^t--> ... ...
M^{t,q_t} |========== |
_____________________________________________________________
Figure 4: External parallel re-keying mechanisms
The frame key K^i, i = 1, ... , t-1, is updated after processing a
certain amount of messages (see Section 5.1).
5.2.1. Parallel Construction Based on a KDF on a Block Cipher
ExtParallelC re-keying mechanism is based on the key derivation
function on a block cipher and is used to generate t frame keys as
follows:
K^1 | K^2 | ... | K^t = ExtParallelC(K, t * k) = MSB_{t *
k}(E_{K}(Vec_n(0)) |
E_{K}(Vec_n(1)) | ... | E_{K}(Vec_n(R - 1))),
where R = ceil(t * k/n).
5.2.2. Parallel Construction Based on a KDF on a Hash Function
ExtParallelH re-keying mechanism is based on the key derivation
function HKDF-Expand, described in [RFC5869], and is used to generate
t frame keys as follows:
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K^1 | K^2 | ... | K^t = ExtParallelH(K, t * k) = HKDF-Expand(K,
label, t * k),
where label is a string (may be a zero-length string) that is defined
by a specific protocol.
5.2.3. Tree-based Construction
The application of external tree-based mechanism leads to the
construction of the key tree with the initial key K (root key) at the
0-level and the frame keys K^1, K^2, ... at the last level as
described in Figure 5.
K_root = K
___________|___________
| ... |
V V
K{1,1} K{1,W1}
______|______ ______|______
| ... | | ... |
V V V V
K{2,1} K{2,W2} K{2,(W1-1)*W2+1} K{2,W1*W2}
__|__ __|__ __|__ __|__
| ... | | ... | | ... | | ... |
V V V V V V V V
K{3,1} ... ... ... ... ... ... K{3,W1*W2*W3}
... ...
__|__ ... __|__
| ... | | ... |
V V V V
K{h,1} K{h,Wh} K{h,(W1*...*W{h-1}-1)*Wh+1} K{h,W1*...*Wh}
// \\ // \\
K^1 K^{Wh} K^{(W1*...*W{h-1}-1)*Wh+1} K^{W1*...*Wh}
____________________________________________________________________
Figure 5: External Tree-based Mechanism
The tree height h and the number of keys Wj, j in {1, ... , h}, which
can be partitioned from "parent" key, are defined in accordance with
a specific protocol and key lifetime limitations for the used
derivation functions.
Each j-level key K{j,w}, where j in {1, ... , h}, w in {1, ... , W1 *
... * Wj}, is derived from the (j-1)-level "parent" key K{j-1,ceil(w/
Wi)} (and other appropriate input data) using the j-th level
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derivation function that can be based on the block cipher function or
on the hash function and that is defined in accordance with a
specific protocol.
The i-th frame K^i, i in {1, 2, ... , W1*...*Wh}, can be calculated
as follows:
K^i = ExtKeyTree(K, i) = KDF_h(KDF_{h-1}(... KDF_1(K, ceil(i / (W2
* ... * Wh)) ... , ceil(i / Wh)), i),
where KDF_j is the j-th level derivation function that takes two
arguments (the parent key value and the integer in range from 1 to W1
* ... * Wj) and outputs the j-th level key value.
The frame key K^i is updated after processing a certain amount of
messages (see Section 5.1).
In order to create an efficient implementation, during frame key K^i
generation the derivation functions KDF_j, j in {1, ... , h-1},
should be used only in case when ceil(i / (W{j+1} * ... * Wh)) !=
ceil((i - 1) / (W{j+1} * ... * Wh)); otherwise it is necessary to use
previously generated value. This approach also makes it possible to
take countermeasures against side channels attacks.
Consider an example. Suppose h = 3, W1 = W2 = W3 = W and KDF_1,
KDF_2, KDF_3 are key derivation functions based on the
KDF_GOSTR3411_2012_256 (hereafter simply KDF) function described in
[RFC7836]. The resulting ExtKeyTree function can be defined as
follows:
ExtKeyTree(K, i) = KDF(KDF(KDF(K, "level1", ceil(i / W^2)),
"level2", ceil(i / W)), "level3", i).
where i in {1, 2, ... , W^3}.
The structure similar to external tree-based mechanism can be found
in Section 6 of [NISTSP800-108].
5.3. Serial Constructions
External serial re-keying mechanisms generate frame keys, each of
which depends on the secret state (K*_1, K*_2, ..., see Figure 6)
that is updated after the generation of each new frame key. Similar
approaches are used in the [SIGNAL] protocol, in the [TLS] updating
traffic keys mechanism and were proposed for use in the [U2F]
protocol.
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External serial re-keying mechanisms have the obvious disadvantage of
the impossibility to be implemented in parallel, but they can be
preferred if additional forward secrecy is desirable: in case all
keys are securely deleted after usage, compromise of a current secret
state at some time does not lead to a compromise of all previous
secret states and frame keys. In terms of [TLS], compromise of
application_traffic_secret_N does not compromise all previous
application_traffic_secret_i, i < N.
The main idea behind external re-keying with a serial construction is
presented in Figure 6:
Maximum message size = m_max.
_____________________________________________________________
m_max
<---------------->
M^{1,1} |=== |
M^{1,2} |=============== |
K*_1 = K --->K^1--> ... ...
| M^{1,q_1} |======== |
|
|
| M^{2,1} |================|
v M^{2,2} |===== |
K*_2 ------->K^2--> ... ...
| M^{2,q_2} |========== |
|
...
| M^{t,1} |============ |
v M^{t,2} |============= |
K*_t ------->K^t--> ... ...
M^{t,q_t} |========== |
_____________________________________________________________
Figure 6: External serial re-keying mechanisms
The frame key K^i, i = 1, ... , t - 1, is updated after processing a
certain amount of messages (see Section 5.1).
5.3.1. Serial Construction Based on a KDF on a Block Cipher
The frame key K^i is calculated using ExtSerialC transformation as
follows:
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K^i = ExtSerialC(K, i) =
MSB_k(E_{K*_i}(Vec_n(0)) |E_{K*_i}(Vec_n(1)) | ... |
E_{K*_i}(Vec_n(J - 1))),
where J = ceil(k / n), i = 1, ... , t, K*_i is calculated as follows:
K*_1 = K,
K*_{j+1} = MSB_k(E_{K*_j}(Vec_n(J)) | E_{K*_j}(Vec_n(J + 1)) |
... |
E_{K*_j}(Vec_n(2 * J - 1))),
where j = 1, ... , t - 1.
5.3.2. Serial Construction Based on a KDF on a Hash Function
The frame key K^i is calculated using ExtSerialH transformation as
follows:
K^i = ExtSerialH(K, i) = HKDF-Expand(K*_i, label1, k),
where i = 1, ... , t, HKDF-Expand is the HMAC-based key derivation
function, described in [RFC5869], K*_i is calculated as follows:
K*_1 = K,
K*_{j+1} = HKDF-Expand(K*_j, label2, k), where j = 1, ... , t - 1,
where label1 and label2 are different strings from V* that are
defined by a specific protocol (see, for example, TLS 1.3 updating
traffic keys algorithm [TLS]).
5.4. Using Additional Entropy during Re-keying
In many cases using additional entropy during re-keying won't
increase security, but may give a false sense of that, therefore one
can rely on additional entropy only after conducting a deep security
analysis. For example, good PRF constructions do not require
additional entropy for the quality of keys, so in most cases there is
no need for using additional entropy with external re-keying
mechanisms based on secure KDFs. However, in some situations mixed-
in entropy can still increase security in the case of a time-limited
but complete breach of the system, when an adversary can access the
frame keys generation interface, but cannot reveal master keys (e.g.,
when master keys are stored in an HSM).
For example, an external parallel construction based on a KDF on a
Hash function with a mixed-in entropy can be described as follows:
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K^i = HKDF-Expand(K, label_i, k),
where label_i is additional entropy that must be sent to the
recipient (e.g., be sent jointly with encrypted message). The
entropy label_i and the corresponding key K^i must be generated
directly before message processing.
6. Internal Re-keying Mechanisms
This section presents an approach to increase the key lifetime by
using a transformation of a data processing key (section key) during
each separate message processing. Each message is processed starting
with the same key (the first section key) and each section key is
updated after processing N bits of message (section).
This section provides internal re-keying mechanisms called ACPKM
(Advanced Cryptographic Prolongation of Key Material) and ACPKM-
Master that do not use a master key and use a master key
respectively. Such mechanisms are integrated into the base modes of
operation and actually form new modes of operation, therefore they
are called "internal re-keying" mechanisms in this document.
Internal re-keying mechanisms are recommended to be used in protocols
that process large single messages (e.g., CMS messages), since the
maximum gain in increasing the key lifetime is achieved by increasing
the length of a message, while it provides almost no increase in the
number of messages that can be processed with one initial key.
Internal re-keying increases the key lifetime through the following
approach. Suppose protocol P uses some base mode of operation. Let
L1 and L2 be a side channel and combinatorial limitations
respectively and for some fixed amount of messages q let m1, m2 be
the lengths of messages, that can be safely processed with a single
initial key K according to these limitations.
Thus, by analogy with the Section 5 without re-keying the final key
lifetime restriction, as displayed in Figure 7, is equal to L1 and
only q messages of the length m1 can be safely processed.
