Internet DRAFT - draft-irtf-cfrg-kangarootwelve
draft-irtf-cfrg-kangarootwelve
Crypto Forum B. Viguier
Internet-Draft ABN AMRO Bank
Intended status: Informational D. Wong, Ed.
Expires: 9 August 2024 zkSecurity
G. Van Assche, Ed.
STMicroelectronics
Q. Dang, Ed.
NIST
J. Daemen, Ed.
Radboud University
6 February 2024
KangarooTwelve and TurboSHAKE
draft-irtf-cfrg-kangarootwelve-13
Abstract
This document defines four eXtendable Output Functions (XOF), hash
functions with output of arbitrary length, named TurboSHAKE128,
TurboSHAKE256, KT128 and KT256.
All four functions provide efficient and secure hashing primitives,
and the last two are able to exploit the parallelism of the
implementation in a scalable way.
This document builds up on the definitions of the permutations and of
the sponge construction in [FIPS 202], and is meant to serve as a
stable reference and an implementation guide.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
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Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 9 August 2024.
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Copyright Notice
Copyright (c) 2024 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
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provided without warranty as described in the Revised BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Conventions . . . . . . . . . . . . . . . . . . . . . . . 4
2. TurboSHAKE . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. Specifications . . . . . . . . . . . . . . . . . . . . . 6
3. KangarooTwelve: Tree hashing over TurboSHAKE . . . . . . . . 7
3.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Specification of KT128 . . . . . . . . . . . . . . . . . 8
3.3. length_encode( x ) . . . . . . . . . . . . . . . . . . . 11
3.4. Specification of KT256 . . . . . . . . . . . . . . . . . 11
4. Message authentication codes . . . . . . . . . . . . . . . . 11
5. Test vectors . . . . . . . . . . . . . . . . . . . . . . . . 12
6. Security Considerations . . . . . . . . . . . . . . . . . . . 20
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.1. Normative References . . . . . . . . . . . . . . . . . . 22
7.2. Informative References . . . . . . . . . . . . . . . . . 22
Appendix A. Pseudocode . . . . . . . . . . . . . . . . . . . . . 23
A.1. Keccak-p[1600,n_r=12] . . . . . . . . . . . . . . . . . . 23
A.2. TurboSHAKE128 . . . . . . . . . . . . . . . . . . . . . . 25
A.3. TurboSHAKE256 . . . . . . . . . . . . . . . . . . . . . . 25
A.4. KT128 . . . . . . . . . . . . . . . . . . . . . . . . . . 26
A.5. KT256 . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 28
1. Introduction
This document defines the TurboSHAKE128, TurboSHAKE256 [TURBOSHAKE],
KT128 and KT256 [KT] eXtendable Output Functions (XOF), i.e., a hash
function generalization that can return an output of arbitrary
length. Both TurboSHAKE128 and TurboSHAKE256 are based on a Keccak-p
permutation specified in [FIPS202] and have a higher speed than the
SHA-3 and SHAKE functions.
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TurboSHAKE is a sponge function family that makes use of Keccak-
p[n_r=12,b=1600], a round-reduced version of the permutation used in
SHA-3. Similarly to the SHAKE's, it proposes two security strengths:
128 bits for TurboSHAKE128 and 256 bits for TurboSHAKE256. Halving
the number of rounds compared to the original SHAKE functions makes
TurboSHAKE roughly twice faster.
KangarooTwelve applies tree hashing on top of TurboSHAKE and
comprises two functions, KT128 and KT256. Note that [KT] only
defined KT128 under the name KangarooTwelve. KT256 is defined in
this document.
The SHA-3 and SHAKE functions process data in a serial manner and are
strongly limited in exploiting available parallelism in modern CPU
architectures. Similar to ParallelHash [SP800-185], KangarooTwelve
splits the input message into fragments. It then applies TurboSHAKE
on each of them separately before applying TurboSHAKE again on the
combination of the first fragment and the digests. More precisely,
KT128 uses TurboSHAKE128 and KT256 uses TurboSHAKE256. They make use
of Sakura coding for ensuring soundness of the tree hashing mode
[SAKURA]. The use of TurboSHAKE in KangarooTwelve makes it faster
than ParallelHash.
The security of TurboSHAKE128, TurboSHAKE256, KT128 and KT256 builds
on the public scrutiny that Keccak has received since its publication
[KECCAK_CRYPTANALYSIS][TURBOSHAKE].