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K
|
v
^ +----------------+------------------------------------+
| |==============L1| L2|
| |================| |
q |================| |
| |================| |
| |================| |
v +----------------+------------------------------------+
<-------m1------->
<----------------------------m2----------------------->
Figure 7: Basic principles of message processing
without internal re-keying
Suppose that the safety margin for the protocol P is fixed and
internal re-keying approach is applied to the base mode of operation.
Suppose further that every message is processed with a section key,
which is transformed after processing N bits of data, where N is a
parameter. If q * N does not exceed L1 then the side channel
limitation L1 goes off and the resulting key lifetime limitation of
the initial key K can be calculated on the basis of a new
combinatorial limitation L2'. The security of the mode of operation
that uses internal re-keying increases when compared to base mode of
operation without re-keying (thus, L2 < L2'). Hence, as displayed in
Figure 8, the resulting key lifetime limitation in case of using
internal re-keying can be increased up to L2'.
K-----> K^1-------------> K^2 -----------> . . .
| |
v v
^ +---------------+---------------+------------------+--...--+
| |=============L1|=============L1|====== L2| L2'|
| |===============|===============|====== | |
q |===============|===============|====== . . . | |
| |===============|===============|====== | |
| |===============|===============|====== | |
v +---------------+---------------+------------------+--...--+
<-------N------->
Figure 8: Basic principles of message processing
with internal re-keying
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Note: the key transformation process is depicted in a simplified
form. A specific approach (ACPKM and ACPKM-Master re-keying
mechanisms) is described below.
Since the performance of encryption can slightly decrease for rather
small values of N, the parameter N should be selected for a
particular protocol as maximum possible to provide necessary key
lifetime for the considered security models.
Consider an example. Suppose L1 = 128 MB and L2 = 10 TB. Let the
message size in the protocol be large/unlimited (may exhaust the
whole key lifetime L2). The most restrictive resulting key lifetime
limitation is equal to 128 MB.
Thus, there is a need to put a limit on the maximum message size
m_max. For example, if m_max = 32 MB, it may happen that the
renegotiation of initial key K would be required after processing
only four messages.
If an internal re-keying mechanism with section size N = 1 MB is
used, more than L1 / N = 128 MB / 1 MB = 128 messages can be
processed before the renegotiation of initial key K (instead of 4
messages in case when an internal re-keying mechanism is not used).
Note that only one section of each message is processed with the
section key K^i, and, consequently, the key lifetime limitation L1
goes off. Hence the resulting key lifetime limitation L2' can be set
to more then 10 TB (in the case when a single large message is
processed using the initial key K).
6.1. Methods of Key Lifetime Control
Suppose L is an amount of data that can be safely processed with one
section key, N is a section size (fixed parameter). Suppose M^{i}_1
is the first section of message M^{i}, i = 1, ... , q (see Figure 9
and Figure 10), then the parameter q can be calculated in accordance
with one of the following two approaches:
o Explicit approach:
q_i is such that |M^{1}_1| + ... + |M^{q}_1| <= L, |M^{1}_1| + ...
+ |M^{q+1}_1| > L
This approach allows to use the section key K^i in an almost
optimal way but it can be applied only in case when messages
cannot be lost or reordered (e.g., TLS records).
o Implicit approach:
q = L / N.
The amount of data processed with one section key K^i is
calculated under the assumption that the length of every message
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is equal or greater than section size N and so it can be
considerably less than the key lifetime limitation L. On the
other hand, this approach can be applied in case when messages may
be lost or reordered (e.g., DTLS records).
6.2. Constructions that Do Not Require Master Key
This section describes the block cipher modes that use the ACPKM re-
keying mechanism, which does not use a master key: an initial key is
used directly for the data encryption.
6.2.1. ACPKM Re-keying Mechanisms
This section defines periodical key transformation without a master
key, which is called ACPKM re-keying mechanism. This mechanism can
be applied to one of the base encryption modes (CTR and GCM block
cipher modes) for getting an extension of this encryption mode that
uses periodical key transformation without a master key. This
extension can be considered as a new encryption mode.
An additional parameter that defines functioning of base encryption
modes with the ACPKM re-keying mechanism is the section size N. The
value of N is measured in bits and is fixed within a specific
protocol based on the requirements of the system capacity and the key
lifetime. The section size N MUST be divisible by the block size n.
The main idea behind internal re-keying without a master key is
presented in Figure 9:
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Section size = const = N,
maximum message size = m_max.
____________________________________________________________________
ACPKM ACPKM ACPKM
K^1 = K ---> K^2 ---...-> K^{l_max-1} ----> K^{l_max}
| | | |
| | | |
v v v v
M^{1} |==========|==========| ... |==========|=======: |
M^{2} |==========|==========| ... |=== | : |
. . . . . . :
: : : : : : :
M^{q} |==========|==========| ... |==========|===== : |
section :
<----------> m_max
N bit
___________________________________________________________________
l_max = ceil(m_max/N).
Figure 9: Internal re-keying without a master key
During the processing of the input message M with the length m in
some encryption mode that uses ACPKM key transformation of the
initial key K the message is divided into l = ceil(m / N) sections
(denoted as M = M_1 | M_2 | ... | M_l, where M_i is in V_N for i in
{1, 2, ... , l - 1} and M_l is in V_r, r <= N). The first section of
each message is processed with the section key K^1 = K. To process
the (i + 1)-th section of each message the section key K^{i+1} is
calculated using ACPKM transformation as follows:
K^{i+1} = ACPKM(K^i) = MSB_k(E_{K^i}(D_1) | ... | E_{K^i}(D_J)),
where J = ceil(k/n) and D_1, D_2, ... , D_J are in V_n and are
calculated as follows:
D_1 | D_2 | ... | D_J = MSB_{J * n}(D),
where D is the following constant in V_{1024}:
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D = ( 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87
| 88 | 89 | 8a | 8b | 8c | 8d | 8e | 8f
| 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97
| 98 | 99 | 9a | 9b | 9c | 9d | 9e | 9f
| a0 | a1 | a2 | a3 | a4 | a5 | a6 | a7
| a8 | a9 | aa | ab | ac | ad | ae | af
| b0 | b1 | b2 | b3 | b4 | b5 | b6 | b7
| b8 | b9 | ba | bb | bc | bd | be | bf
| c0 | c1 | c2 | c3 | c4 | c5 | c6 | c7
| c8 | c9 | ca | cb | cc | cd | ce | cf
| d0 | d1 | d2 | d3 | d4 | d5 | d6 | d7
| d8 | d9 | da | db | dc | dd | de | df
| e0 | e1 | e2 | e3 | e4 | e5 | e6 | e7
| e8 | e9 | ea | eb | ec | ed | ee | ef
| f0 | f1 | f2 | f3 | f4 | f5 | f6 | f7
| f8 | f9 | fa | fb | fc | fd | fe | ff)
N o t e : The constant D is such that D_1, ... , D_J are pairwise
different for any allowed n and k values.
N o t e : The highest bit of each octet of the constant D is equal to
1. This condition is important, as in conjunction with a certain
mode message length limitation it allows to prevent collisions of
block cipher permutation inputs in cases of key transformation and
message processing (for more details see Section 4.4 of [AAOS2017]).
6.2.2. CTR-ACPKM Encryption Mode
This section defines a CTR-ACPKM encryption mode that uses the ACPKM
internal re-keying mechanism for the periodical key transformation.
The CTR-ACPKM mode can be considered as the base encryption mode CTR
(see [MODES]) extended by the ACPKM re-keying mechanism.
The CTR-ACPKM encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512;
o the number c of bits in a specific part of the block to be
incremented is such that 32 <= c <= 3 / 4 n, c is a multiple of 8;
o the maximum message size m_max = n * 2^{c-1}.
The CTR-ACPKM mode encryption and decryption procedures are defined
as follows:
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+----------------------------------------------------------------+
| CTR-ACPKM-Encrypt(N, K, ICN, P) |
|----------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - initial counter nonce ICN in V_{n-c}, |
| - plaintext P = P_1 | ... | P_b, |P| <= m_max. |
| Output: |
| - ciphertext C. |
|----------------------------------------------------------------|
| 1. CTR_1 = ICN | 0^c |
| 2. For j = 2, 3, ... , b do |
| CTR_{j} = Inc_c(CTR_{j-1}) |
| 3. K^1 = K |
| 4. For i = 2, 3, ... , ceil(|P| / N) |
| K^i = ACPKM(K^{i-1}) |
| 5. For j = 1, 2, ... , b do |
| i = ceil(j * n / N), |
| G_j = E_{K^i}(CTR_j) |
| 6. C = P (xor) MSB_{|P|}(G_1 | ... | G_b) |
| 7. Return C |
+----------------------------------------------------------------+
+----------------------------------------------------------------+
| CTR-ACPKM-Decrypt(N, K, ICN, C) |
|----------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - initial counter nonce ICN in V_{n-c}, |
| - ciphertext C = C_1 | ... | C_b, |C| <= m_max. |
| Output: |
| - plaintext P. |
|----------------------------------------------------------------|
| 1. P = CTR-ACPKM-Encrypt(N, K, ICN, C) |
| 2. Return P |
+----------------------------------------------------------------+
The initial counter nonce ICN value for each message that is
encrypted under the given initial key K must be chosen in a unique
manner.
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6.2.3. GCM-ACPKM Authenticated Encryption Mode
This section defines GCM-ACPKM authenticated encryption mode that
uses the ACPKM internal re-keying mechanism for the periodical key
transformation.
The GCM-ACPKM mode can be considered as the base authenticated
encryption mode GCM (see [GCM]) extended by the ACPKM re-keying
mechanism.
The GCM-ACPKM authenticated encryption mode can be used with the
following parameters:
o n in {128, 256};
o 128 <= k <= 512;
o the number c of bits in a specific part of the block to be
incremented is such that 1 / 4 n <= c <= 1 / 2 n, c is a multiple
of 8;
o authentication tag length t;
o the maximum message size m_max = min{n * (2^{c-1} - 2), 2^{n/2} -
1}.
The GCM-ACPKM mode encryption and decryption procedures are defined
as follows:
+-------------------------------------------------------------------+
| GHASH(X, H) |
|-------------------------------------------------------------------|
| Input: |
| - bit string X = X_1 | ... | X_m, X_1, ... , X_m in V_n. |
| Output: |
| - block GHASH(X, H) in V_n. |
|-------------------------------------------------------------------|
| 1. Y_0 = 0^n |
| 2. For i = 1, ... , m do |
| Y_i = (Y_{i-1} (xor) X_i) * H |
| 3. Return Y_m |
+-------------------------------------------------------------------+
+-------------------------------------------------------------------+
| GCTR(N, K, ICB, X) |
|-------------------------------------------------------------------|
| Input: |
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| - section size N, |
| - initial key K, |
| - initial counter block ICB, |
| - X = X_1 | ... | X_b. |
| Output: |
| - Y in V_{|X|}. |
|-------------------------------------------------------------------|
| 1. If X in V_0 then return Y, where Y in V_0 |
| 2. GCTR_1 = ICB |
| 3. For i = 2, ... , b do |
| GCTR_i = Inc_c(GCTR_{i-1}) |
| 4. K^1 = K |
| 5. For j = 2, ... , ceil(|X| / N) |
| K^j = ACPKM(K^{j-1}) |
| 6. For i = 1, ... , b do |
| j = ceil(i * n / N), |
| G_i = E_{K_j}(GCTR_i) |
| 7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b) |
| 8. Return Y |
+-------------------------------------------------------------------+
+-------------------------------------------------------------------+
| GCM-ACPKM-Encrypt(N, K, ICN, P, A) |
|-------------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - initial counter nonce ICN in V_{n-c}, |
| - plaintext P = P_1 | ... | P_b, |P| <= m_max, |
| - additional authenticated data A. |
| Output: |
| - ciphertext C, |
| - authentication tag T. |
|-------------------------------------------------------------------|
| 1. H = E_{K}(0^n) |
| 2. ICB_0 = ICN | 0^{c-1} | 1 |
| 3. C = GCTR(N, K, Inc_c(ICB_0), P) |
| 4. u = n * ceil(|C| / n) - |C| |
| v = n * ceil(|A| / n) - |A| |
| 5. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | |
| | Vec_{n/2}(|C|), H) |
| 6. T = MSB_t(E_{K}(ICB_0) (xor) S) |
| 7. Return C | T |
+-------------------------------------------------------------------+
+-------------------------------------------------------------------+
| GCM-ACPKM-Decrypt(N, K, ICN, A, C, T) |
|-------------------------------------------------------------------|
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| Input: |
| - section size N, |
| - initial key K, |
| - initial counter block ICN, |
| - additional authenticated data A, |
| - ciphertext C = C_1 | ... | C_b, |C| <= m_max, |
| - authentication tag T. |
| Output: |
| - plaintext P or FAIL. |
|-------------------------------------------------------------------|
| 1. H = E_{K}(0^n) |
| 2. ICB_0 = ICN | 0^{c-1} | 1 |
| 3. P = GCTR(N, K, Inc_c(ICB_0), C) |
| 4. u = n * ceil(|C| / n) - |C| |
| v = n * ceil(|A| / n) - |A| |
| 5. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | |
| | Vec_{n/2}(|C|), H) |
| 6. T' = MSB_t(E_{K}(ICB_0) (xor) S) |
| 7. If T = T' then return P; else return FAIL |
+-------------------------------------------------------------------+
The * operation on (pairs of) the 2^n possible blocks corresponds to
the multiplication operation for the binary Galois (finite) field of
2^n elements defined by the polynomial f as follows (by analogy with
[GCM]):
n = 128: f = a^128 + a^7 + a^2 + a^1 + 1,
n = 256: f = a^256 + a^10 + a^5 + a^2 + 1.
The initial counter nonce ICN value for each message that is
encrypted under the given initial key K must be chosen in a unique
manner.
The key for computing values E_{K}(ICB_0) and H is not updated and is
equal to the initial key K.
6.3. Constructions that Require Master Key
This section describes the block cipher modes that use the ACPKM-
Master re-keying mechanism, which use the initial key K as a master
key, so K is never used directly for data processing but is used for
key derivation.
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6.3.1. ACPKM-Master Key Derivation from the Master Key
This section defines periodical key transformation with a master key,
which is called ACPKM-Master re-keying mechanism. This mechanism can
be applied to one of the base modes of operation (CTR, GCM, CBC, CFB,
OMAC modes) for getting an extension that uses periodical key
transformation with a master key. This extension can be considered
as a new mode of operation.
Additional parameters that define the functioning of modes of
operation that use the ACPKM-Master re-keying mechanism are the
section size N, the change frequency T* of the master keys K*_1,
K*_2, ... (see Figure 10) and the size d of the section key material.
The values of N and T* are measured in bits and are fixed within a
specific protocol, based on the requirements of the system capacity
and the key lifetime. The section size N MUST be divisible by the
block size n. The master key frequency T* MUST be divisible by d and
by n.
The main idea behind internal re-keying with a master key is
presented in Figure 10:
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Master key frequency T*,
section size N,
maximum message size = m_max.
_____________________________________________________________________
ACPKM ACPKM
K*_1 = K----------> K*_2 ---------...-----> K*_l_max
___|___ ___|___ ___|___
| | | | | |
v ... v v ... v v ... v
K[1] K[t] K[t+1] K[2*t] K[(l_max-1)t+1] K[l_max*t]
| | | | | |
| | | | | |
v v v v v v
M^{1}||======|...|======||======|...|======||...||======|...|== : ||
M^{2}||======|...|======||======|...|======||...||======|...|====: ||
... || | | || | | || || | | : ||
M^{q}||======|...|======||==== |...| ||...|| |...| : ||
section :
<------> :
N bit m_max
_____________________________________________________________________
|K[i]| = d,
t = T* / d,
l_max = ceil(m_max / (N * t)).
Figure 10: Internal re-keying with a master key
During the processing of the input message M with the length m in
some mode of operation that uses ACPKM-Master key transformation with
the initial key K and the master key frequency T* the message M is
divided into l = ceil(m / N) sections (denoted as M = M_1 | M_2 |
... | M_l, where M_i is in V_N for i in {1, 2, ... , l - 1} and M_l
is in V_r, r <= N). The j-th section of each message is processed
with the key material K[j], j in {1, ... , l}, |K[j]| = d, that is
calculated with the ACPKM-Master algorithm as follows:
K[1] | ... | K[l] = ACPKM-Master(T*, K, d, l) = CTR-ACPKM-Encrypt
(T*, K, 1^{n/2}, 0^{d*l}).
Note: the parameters d and l MUST be such that d * l <= n *
2^{n/2-1}.
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6.3.2. CTR-ACPKM-Master Encryption Mode
This section defines a CTR-ACPKM-Master encryption mode that uses the
ACPKM-Master internal re-keying mechanism for the periodical key
transformation.
The CTR-ACPKM-Master encryption mode can be considered as the base
encryption mode CTR (see [MODES]) extended by the ACPKM-Master re-
keying mechanism.
The CTR-ACPKM-Master encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512;
o the number c of bits in a specific part of the block to be
incremented is such that 32 <= c <= 3 / 4 n, c is a multiple of 8;
o the maximum message size m_max = min{N * (n * 2^{n/2-1} / k), n *
2^c}.
The key material K[j] that is used for one section processing is
equal to K^j, |K^j| = k bits.
The CTR-ACPKM-Master mode encryption and decryption procedures are
defined as follows:
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+----------------------------------------------------------------+
| CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, P) |
|----------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initial counter nonce ICN in V_{n-c}, |
| - plaintext P = P_1 | ... | P_b, |P| <= m_max. |
| Output: |
| - ciphertext C. |
|----------------------------------------------------------------|
| 1. CTR_1 = ICN | 0^c |
| 2. For j = 2, 3, ... , b do |
| CTR_{j} = Inc_c(CTR_{j-1}) |
| 3. l = ceil(|P| / N) |
| 4. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) |
| 5. For j = 1, 2, ... , b do |
| i = ceil(j * n / N), |
| G_j = E_{K^i}(CTR_j) |
| 6. C = P (xor) MSB_{|P|}(G_1 | ... |G_b) |
| 7. Return C |
|----------------------------------------------------------------+
+----------------------------------------------------------------+
| CTR-ACPKM-Master-Decrypt(N, K, T*, ICN, C) |
|----------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initial counter nonce ICN in V_{n-c}, |
| - ciphertext C = C_1 | ... | C_b, |C| <= m_max. |
| Output: |
| - plaintext P. |
|----------------------------------------------------------------|
| 1. P = CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, C) |
| 1. Return P |
+----------------------------------------------------------------+
The initial counter nonce ICN value for each message that is
encrypted under the given initial key must be chosen in a unique
manner.
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6.3.3. GCM-ACPKM-Master Authenticated Encryption Mode
This section defines a GCM-ACPKM-Master authenticated encryption mode
that uses the ACPKM-Master internal re-keying mechanism for the
periodical key transformation.