With respect to [FIPS202] and [SP800-185] functions, TurboSHAKE128,
TurboSHAKE256, KT128 and KT256 feature the following advantages:
* Unlike SHA3-224, SHA3-256, SHA3-384, SHA3-512, the TurboSHAKE and
KangarooTwelve functions have an extendable output.
* Unlike any [FIPS202] defined function, similarly to functions
defined in [SP800-185], KT128 and KT256 allow the use of a
customization string.
* Unlike any [FIPS202] and [SP800-185] functions but ParallelHash,
KT128 and KT256 exploit available parallelism.
* Unlike ParallelHash, KT128 and KT256 do not have overhead when
processing short messages.
* The permutation in the TurboSHAKE functions has half the number of
rounds compared to the one in the SHA-3 and SHAKE functions,
making them faster than any function defined in [FIPS202]. The
KangarooTwelve functions immediately benefit from the same
speedup, improving over [FIPS202] and [SP800-185].
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With respect to SHA-256 and SHA-512 and other [FIPS180] functions,
TurboSHAKE128, TurboSHAKE256, KT128 and KT256 feature the following
advantages:
* Unlike [FIPS180] functions, the TurboSHAKE and KangarooTwelve
functions have an extendable output.
* The TurboSHAKE functions produce output at the same rate as they
process input, whereas SHA-256 and SHA-512 produce output half as
fast as they process input.
* Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128,
TurboSHAKE256, KT128 and KT256 do not suffer from the length
extension weakness.
* Unlike any [FIPS180] functions, TurboSHAKE128, TurboSHAKE256,
KT128 and KT256 use a round function with algebraic degree 2,
which makes them more suitable to masking techniques for
protections against side-channel attacks.
1.1. Conventions
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 RFC 2119 [RFC2119].
The following notations are used throughout the document:
`...` denotes a string of bytes given in hexadecimal. For example,
`0B 80`.
|s| denotes the length of a byte string `s`. For example, |`FF FF`|
= 2.
`00`^b denotes a byte string consisting of the concatenation of b
bytes `00`. For example, `00`^7 = `00 00 00 00 00 00 00`.
`00`^0 denotes the empty byte-string.
a||b denotes the concatenation of two strings a and b. For example,
`10`||`F1` = `10 F1`
s[n:m] denotes the selection of bytes from n (inclusive) to m
(exclusive) of a string s. The indexing of a byte-string starts
at 0. For example, for s = `A5 C6 D7`, s[0:1] = `A5` and s[1:3] =
`C6 D7`.
s[n:] denotes the selection of bytes from n to the end of a string
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s. For example, for s = `A5 C6 D7`, s[0:] = `A5 C6 D7` and s[2:]
= `D7`.
In the following, x and y are byte strings of equal length:
x^=y denotes x takes the value x XOR y.
x & y denotes x AND y.
In the following, x and y are integers:
x+=y denotes x takes the value x + y.
x-=y denotes x takes the value x - y.
x**y denotes the exponentiation of x by y.
x mod y denotes reminder of the division of x by y.
x / y denotes the integer dividend of the division of x by y.
2. TurboSHAKE
2.1. Interface
TurboSHAKE is a family of eXtendable Output Functions (XOF). This
document focuses on only two instances, namely, TurboSHAKE128 and
TurboSHAKE256. (Note that the original definition includes a wider
range of instances parameterized by their capacity [TURBOSHAKE]. The
capacity is an essential parameter of the sponge construction, see
[FIPS202] for more details.)
An instance of TurboSHAKE takes as input parameters a byte-string M,
an OPTIONAL byte D and a positive integer L where
M byte-string, is the Message and
D byte in the range [`01`, `02`, .. , `7F`], is an OPTIONAL Domain
separation byte and
L positive integer, is the requested number of output bytes.
Conceptually, a XOF can be viewed as a hash function with an
infinitely long output truncated to L bytes. This means that calling
a XOF with the same input parameters but two different lengths yields
outputs such that the shorter one is a prefix of the longer one.
Specifically, if L1 < L2, then TurboSHAKE(M, D, L1) is the same as
the first L1 bytes of TurboSHAKE(M, D, L2).
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By default, the Domain separation byte is `1F`. For an API that does
not support a domain separation byte, D MUST be the `1F`.
The TurboSHAKE instance produces output that is a hash of the (M, D)
couple. If D is fixed, this becomes a hash of the Message M.
However, a protocol that requires a number of independent hash
functions can choose different values for D to implement these.