The GCM-ACPKM-Master authenticated encryption mode can be considered
as the base authenticated encryption mode GCM (see [GCM]) extended by
the ACPKM-Master re-keying mechanism.
The GCM-ACPKM-Master authenticated encryption mode can be used with
the following parameters:
o n in {128, 256};
o 128 <= k <= 512;
o the number c of bits in a specific part of the block to be
incremented is such that 1 / 4 n <= c <= 1 / 2 n, c is a multiple
of 8;
o authentication tag length t;
o the maximum message size m_max = min{N * ( n * 2^{n/2-1} / k), n *
(2^c - 2), 2^{n/2} - 1}.
The key material K[j] that is used for the j-th section processing is
equal to K^j, |K^j| = k bits.
The GCM-ACPKM-Master mode encryption and decryption procedures are
defined as follows:
+-------------------------------------------------------------------+
| GHASH(X, H) |
|-------------------------------------------------------------------|
| Input: |
| - bit string X = X_1 | ... | X_m, X_i in V_n for i in {1, ... ,m}|
| Output: |
| - block GHASH(X, H) in V_n |
|-------------------------------------------------------------------|
| 1. Y_0 = 0^n |
| 2. For i = 1, ... , m do |
| Y_i = (Y_{i-1} (xor) X_i) * H |
| 3. Return Y_m |
+-------------------------------------------------------------------+
+-------------------------------------------------------------------+
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| GCTR(N, K, T*, ICB, X) |
|-------------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initial counter block ICB, |
| - X = X_1 | ... | X_b. |
| Output: |
| - Y in V_{|X|}. |
|-------------------------------------------------------------------|
| 1. If X in V_0 then return Y, where Y in V_0 |
| 2. GCTR_1 = ICB |
| 3. For i = 2, ... , b do |
| GCTR_i = Inc_c(GCTR_{i-1}) |
| 4. l = ceil(|X| / N) |
| 5. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) |
| 6. For j = 1, ... , b do |
| i = ceil(j * n / N), |
| G_j = E_{K^i}(GCTR_j) |
| 7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b) |
| 8. Return Y |
+-------------------------------------------------------------------+
+-------------------------------------------------------------------+
| GCM-ACPKM-Master-Encrypt(N, K, T*, ICN, P, A) |
|-------------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initial counter nonce ICN in V_{n-c}, |
| - plaintext P = P_1 | ... | P_b, |P| <= m_max. |
| - additional authenticated data A. |
| Output: |
| - ciphertext C, |
| - authentication tag T. |
|-------------------------------------------------------------------|
| 1. K^1 = ACPKM-Master(T*, K, k, 1) |
| 2. H = E_{K^1}(0^n) |
| 3. ICB_0 = ICN | 0^{c-1} | 1 |
| 4. C = GCTR(N, K, T*, Inc_c(ICB_0), P) |
| 5. u = n * ceil(|C| / n) - |C| |
| v = n * ceil(|A| / n) - |A| |
| 6. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | |
| | Vec_{n/2}(|C|), H) |
| 7. T = MSB_t(E_{K^1}(ICB_0) (xor) S) |
| 8. Return C | T |
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+-------------------------------------------------------------------+
+-------------------------------------------------------------------+
| GCM-ACPKM-Master-Decrypt(N, K, T*, ICN, A, C, T) |
|-------------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initial counter nonce ICN in V_{n-c}, |
| - additional authenticated data A. |
| - ciphertext C = C_1 | ... | C_b, |C| <= m_max, |
| - authentication tag T. |
| Output: |
| - plaintext P or FAIL. |
|-------------------------------------------------------------------|
| 1. K^1 = ACPKM-Master(T*, K, k, 1) |
| 2. H = E_{K^1}(0^n) |
| 3. ICB_0 = ICN | 0^{c-1} | 1 |
| 4. P = GCTR(N, K, T*, Inc_c(ICB_0), C) |
| 5. u = n * ceil(|C| / n) - |C| |
| v = n * ceil(|A| / n) - |A| |
| 6. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | |
| | Vec_{n/2}(|C|), H) |
| 7. T' = MSB_t(E_{K^1}(ICB_0) (xor) S) |
| 8. IF T = T' then return P; else return FAIL. |
+-------------------------------------------------------------------+
The * operation on (pairs of) the 2^n possible blocks corresponds to
the multiplication operation for the binary Galois (finite) field of
2^n elements defined by the polynomial f as follows (by analogy with
[GCM]):
n = 128: f = a^128 + a^7 + a^2 + a^1 + 1,
n = 256: f = a^256 + a^10 + a^5 + a^2 + 1.
The initial counter nonce ICN value for each message that is
encrypted under the given initial key must be chosen in a unique
manner.
6.3.4. CBC-ACPKM-Master Encryption Mode
This section defines a CBC-ACPKM-Master encryption mode that uses the
ACPKM-Master internal re-keying mechanism for the periodical key
transformation.
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The CBC-ACPKM-Master encryption mode can be considered as the base
encryption mode CBC (see [MODES]) extended by the ACPKM-Master re-
keying mechanism.
The CBC-ACPKM-Master encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512;
o the maximum message size m_max = N * (n * 2^{n/2-1} / k).
In the specification of the CBC-ACPKM-Master mode the plaintext and
ciphertext must be a sequence of one or more complete data blocks.
If the data string to be encrypted does not initially satisfy this
property, then it MUST be padded to form complete data blocks. The
padding methods are out of the scope of this document. An example of
a padding method can be found in Appendix A of [MODES].
The key material K[j] that is used for the j-th section processing is
equal to K^j, |K^j| = k bits.
We will denote by D_{K} the decryption function which is a
permutation inverse to E_{K}.
The CBC-ACPKM-Master mode encryption and decryption procedures are
defined as follows:
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+----------------------------------------------------------------+
| CBC-ACPKM-Master-Encrypt(N, K, T*, IV, P) |
|----------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initialization vector IV in V_n, |
| - plaintext P = P_1 | ... | P_b, |P_b| = n, |P| <= m_max. |
| Output: |
| - ciphertext C. |
|----------------------------------------------------------------|
| 1. l = ceil(|P| / N) |
| 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) |
| 3. C_0 = IV |
| 4. For j = 1, 2, ... , b do |
| i = ceil(j * n / N), |
| C_j = E_{K^i}(P_j (xor) C_{j-1}) |
| 5. Return C = C_1 | ... | C_b |
|----------------------------------------------------------------+
+----------------------------------------------------------------+
| CBC-ACPKM-Master-Decrypt(N, K, T*, IV, C) |
|----------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initialization vector IV in V_n, |
| - ciphertext C = C_1 | ... | C_b, |C_b| = n, |C| <= m_max. |
| Output: |
| - plaintext P. |
|----------------------------------------------------------------|
| 1. l = ceil(|C| / N) |
| 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) |
| 3. C_0 = IV |
| 4. For j = 1, 2, ... , b do |
| i = ceil(j * n / N) |
| P_j = D_{K^i}(C_j) (xor) C_{j-1} |
| 5. Return P = P_1 | ... | P_b |
+----------------------------------------------------------------+
The initialization vector IV for any particular execution of the
encryption process must be unpredictable.
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6.3.5. CFB-ACPKM-Master Encryption Mode
This section defines a CFB-ACPKM-Master encryption mode that uses the
ACPKM-Master internal re-keying mechanism for the periodical key
transformation.
The CFB-ACPKM-Master encryption mode can be considered as the base
encryption mode CFB (see [MODES]) extended by the ACPKM-Master re-
keying mechanism.
The CFB-ACPKM-Master encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512;
o the maximum message size m_max = N * (n * 2^{n/2-1} / k).
The key material K[j] that is used for the j-th section processing is
equal to K^j, |K^j| = k bits.
The CFB-ACPKM-Master mode encryption and decryption procedures are
defined as follows:
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+-------------------------------------------------------------+
| CFB-ACPKM-Master-Encrypt(N, K, T*, IV, P) |
|-------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initialization vector IV in V_n, |
| - plaintext P = P_1 | ... | P_b, |P| <= m_max. |
| Output: |
| - ciphertext C. |
|-------------------------------------------------------------|
| 1. l = ceil(|P| / N) |
| 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) |
| 3. C_0 = IV |
| 4. For j = 1, 2, ... , b - 1 do |
| i = ceil(j * n / N), |
| C_j = E_{K^i}(C_{j-1}) (xor) P_j |
| 5. C_b = MSB_{|P_b|}(E_{K^l}(C_{b-1})) (xor) P_b |
| 6. Return C = C_1 | ... | C_b |
|-------------------------------------------------------------+
+-------------------------------------------------------------+
| CFB-ACPKM-Master-Decrypt(N, K, T*, IV, C) |
|-------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - initialization vector IV in V_n, |
| - ciphertext C = C_1 | ... | C_b, |C| <= m_max. |
| Output: |
| - plaintext P. |
|-------------------------------------------------------------|
| 1. l = ceil(|C| / N) |
| 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) |
| 3. C_0 = IV |
| 4. For j = 1, 2, ... , b - 1 do |
| i = ceil(j * n / N), |
| P_j = E_{K^i}(C_{j-1}) (xor) C_j |
| 5. P_b = MSB_{|C_b|}(E_{K^l}(C_{b-1})) (xor) C_b |
| 6. Return P = P_1 | ... | P_b |
+-------------------------------------------------------------+
The initialization vector IV for any particular execution of the
encryption process must be unpredictable.