Specifically, for any distinct values D1 and D2, TurboSHAKE(M, D1,
L1) and TurboSHAKE(M, D2, L2) yield independent hashes of M.
Note that an implementation MAY propose an incremental input
interface where the input string M is given in pieces. If so, the
output MUST be the same as if the function was called with M equal to
the concatenation of the different pieces in the order they were
given. Independently, an implementation MAY propose an incremental
output interface where the output string is requested in pieces of
given lengths. When the output is formed by concatenating the pieces
in the requested order, it MUST be the same as if the function was
called with L equal to the sum of the given lengths.
2.2. Specifications
TurboSHAKE makes use of the permutation Keccak-p[1600,n_r=12], i.e.,
the permutation used in SHAKE and SHA-3 functions reduced to its last
n_r=12 rounds and specified in FIPS 202, Sections 3.3 and 3.4
[FIPS202]. KP denotes this permutation.
Similarly to SHAKE128, TurboSHAKE128 is a sponge function calling
this permutation KP with a rate of 168 bytes or 1344 bits. It
follows that TurboSHAKE128 has a capacity of 1600 - 1344 = 256 bits
or 32 bytes. Respectively to SHAKE256, TurboSHAKE256 makes use of a
rate of 136 bytes or 1088 bits, and has a capacity of 512 bits or 64
bytes.
+-------------+--------------+
| Rate | Capacity |
+----------------+-------------+--------------+
| TurboSHAKE128 | 168 Bytes | 32 Bytes |
| | | |
| TurboSHAKE256 | 136 Bytes | 64 Bytes |
+----------------+-------------+--------------+
We now describe the operations inside TurboSHAKE128.
* First the input M' is formed by appending the domain separation
byte D to the message M.
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* Non-multiple of 168-bytes-length M' are padded with zeroes to the
next multiple of 168 bytes while M' with length multiple of 168
bytes are kept as is. Then a byte `80` is XORed to the last byte
of the padded input M' and the resulting string is split into a
sequence of 168-byte blocks.
* M' never has a length of 0 bytes due to the presence of the domain
separation byte.
* As defined by the sponge construction, the process operates on a
state and consists of two phases: the absorbing phase that
processes the padded input M' and the squeezing phase that
produces the output.
* In the absorbing phase the state is initialized to all-zero. The
message blocks are XORed into the first 168 bytes of the state.
Each block absorbed is followed with an application of KP to the
state.
* In the squeezing phase output is formed by taking the first 168
bytes of the state, repeated as many times as necessary until
outputByteLen bytes are obtained, interleaved with the application
of KP to the state.
TurboSHAKE256 performs the same steps but makes use of 136-byte
blocks with respect to padding, absorbing, and squeezing phases.
The definition of the TurboSHAKE functions equivalently implements
the pad10*1 rule; see Section 5.1 of [FIPS202] for a definition of
pad10*1. While M can be empty, the D byte is always present and is
in the `01`-`7F` range. This last byte serves as domain separation
and integrates the first bit of padding of the pad10*1 rule (hence it
cannot be `00`). Additionally, it must leave room for the second bit
of padding (hence it cannot have the MSB set to 1), should it be the
last byte of the block. For more details, refer to Section 6.1 of
[KT] and Section 3 of [TURBOSHAKE].
The pseudocode versions of TurboSHAKE128 and TurboSHAKE256 are
provided respectively in Appendix A.2 and Appendix A.3.
3. KangarooTwelve: Tree hashing over TurboSHAKE
3.1. Interface
KangarooTwelve is a family of eXtendable Output Functions (XOF)
consisting of the KT128 and KT256 instances. A KangarooTwelve
instance takes as input parameters two byte-strings (M, C) and a
positive integer L where
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M byte-string, is the Message and
C byte-string, is an OPTIONAL Customization string and
L positive integer, the requested number of output bytes.
The Customization string MAY serve as domain separation. It is
typically a short string such as a name or an identifier (e.g. URI,
ODI...). It can serve the same purpose as TurboSHAKE's D input
parameter (see Section 2.1), but with a larger range.
By default, the Customization string is the empty string. For an API
that does not support a customization string parameter, C MUST be the
empty string.
Note that an implementation MAY propose an interface with input and/
or output incrementality as specified in Section 2.1.
3.2. Specification of KT128
On top of the sponge function TurboSHAKE128, KT128 uses a Sakura-
compatible tree hash mode [SAKURA]. First, merge M and the OPTIONAL
C to a single input string S in a reversible way. length_encode( |C|
) gives the length in bytes of C as a byte-string. See Section 3.3.