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6.3.6. OMAC-ACPKM-Master Authentication Mode
This section defines an OMAC-ACPKM-Master message authentication code
calculation mode that uses the ACPKM-Master internal re-keying
mechanism for the periodical key transformation.
The OMAC-ACPKM-Master mode can be considered as the base message
authentication code calculation mode OMAC, which is also known as
CMAC (see [RFC4493]), extended by the ACPKM-Master re-keying
mechanism.
The OMAC-ACPKM-Master message authentication code calculation mode
can be used with the following parameters:
o n in {64, 128, 256};
o 128 <= k <= 512;
o the maximum message size m_max = N * (n * 2^{n/2-1} / (k + n)).
The key material K[j] that is used for one section processing is
equal to K^j | K^j_1, where |K^j| = k and |K^j_1| = n.
The following is a specification of the subkey generation process of
OMAC:
+-------------------------------------------------------------------+
| Generate_Subkey(K1, r) |
|-------------------------------------------------------------------|
| Input: |
| - key K1. |
| Output: |
| - key SK. |
|-------------------------------------------------------------------|
| 1. If r = n then return K1 |
| 2. If r < n then |
| if MSB_1(K1) = 0 |
| return K1 << 1 |
| else |
| return (K1 << 1) (xor) R_n |
| |
+-------------------------------------------------------------------+
Here R_n takes the following values:
o n = 64: R_{64} = 0^{59} | 11011;
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o n = 128: R_{128} = 0^{120} | 10000111;
o n = 256: R_{256} = 0^{145} | 10000100101.
The OMAC-ACPKM-Master message authentication code calculation mode is
defined as follows:
+-------------------------------------------------------------------+
| OMAC-ACPKM-Master(K, N, T*, M) |
|-------------------------------------------------------------------|
| Input: |
| - section size N, |
| - initial key K, |
| - master key frequency T*, |
| - plaintext M = M_1 | ... | M_b, |M| <= m_max. |
| Output: |
| - message authentication code T. |
|-------------------------------------------------------------------|
| 1. C_0 = 0^n |
| 2. l = ceil(|M| / N) |
| 3. K^1 | K^1_1 | ... | K^l | K^l_1 = |
= ACPKM-Master(T*, K, (k + n), l) |
| 4. For j = 1, 2, ... , b - 1 do |
| i = ceil(j * n / N), |
| C_j = E_{K^i}(M_j (xor) C_{j-1}) |
| 5. SK = Generate_Subkey(K^l_1, |M_b|) |
| 6. If |M_b| = n then M*_b = M_b |
| else M*_b = M_b | 1 | 0^{n - 1 -|M_b|} |
| 7. T = E_{K^l}(M*_b (xor) C_{b-1} (xor) SK) |
| 8. Return T |
+-------------------------------------------------------------------+
7. Joint Usage of External and Internal Re-keying
Both external re-keying and internal re-keying have their own
advantages and disadvantages discussed in Section 1. For instance,
using external re-keying can essentially limit the message length,
while in the case of internal re-keying the section size, which can
be chosen as the maximal possible for operational properties, limits
the amount of separate messages. Therefore, the choice of re-keying
mechanism (either external or internal) depends on particular
protocol features. However, some protocols may have features that
require to take advantages provided by both external and internal re-
keying mechanisms: for example, the protocol mainly transmits
messages of small length, but it must additionally support very long
messages processing. In such situations it is necessary to use
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external and internal re-keying jointly, since these techniques
negate each other's disadvantages.
For composition of external and internal re-keying techniques any
mechanism described in Section 5 can be used with any mechanism
described in Section 6.
For example, consider the GCM-ACPKM mode with external serial re-
keying based on a KDF on a Hash function. Denote by a frame size the
number of messages in each frame (in the case of implicit approach to
the key lifetime control) for external re-keying.
Let L be a key lifetime limitation. The section size N for internal
re-keying and the frame size q for external re-keying must be chosen
in such a way that q * N must not exceed L.
Suppose that t messages (ICN_i, P_i, A_i), with initial counter nonce
ICN_i, plaintext P_i and additional authenticated data A_i, will be
processed before renegotiation.
For authenticated encryption of each message (ICN_i, P_i, A_i), i =
1, ..., t, the following algorithm can be applied:
1. j = ceil(i / q),
2. K^j = ExtSerialH(K, j),
3. C_i | T_i = GCM-ACPKM-Encrypt(N, K^j, ICN_i, P_i, A_i).
Note that nonces ICN_i, that are used under the same frame key, must
be unique for each message.
8. Security Considerations
Re-keying should be used to increase "a priori" security properties
of ciphers in hostile environments (e.g., with side-channel
adversaries). If some efficient attacks are known for a cipher, it
must not be used. So re-keying cannot be used as a patch for
vulnerable ciphers. Base cipher properties must be well analyzed,
because the security of re-keying mechanisms is based on the security
of a block cipher as a pseudorandom function.
Re-keying is not intended to solve any post-quantum security issues
for symmetric cryptography, since the reduction of security caused by
Grover's algorithm is not connected with a size of plaintext
transformed by a cipher - only a negligible (sufficient for key
uniqueness) material is needed; and the aim of re-keying is to limit
a size of plaintext transformed under one initial key.
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Re-keying can provide backward security only if previous key material
is securely deleted after usage by all parties.
9. IANA Considerations
This document does not require any IANA actions.
10. References
10.1. Normative References
[CMS] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
RFC 5652, DOI 10.17487/RFC5652, September 2009,
<http://www.rfc-editor.org/info/rfc5652>.
[DTLS] Rescorla, E. and N. Modadugu, "Datagram Transport Layer
Security Version 1.2", RFC 6347, DOI 10.17487/RFC6347,
January 2012, <http://www.rfc-editor.org/info/rfc6347>.
[ESP] Kent, S., "IP Encapsulating Security Payload (ESP)",
RFC 4303, DOI 10.17487/RFC4303, December 2005,
<http://www.rfc-editor.org/info/rfc4303>.
[GCM] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Galois/Counter Mode (GCM) and GMAC", NIST
Special Publication 800-38D
http://nvlpubs.nist.gov/nistpubs/Legacy/SP/
nistspecialpublication800-38d.pdf, November 2007.
[MODES] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Methods and Techniques", NIST Special
Publication 800-38A, December 2001.
[NISTSP800-108]
National Institute of Standards and Technology,
"Recommendation for Key Derivation Using Pseudorandom
Functions", NIST Special Publication 800-108, November
2008, <http://nvlpubs.nist.gov/nistpubs/Legacy/SP/
nistspecialpublication800-108.pdf>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC4493] Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The
AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June
2006, <https://www.rfc-editor.org/info/rfc4493>.
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[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
<https://www.rfc-editor.org/info/rfc5869>.
[RFC7836] Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V.,
Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines
on the Cryptographic Algorithms to Accompany the Usage of
Standards GOST R 34.10-2012 and GOST R 34.11-2012",
RFC 7836, DOI 10.17487/RFC7836, March 2016,
<https://www.rfc-editor.org/info/rfc7836>.
[SSH] Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
January 2006, <http://www.rfc-editor.org/info/rfc4253>.
[TLS] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<http://www.rfc-editor.org/info/rfc8446>.
10.2. Informative References
[AAOS2017]
Ahmetzyanova, L., Alekseev, E., Oshkin, I., and S.
Smyshlyaev, "Increasing the Lifetime of Symmetric Keys for
the GCM Mode by Internal Re-keying", Cryptology ePrint
Archive Report 2017/697, 2017,
<https://eprint.iacr.org/2017/697.pdf>.
[AbBell] Michel Abdalla and Mihir Bellare, "Increasing the Lifetime
of a Key: A Comparative Analysis of the Security of Re-
keying Techniques", ASIACRYPT2000, LNCS 1976, pp. 546-559,
2000.
[AESDUKPT]
ANSI, "Retail Financial Services Symmetric Key Management
- Part 3: Derived Unique Key Per Transaction", ANSI
X9.24-3-2017, 2017.
[FKK2005] Fu, K., Kamara, S., and T. Kohno, "Key Regression:
Enabling Efficient Key Distribution for Secure Distributed
Storage", November 2005,
<https://homes.cs.washington.edu/~yoshi/papers/KR/
NDSS06.pdf>.
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[FPS2012] Faust, S., Pietrzak, K., and j. Schipper, "Practical
Leakage-Resilient Symmetric Cryptography", CHES2012 LNCS,
vol. 7428, pp. 213-232,, 2012,
<https://link.springer.com/content/
pdf/10.1007%2F978-3-642-33027-8_13.pdf>.
[FRESHREKEYING]
Dziembowski, S., Faust, S., Herold, G., Journault, A.,
Masny, D., and F. Standaert, "Towards Sound Fresh Re-
Keying with Hard (Physical) Learning Problems", Cryptology
ePrint Archive Report 2016/573, June 2016,
<https://eprint.iacr.org/2016/573>.
[GGM] Goldreich, O., Goldwasser, S., and S. Micali, "How to
Construct Random Functions", Journal of the Association
for Computing Machinery Vol.33, No.4, pp. 792-807, October
1986, <http://www.wisdom.weizmann.ac.il/~/oded/X/ggm.pdf>.
[KMNT2003]
Kim, Y., Maino, F., Narasimha, M., and G. Tsudik, "Secure
Group Services for Storage Area Networks",
IEEE Communication Magazine 41, pp. 92-99, 2003,
<http://www.ics.uci.edu/~gts/paps/kmnt02.pdf>.