S = M || C || length_encode( |C| )
Then, split S into n chunks of 8192 bytes.
S = S_0 || .. || S_(n-1)
|S_0| = .. = |S_(n-2)| = 8192 bytes
|S_(n-1)| <= 8192 bytes
From S_1 .. S_(n-1), compute the 32-byte Chaining Values CV_1 ..
CV_(n-1). In order to be optimally efficient, this computation MAY
exploit the parallelism available on the platform such as SIMD
instructions.
CV_i = TurboSHAKE128( S_i, `0B`, 32 )
Compute the final node: FinalNode.
* If |S| <= 8192 bytes, FinalNode = S
* Otherwise compute FinalNode as follows:
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FinalNode = S_0 || `03 00 00 00 00 00 00 00`
FinalNode = FinalNode || CV_1
..
FinalNode = FinalNode || CV_(n-1)
FinalNode = FinalNode || length_encode(n-1)
FinalNode = FinalNode || `FF FF`
Finally, the KT128 output is retrieved:
* If |S| <= 8192 bytes, from TurboSHAKE128( FinalNode, `07`, L )
KT128( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L )
* Otherwise from TurboSHAKE128( FinalNode, `06`, L )
KT128( M, C, L ) = TurboSHAKE128( FinalNode, `06`, L )
The following figure illustrates the computation flow of KT128
for |S| <= 8192 bytes:
+--------------+ TurboSHAKE128(.., `07`, L)
| S |-----------------------------> output
+--------------+
The following figure illustrates the computation flow of KT128
for |S| > 8192 bytes and where TurboSHAKE128 and length_encode( x )
are abbreviated as respectively TSHK128 and l_e( x ) :
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+--------------+
| S_0 |
+--------------+
||
+--------------+
| `03`||`00`^7 |
+--------------+
||
+---------+ TSHK128(..,`0B`,32) +--------------+
| S_1 |---------------------->| CV_1 |
+---------+ +--------------+
||
+---------+ TSHK128(..,`0B`,32) +--------------+
| S_2 |---------------------->| CV_2 |
+---------+ +--------------+
||
.. ..
||
+---------+ TSHK128(..,`0B`,32) +--------------+
| S_(n-1) |----------------------->| CV_(n-1) |
+---------+ +--------------+
||
+--------------+
| l_e( n-1 ) |
+--------------+
||
+--------------+
| `FF FF` |
+--------------+
| TSHK128(.., `06`, L)
+--------------------> output
A pseudocode version is provided in Appendix A.4.
The table below gathers the values of the domain separation bytes
used by the tree hash mode:
+--------------------+------------------+
| Type | Byte |
+--------------------+------------------+
| SingleNode | `07` |
| | |
| IntermediateNode | `0B` |
| | |
| FinalNode | `06` |
+--------------------+------------------+
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3.3. length_encode( x )
The function length_encode takes as inputs a non-negative integer x <
256**255 and outputs a string of bytes x_(n-1) || .. || x_0 || n
where
x = sum of 256**i * x_i for i from 0 to n-1
and where n is the smallest non-negative integer such that x <
256**n. n is also the length of x_(n-1) || .. || x_0.
As example, length_encode(0) = `00`, length_encode(12) = `0C 01` and
length_encode(65538) = `01 00 02 03`
A pseudocode version is as follows where { b } denotes the byte of
numerical value b.
length_encode(x):
S = `00`^0
while x > 0
S = { x mod 256 } || S
x = x / 256
S = S || { |S| }
return S
end
3.4. Specification of KT256
KT256 is specified exactly like KT128, with two differences:
* All the calls to TurboSHAKE128 in KT128 are replaced with calls to
TurboSHAKE256 in KT256.
* The chaining values CV_1 to CV_(n-1) are 64-byte long in KT256 and
are computed as follows:
CV_i = TurboSHAKE256( S_i, `0B`, 64 )
A pseudocode version is provided in Appendix A.5.
4. Message authentication codes
Implementing a MAC with KT128 or KT256 SHOULD use a HASH-then-MAC
construction. This document recommends a method called HopMAC,
defined as follows:
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HopMAC128(Key, M, C, L) = KT128(Key, KT128(M, C, 32), L)
HopMAC256(Key, M, C, L) = KT256(Key, KT256(M, C, 64), L)
Similarly to HMAC, HopMAC consists of two calls: an inner call
compressing the message M and the optional customization string C to
a digest, and an outer call computing the tag from the key and the
digest.