[LDC] Howard M. Heys, "A Tutorial on Linear and Differential
Cryptanalysis", 2017,
<http://www.cs.bc.edu/~straubin/crypto2017/heys.pdf>.
[OWT] Joye, M. and S. Yen, "One-Way Cross-Trees and Their
Applications", DOI 10.1007/3-540-45664-3_25, February
2002, <https://link.springer.com/content/
pdf/10.1007%2F3-540-45664-3_25.pdf>.
[P3] Peter Alexander, "Dynamic Key Changes on Encrypted
Sessions", CFRG mail archive , December 2017,
<https://www.ietf.org/mail-archive/web/cfrg/current/
msg09401.html>.
[Pietrzak2009]
Pietrzak, K., "A Leakage-Resilient Mode of Operation",
EUROCRYPT2009 LNCS, vol. 5479, pp. 462-482,, 2009,
<https://iacr.org/archive/
eurocrypt2009/54790461/54790461.pdf>.
[SIGNAL] Perrin, T., Ed. and M. Marlinspike, "The Double Ratchet
Algorithm", November 2016,
<https://signal.org/docs/specifications/doubleratchet/
doubleratchet.pdf>.
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[Sweet32] Karthikeyan Bhargavan, Gaetan Leurent, "On the Practical
(In-)Security of 64-bit Block Ciphers: Collision Attacks
on HTTP over TLS and OpenVPN", Cryptology ePrint
Archive Report 2016/798, 2016,
<https://sweet32.info/SWEET32_CCS16.pdf>.
[TAHA] Taha, M. and P. Schaumont, "Key Updating for Leakage
Resiliency With Application to AES Modes of Operation",
DOI 10.1109/TIFS.2014.2383359, December 2014,
<http://ieeexplore.ieee.org/document/6987331/>.
[TEMPEST] By Craig Ramsay, Jasper Lohuis, "TEMPEST attacks against
AES. Covertly stealing keys for 200 euro", 2017,
<https://www.fox-it.com/en/wp-content/uploads/sites/11/
Tempest_attacks_against_AES.pdf>.
[U2F] Chang, D., Mishra, S., Sanadhya, S., and A. Singhl, "On
Making U2F Protocol Leakage-Resilient via Re-keying.",
Cryptology ePrint Archive Report 2017/721, August 2017,
<https://eprint.iacr.org/2017/721.pdf>.
Appendix A. Test Examples
A.1. Test Examples for External Re-keying
A.1.1. External Re-keying with a Parallel Construction
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External re-keying with a parallel construction based on AES-256
****************************************************************
k = 256
t = 128
Initial key:
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00
K^1:
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
K^2:
6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
B8 02 92 32 D8 D3 8D 73 FE DC DD C6 C8 36 78 BD
K^3:
B6 40 24 85 A4 24 BD 35 B4 26 43 13 76 26 70 B6
5B F3 30 3D 3B 20 EB 14 D1 3B B7 91 74 E3 DB EC
...
K^126:
2F 3F 15 1B 53 88 23 CD 7D 03 FC 3D FD B3 57 5E
23 E4 1C 4E 46 FF 6B 33 34 12 27 84 EF 5D 82 23
K^127:
8E 51 31 FB 0B 64 BB D0 BC D4 C5 7B 1C 66 EF FD
97 43 75 10 6C AF 5D 5E 41 E0 17 F4 05 63 05 ED
K^128:
77 4F BF B3 22 60 C5 3B A3 8E FE B1 96 46 76 41
94 49 AF 84 2D 84 65 A7 F4 F7 2C DC A4 9D 84 F9
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External re-keying with a parallel construction based on SHA-256
****************************************************************
k = 256
t = 128
label:
SHA2label
Initial key:
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00
K^1:
C1 A1 4C A0 30 29 BE 43 9F 35 3C 79 1A 51 48 57
26 7A CD 5A E8 7D E7 D1 B2 E2 C7 AF A4 29 BD 35
K^2:
03 68 BB 74 41 2A 98 ED C4 7B 94 CC DF 9C F4 9E
A9 B8 A9 5F 0E DC 3C 1E 3B D2 59 4D D1 75 82 D4
K^3:
2F D3 68 D3 A7 8F 91 E6 3B 68 DC 2B 41 1D AC 80
0A C3 14 1D 80 26 3E 61 C9 0D 24 45 2A BD B1 AE
...
K^126:
55 AC 2B 25 00 78 3E D4 34 2B 65 0E 75 E5 8B 76
C8 04 E9 D3 B6 08 7D C0 70 2A 99 A4 B5 85 F1 A1
K^127:
77 4D 15 88 B0 40 90 E5 8C 6A D7 5D 0F CF 0A 4A
6C 23 F1 B3 91 B1 EF DF E5 77 64 CD 09 F5 BC AF
K^128:
E5 81 FF FB 0C 90 88 CD E5 F4 A5 57 B6 AB D2 2E
94 C3 42 06 41 AB C1 72 66 CC 2F 59 74 9C 86 B3
A.1.2. External Re-keying with a Serial Construction
External re-keying with a serial construction based on AES-256
**************************************************************
AES 256 examples:
k = 256
t = 128
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Initial key:
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00
K*_1:
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00
K^1:
66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
K*_2:
64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
K^2:
66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
K*_3:
64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
K^3:
66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
...
K*_126:
64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
K^126:
66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
K*_127:
64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
K^127:
66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
K*_128:
64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1
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6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15
K^128:
66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0
51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86
External re-keying with a serial construction based on SHA-256
**************************************************************
k = 256
t = 128
Initial key:
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00
label1:
SHA2label1
label2:
SHA2label2
K*_1:
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00
K^1:
2D A8 D1 37 6C FD 52 7F F7 36 A4 E2 81 C6 0A 9B
F3 8E 66 97 ED 70 4F B5 FB 10 33 CC EC EE D5 EC
K*_2:
14 65 5A D1 7C 19 86 24 9B D3 56 DF CC BE 73 6F
52 62 4A 9D E3 CC 40 6D A9 48 DA 5C D0 68 8A 04
K^2:
2F EA 8D 57 2B EF B8 89 42 54 1B 8C 1B 3F 8D B1
84 F9 56 C7 FE 01 11 99 1D FB 98 15 FE 65 85 CF
K*_3:
18 F0 B5 2A D2 45 E1 93 69 53 40 55 43 70 95 8D
70 F0 20 8C DF B0 5D 67 CD 1B BF 96 37 D3 E3 EB
K^3:
53 C7 4E 79 AE BC D1 C8 24 04 BF F6 D7 B1 AC BF
F9 C0 0E FB A8 B9 48 29 87 37 E1 BA E7 8F F7 92
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...
K*_126:
A3 6D BF 02 AA 0B 42 4A F2 C0 46 52 68 8B C7 E6
5E F1 62 C3 B3 2F DD EF E4 92 79 5D BB 45 0B CA
K^126:
6C 4B D6 22 DC 40 48 0F 29 C3 90 B8 E5 D7 A7 34
23 4D 34 65 2C CE 4A 76 2C FE 2A 42 C8 5B FE 9A
K*_127:
84 5F 49 3D B8 13 1D 39 36 2B BE D3 74 8F 80 A1
05 A7 07 37 BA 15 72 E0 73 49 C2 67 5D 0A 28 A1
K^127:
57 F0 BD 5A B8 2A F3 6B 87 33 CF F7 22 62 B4 D0
F0 EE EF E1 50 74 E5 BA 13 C1 23 68 87 36 29 A2
K*_128:
52 F2 0F 56 5C 9C 56 84 AF 69 AD 45 EE B8 DA 4E
7A A6 04 86 35 16 BA 98 E4 CB 46 D2 E8 9A C1 09
K^128:
9B DD 24 7D F3 25 4A 75 E0 22 68 25 68 DA 9D D5
C1 6D 2D 2B 4F 3F 1F 2B 5E 99 82 7F 15 A1 4F A4
A.2. Test Examples for Internal Re-keying
A.2.1. Internal Re-keying Mechanisms that Do Not Require Master Key
CTR-ACPKM mode with AES-256
***************************
k = 256
n = 128
c = 64
N = 256
Initial key K:
00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Plain text P:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
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00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
00060: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44
ICN:
12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12
23 34 45 56 67 78 89 90 12 13 14 15 16 17 18 19
D_1:
00000: 80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F
D_2:
00000: 90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F
Section_1
Section key K^1:
00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Input block CTR_1:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00
Output block G_1:
00000: FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0
Input block CTR_2:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01
Output block G_2:
00000: 19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2
Section_2
Section key K^2:
00000: F6 80 D1 21 2F A4 3D F4 EC 3A 91 DE 2A B1 6F 1B
00010: 36 B0 48 8A 4F C1 2E 09 98 D2 E4 A8 88 E8 4F 3D
Input block CTR_3:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02
Output block G_3:
00000: E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA
Input block CTR_4:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03
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Output block G_4:
00000: BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4
Section_3
Section key K^3:
00000: 8E B9 7E 43 27 1A 42 F1 CA 8E E2 5F 5C C7 C8 3B
00010: 1A CE 9E 5E D0 6A A5 3B 57 B9 6A CF 36 5D 24 B8
Input block CTR_5:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04
Output block G_5:
00000: 68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7
Input block CTR_6:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05
Output block G_6:
00000: C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87
Section_4
Section key K^4:
00000: C5 71 6C C9 67 98 BC 2D 4A 17 87 B7 8A DF 94 AC
00010: E8 16 F8 0B DB BC AD 7D 60 78 12 9C 0C B4 02 F5
Block number 7:
Input block CTR_7:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06
Output block G_7:
00000: 03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D
The result G = G_1 | G_2 | G_3 | G_4 | G_5 | G_6 | G_7:
00000: FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0
00010: 19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2
00020: E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA
00030: BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4
00040: 68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7
00050: C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87
00060: 03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D
The result ciphertext C = P (xor) MSB_{|P|}(G):
00000: EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58
00010: 19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8
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00020: F5 AA BA 0B E3 64 F0 53 EE F0 BC 15 C2 76 4C EA
00030: 9E 7C C3 76 BD 87 19 C9 77 0F CA 2D E2 A3 7C B5
00040: 5B 2B 77 1B F8 3A 05 17 BE 04 2D 82 28 FE 2A 95
00050: 84 4E 9F 08 FD F7 B8 94 4C B7 AA B7 DE 3C 67 B4
00060: 56 B8 43 FC 32 31 DE 46 D5 AB 14 F8 AC 09 C7 39
GCM-ACPKM mode with AES-128
***************************
k = 128
n = 128
c = 32
N = 256
Initilal Key K:
00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Additional data A:
00000: 11 22 33
Plaintext:
00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00010: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00020: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
ICN:
00000: 00 00 00 00 00 00 00 00 00 00 00 00
Number of sections: 2
Section key K^1:
00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Section key K^2:
00000: 15 1A 9F B0 B6 AC C5 97 6A FB 50 31 D1 DE C8 41
Encrypted GCTR_1 | GCTR_2 | GCTR_3:
00000: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
00010: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
00020: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD
Ciphertext C:
00000: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
00010: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
00020: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD
GHASH input:
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00000: 11 22 33 00 00 00 00 00 00 00 00 00 00 00 00 00
00010: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
00020: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
00030: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD
00040: 00 00 00 00 00 00 00 18 00 00 00 00 00 00 01 80
GHASH output S:
00000: E8 ED E9 94 9A DD 55 30 B0 F4 4E F5 00 FC 3E 3C
Authentication tag T:
00000: B0 0F 15 5A 60 A3 65 51 86 8B 53 A2 A4 1B 7B 66
The result C | T:
00000: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78
00010: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0
00020: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD
00030: B0 0F 15 5A 60 A3 65 51 86 8B 53 A2 A4 1B 7B 66
A.2.2. Internal Re-keying Mechanisms with a Master Key
CTR-ACPKM-Master mode with AES-256
**********************************
k = 256
n = 128
c for CTR-ACPKM mode = 64
c for CTR-ACPKM-Master mode = 64
N = 256
T* = 512
Initial key K:
00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Initial vector ICN:
00000: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12
Plaintext P:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
00060: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44
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K^1 | K^2 | K^3 | K^4:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
00040: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
00050: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
Section_1
K^1:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
Input block CTR_1:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00
Output block G_1:
00000: 8C A2 B6 82 A7 50 65 3F 8E BF 08 E7 9F 99 4D 5C
Input block CTR_2:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01
Output block G_2:
00000: F6 A6 A5 BA 58 14 1E ED 23 DC 31 68 D2 35 89 A1
Section_2
K^2:
00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00010: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
Input block CTR_3:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02
Output block G_3:
00000: 4A 07 5F 86 05 87 72 94 1D 8E 7D F8 32 F4 23 71
Input block CTR_4:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03
Output block G_4:
00000: 23 35 66 AF 61 DD FE A7 B1 68 3F BA B0 52 4A D7
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Section_3
K^3:
00000: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
00010: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
Input block CTR_5:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04
Output block G_5:
00000: A8 09 6D BC E8 BB 52 FC DE 6E 03 70 C1 66 95 E8
Input block CTR_6:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05
Output block G_6:
00000: C6 E3 6E 8E 5B 82 AA C4 A6 6C 14 8D B1 F6 9B EF
Section_4
K^4:
00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
Input block CTR_7:
00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06
Output block G_7:
00000: 82 2B E9 07 96 37 44 95 75 36 3F A7 07 F8 40 22
The result G = G_1 | G_2 | G_3 | G_4 | G_5 | G_6 | G_7:
00000: 8C A2 B6 82 A7 50 65 3F 8E BF 08 E7 9F 99 4D 5C
00010: F6 A6 A5 BA 58 14 1E ED 23 DC 31 68 D2 35 89 A1
00020: 4A 07 5F 86 05 87 72 94 1D 8E 7D F8 32 F4 23 71
00030: 23 35 66 AF 61 DD FE A7 B1 68 3F BA B0 52 4A D7
00040: A8 09 6D BC E8 BB 52 FC DE 6E 03 70 C1 66 95 E8
00050: C6 E3 6E 8E 5B 82 AA C4 A6 6C 14 8D B1 F6 9B EF
00060: 82 2B E9 07 96 37 44 95 75 36 3F A7 07 F8 40 22
The result ciphertext C = P (xor) MSB_{|P|}(G):
00000: 9D 80 85 C6 F2 36 12 3F 71 51 D5 2B 24 33 D4 D4
00010: F6 B7 87 89 1C 41 78 9A AB 45 9B D3 1E DB 76 AB
00020: 5B 25 6C C2 50 E1 05 1C 84 24 C6 34 DC 0B 29 71
00030: 01 06 22 FA 07 AA 76 3E 1B D3 F3 54 4F 58 4A C6
00040: 9B 4D 38 DA 9F 33 CB 56 65 A2 ED 8F CB 66 84 CA
00050: 82 B6 08 F9 D3 1B 00 7F 6A 82 EB 87 B1 E7 B9 DC
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00060: D7 4D 9E 8F 0F 9D FF 59 9B C9 35 A7 16 DA 73 66
GCM-ACPKM-Master mode with AES-256
**********************************
k = 192
n = 128
c for the CTR-ACPKM mode = 64
c for the GCM-ACPKM-Master mode = 32
T* = 384
N = 256
Initila Key K:
00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00010: 00 00 00 00 00 00 00 00
Additional data A:
00000: 11 22 33
Plaintext:
00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00010: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00020: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00030: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
00040: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
ICN:
00000: 00 00 00 00 00 00 00 00 00 00 00 00
Number of sections: 3
K^1 | K^2 | K^3:
00000: 93 BA AF FB 35 FB E7 39 C1 7C 6A C2 2E EC F1 8F
00010: 7B 89 F0 BF 8B 18 07 05 96 48 68 9F 36 A7 65 CC
00020: CD 5D AC E2 0D 47 D9 18 D7 86 D0 41 A8 3B AB 99
00030: F5 F8 B1 06 D2 71 78 B1 B0 08 C9 99 0B 72 E2 87
00040: 5A 2D 3C BE F1 6E 67 3C
Encrypted GCTR_1 | ... | GCTR_5
00000: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
00010: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
00020: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
00030: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
00040: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08
Ciphertext C:
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00000: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
00010: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
00020: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
00030: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
00040: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08
GHASH input:
00000: 11 22 33 00 00 00 00 00 00 00 00 00 00 00 00 00
00010: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
00020: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
00030: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
00040: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
00050: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08
00060: 00 00 00 00 00 00 00 18 00 00 00 00 00 00 02 80
GHASH output S:
00000: 6E A3 4B D5 6A C5 40 B7 3E 55 D5 86 D1 CC 09 7D
Authentication tag T:
00050: CC 3A BA 11 8C E7 85 FD 77 78 94 D4 B5 20 69 F8
The result C | T:
00000: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52
00010: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8
00020: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE
00030: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14
00040: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08
00050: CC 3A BA 11 8C E7 85 FD 77 78 94 D4 B5 20 69 F8
CBC-ACPKM-Master mode with AES-256
**********************************
k = 256
n = 128
c for the CTR-ACPKM mode = 64
N = 256
T* = 512
Initial key K:
00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Initial vector IV:
00000: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12
Plaintext P:
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00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
00060: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44
K^1 | K^2 | K^3 | K^4:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
00040: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
00050: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
Section_1
K^1:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
Plaintext block P_1:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
Input block P_1 (xor) C_0:
00000: 03 16 65 3C C5 CD B9 F0 5E 5C 1E 18 5E 5A 98 9A
Output block C_1:
00000: 59 CB 5B CA C2 69 2C 60 0D 46 03 A0 C7 40 C9 7C
Plaintext block P_2:
00000: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
Input block P_2 (xor) C_1:
00000: 59 DA 79 F9 86 3C 4A 17 85 DF A9 1B 0B AE 36 76
Output block C_2:
00000: 80 B6 02 74 54 8B F7 C9 78 1F A1 05 8B F6 8B 42
Section_2
K^2:
00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00010: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
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Plaintext block P_3:
00000: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
Input block P_3 (xor) C_2:
00000: 91 94 31 30 01 ED 80 41 E1 B5 1A C9 65 09 81 42
Output block C_3:
00000: 8C 24 FB CF 68 15 B1 AF 65 FE 47 75 95 B4 97 59
Plaintext block P_4:
00000: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
Input block P_4 (xor) C_3:
00000: AE 17 BF 9A 0E 62 39 36 CF 45 8B 9B 6A BE 97 48
Output block C_4:
00000: 19 65 A5 00 58 0D 50 23 72 1B E9 90 E1 83 30 E9
Section_3
K^3:
00000: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
00010: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
Plaintext block P_5:
00000: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
Input block P_5 (xor) C_4:
00000: 2A 21 F0 66 2F 85 C9 89 C9 D7 07 6F EB 83 21 CB
Output block C_5:
00000: 56 D8 34 F4 6F 0F 4D E6 20 53 A9 5C B5 F6 3C 14
Plaintext block P_6:
00000: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
Input block P_6 (xor) C_5:
00000: 12 8D 52 83 E7 96 E7 5D EC BD 56 56 B5 E7 1E 27
Output block C_6:
00000: 66 68 2B 8B DD 6E B2 7E DE C7 51 D6 2F 45 A5 45
Section_4
K^4:
00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
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Plaintext block P_7:
00000: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44
Input block P_7 (xor) C_6:
00000: 33 0E 5C 03 44 C4 09 B2 30 38 5B D6 3E 67 96 01
Output block C_7:
00000: 7F 4D 87 F9 CA E9 56 09 79 C4 FA FE 34 0B 45 34
Cipher text C:
00000: 59 CB 5B CA C2 69 2C 60 0D 46 03 A0 C7 40 C9 7C
00010: 80 B6 02 74 54 8B F7 C9 78 1F A1 05 8B F6 8B 42
00020: 8C 24 FB CF 68 15 B1 AF 65 FE 47 75 95 B4 97 59
00030: 19 65 A5 00 58 0D 50 23 72 1B E9 90 E1 83 30 E9
00040: 56 D8 34 F4 6F 0F 4D E6 20 53 A9 5C B5 F6 3C 14
00050: 66 68 2B 8B DD 6E B2 7E DE C7 51 D6 2F 45 A5 45
00060: 7F 4D 87 F9 CA E9 56 09 79 C4 FA FE 34 0B 45 34
CFB-ACPKM-Master mode with AES-256
**********************************
k = 256
n = 128
c for the CTR-ACPKM mode = 64
N = 256
T* = 512
Initial key K:
00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Initial vector IV:
00000: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12
Plaintext P:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
00060: 55 66 77 88 99 AA BB CC
K^1 | K^2 | K^3 | K^4
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
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00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
00040: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
00050: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
Section_1
K^1:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
Plaintext block P_1:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
Encrypted block E_{K^1}(C_0):
00000: 1C 39 9D 59 F8 5D 91 91 A9 D2 12 9F 63 15 90 03
Output block C_1 = E_{K^1}(C_0) (xor) P_1:
00000: 0D 1B AE 1D AD 3B E6 91 56 3C CF 53 D8 BF 09 8B
Plaintext block P_2:
00000: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
Encrypted block E_{K^1}(C_1):
00000: 6B A2 C5 42 52 69 C6 0B 15 14 06 87 90 46 F6 2E
Output block C_2 = E_{K^1}(C_1) (xor) P_2:
00000: 6B B3 E7 71 16 3C A0 7C 9D 8D AC 3C 5C A8 09 24
Section_2
K^2:
00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00010: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
Plaintext block P_3:
00000: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
Encrypted block E_{K^2}(C_2):
00000: 95 45 5F DB C3 9E 0A 13 9F CB 10 F5 BD 79 A3 88
Output block C_3 = E_{K^2}(C_2) (xor) P_3:
00000: 84 67 6C 9F 96 F8 7D 9B 06 61 AB 39 53 86 A9 88
Plaintext block P_4:
00000: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
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Encrypted block E_{K^2}(C_3):
00000: E0 AA 32 5D 80 A4 47 95 BA 42 BF 63 F8 4A C8 B2
Output block C_4 = E_{K^2}(C_3) (xor) P_4:
00000: C2 99 76 08 E6 D3 CF 0C 10 F9 73 8D 07 40 C8 A3
Section_3
K^3:
00000: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4
00010: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94
Plaintext block P_5:
00000: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
Encrypted block E_{K^3}(C_4):
00000: FE 42 8C 70 C2 51 CE 13 36 C1 BF 44 F8 49 66 89
Output block C_5 = E_{K^3}(C_4) (xor) P_5:
00000: CD 06 D9 16 B5 D9 57 B9 8D 0D 51 BB F2 49 77 AB
Plaintext block P_6:
00000: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
Encrypted block E_{K^3}(C_5):
00000: 01 24 80 87 86 18 A5 43 11 0A CC B5 0A E5 02 A3
Output block C_6 = E_{K^3}(C_5) (xor) P_6:
00000: 45 71 E6 F0 0E 81 0F F8 DD E4 33 BF 0A F4 20 90
Section_4
K^4:
00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
Plaintext block P_7:
00000: 55 66 77 88 99 AA BB CC
Encrypted block MSB_{|P_7|}(E_{K^4}(C_6)):
00000: 97 5C 96 37 55 1E 8C 7F
Output block C_7 = MSB_{|P_7|}(E_{K^4}(C_6)) (xor) P_7
00000: C2 3A E1 BF CC B4 37 B3
Cipher text C:
00000: 0D 1B AE 1D AD 3B E6 91 56 3C CF 53 D8 BF 09 8B
00010: 6B B3 E7 71 16 3C A0 7C 9D 8D AC 3C 5C A8 09 24
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00020: 84 67 6C 9F 96 F8 7D 9B 06 61 AB 39 53 86 A9 88
00030: C2 99 76 08 E6 D3 CF 0C 10 F9 73 8D 07 40 C8 A3
00040: CD 06 D9 16 B5 D9 57 B9 8D 0D 51 BB F2 49 77 AB
00050: 45 71 E6 F0 0E 81 0F F8 DD E4 33 BF 0A F4 20 90
00060: C2 3A E1 BF CC B4 37 B3
OMAC-ACPKM-Master mode with AES-256
***********************************
k = 256
n = 128
c for the CTR-ACPKM mode = 64
N = 256
T* = 768
Initial key K:
00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Plaintext M:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
K^1 | K^1_1 | K^2 | K^2_1 | K^3 | K^3_1:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
00040: 9D CC 66 42 0D FF 45 5B 21 F3 93 F0 D4 D6 6E 67
00050: BB 1B 06 0B 87 66 6D 08 7A 9D A7 49 55 C3 5B 48
00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
00080: 78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07
Section_1
K^1:
00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64
00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60
K^1_1:
00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0
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Plaintext block M_1:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
Input block M_1 (xor) C_0:
00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
Output block C_1:
00000: 0B A5 89 BF 55 C1 15 42 53 08 89 76 A0 FE 24 3E
Plaintext block M_2:
00000: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
Input block M_2 (xor) C_1:
00000: 0B B4 AB 8C 11 94 73 35 DB 91 23 CD 6C 10 DB 34
Output block C_2:
00000: 1C 53 DD A3 6D DC E1 17 ED 1F 14 09 D8 6A F3 2C
Section_2
K^2:
00000: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3
00010: 9D CC 66 42 0D FF 45 5B 21 F3 93 F0 D4 D6 6E 67
K^2_1:
00000: BB 1B 06 0B 87 66 6D 08 7A 9D A7 49 55 C3 5B 48
Plaintext block M_3:
00000: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
Input block M_3 (xor) C_2:
00000: 0D 71 EE E7 38 BA 96 9F 74 B5 AF C5 36 95 F9 2C
Output block C_3:
00000: 4E D4 BC A6 CE 6D 6D 16 F8 63 85 13 E0 48 59 75
Plaintext block M_4:
00000: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
Input block M_4 (xor) C_3:
00000: 6C E7 F8 F3 A8 1A E5 8F 52 D8 49 FD 1F 42 59 64
Output block C_4:
00000: B6 83 E3 96 FD 30 CD 46 79 C1 8B 24 03 82 1D 81
Section_3
K^3:
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00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9
00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12
K^3_1:
00000: 78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07
MSB1(K1) == 0 -> K2 = K1 << 1
K1:
00000: 78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07
K2:
00000: F0 43 8F 8E D9 7A F2 C6 AD 59 F1 1C D2 D4 00 0E
Plaintext M_5:
00000: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
Using K1, padding is not required
Input block M_5 (xor) C_4:
00000: FD E6 71 37 E6 05 2D 8F 94 A1 9D 55 60 E8 0C A4
Output block C_5:
00000: B3 AD B8 92 18 32 05 4C 09 21 E7 B8 08 CF A0 B8
Message authentication code T:
00000: B3 AD B8 92 18 32 05 4C 09 21 E7 B8 08 CF A0 B8
Appendix B. Contributors
o Russ Housley
Vigil Security, LLC
housley@vigilsec.com
o Evgeny Alekseev
CryptoPro
alekseev@cryptopro.ru
o Ekaterina Smyshlyaeva
CryptoPro
ess@cryptopro.ru
o Shay Gueron
University of Haifa, Israel
Intel Corporation, Israel Development Center, Israel
shay.gueron@gmail.com
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o Daniel Fox Franke
Akamai Technologies
dfoxfranke@gmail.com
o Lilia Ahmetzyanova
CryptoPro
lah@cryptopro.ru
Appendix C. Acknowledgments
We thank Mihir Bellare, Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim
Schaad, Paul Hoffman, Dmitry Belyavsky, Yaron Sheffer, Alexey
Melnikov and Spencer Dawkins for their useful comments.
Author's Address
Stanislav Smyshlyaev (editor)
CryptoPro
18, Suschevskiy val
Moscow 127018
Russian Federation
Phone: +7 (495) 995-48-20
Email: svs@cryptopro.ru
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