Unlike HMAC, the inner call to KangarooTwelve in HopMAC is keyless
and does not require additional protection against side channel
attacks (SCA). Consequently, in an implementation that has to
protect the HopMAC key against SCA only the outer call does need
protection, and this amounts to a single execution of the underlying
permutation.
In any case, TurboSHAKE128, TurboSHAKE256, KT128 and KT256 MAY be
used to compute a MAC with the key reversibly prepended or appended
to the input. For instance, one MAY compute a MAC on short messages
simply calling KT128 with the key as the customization string, i.e.,
MAC = KT128(M, Key, L).
5. Test vectors
Test vectors are based on the repetition of the pattern `00 01 02 ..
F9 FA` with a specific length. ptn(n) defines a string by repeating
the pattern `00 01 02 .. F9 FA` as many times as necessary and
truncated to n bytes e.g.
Pattern for a length of 17 bytes:
ptn(17) =
`00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 10`
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Pattern for a length of 17**2 bytes:
ptn(17**2) =
`00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F
30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F
40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F
50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F
60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F
70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F
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
00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
20 21 22 23 24 25`
TurboSHAKE128(M=`00`^0, D=`1F`, 32):
`1E 41 5F 1C 59 83 AF F2 16 92 17 27 7D 17 BB 53
8C D9 45 A3 97 DD EC 54 1F 1C E4 1A F2 C1 B7 4C`
TurboSHAKE128(M=`00`^0, D=`1F`, 64):
`1E 41 5F 1C 59 83 AF F2 16 92 17 27 7D 17 BB 53
8C D9 45 A3 97 DD EC 54 1F 1C E4 1A F2 C1 B7 4C
3E 8C CA E2 A4 DA E5 6C 84 A0 4C 23 85 C0 3C 15
E8 19 3B DF 58 73 73 63 32 16 91 C0 54 62 C8 DF`
TurboSHAKE128(M=`00`^0, D=`1F`, 10032), last 32 bytes:
`A3 B9 B0 38 59 00 CE 76 1F 22 AE D5 48 E7 54 DA
10 A5 24 2D 62 E8 C6 58 E3 F3 A9 23 A7 55 56 07`
TurboSHAKE128(M=ptn(17**0 bytes), D=`1F`, 32):
`55 CE DD 6F 60 AF 7B B2 9A 40 42 AE 83 2E F3 F5
8D B7 29 9F 89 3E BB 92 47 24 7D 85 69 58 DA A9`
TurboSHAKE128(M=ptn(17**1 bytes), D=`1F`, 32):
`9C 97 D0 36 A3 BA C8 19 DB 70 ED E0 CA 55 4E C6
E4 C2 A1 A4 FF BF D9 EC 26 9C A6 A1 11 16 12 33`
TurboSHAKE128(M=ptn(17**2 bytes), D=`1F`, 32):
`96 C7 7C 27 9E 01 26 F7 FC 07 C9 B0 7F 5C DA E1
E0 BE 60 BD BE 10 62 00 40 E7 5D 72 23 A6 24 D2`
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TurboSHAKE128(M=ptn(17**3 bytes), D=`1F`, 32):
`D4 97 6E B5 6B CF 11 85 20 58 2B 70 9F 73 E1 D6
85 3E 00 1F DA F8 0E 1B 13 E0 D0 59 9D 5F B3 72`
TurboSHAKE128(M=ptn(17**4 bytes), D=`1F`, 32):
`DA 67 C7 03 9E 98 BF 53 0C F7 A3 78 30 C6 66 4E
14 CB AB 7F 54 0F 58 40 3B 1B 82 95 13 18 EE 5C`
TurboSHAKE128(M=ptn(17**5 bytes), D=`1F`, 32):
`B9 7A 90 6F BF 83 EF 7C 81 25 17 AB F3 B2 D0 AE
A0 C4 F6 03 18 CE 11 CF 10 39 25 12 7F 59 EE CD`
TurboSHAKE128(M=ptn(17**6 bytes), D=`1F`, 32):
`35 CD 49 4A DE DE D2 F2 52 39 AF 09 A7 B8 EF 0C
4D 1C A4 FE 2D 1A C3 70 FA 63 21 6F E7 B4 C2 B1`
TurboSHAKE128(M=`FF FF FF`, D=`01`, 32):
`BF 32 3F 94 04 94 E8 8E E1 C5 40 FE 66 0B E8 A0
C9 3F 43 D1 5E C0 06 99 84 62 FA 99 4E ED 5D AB`
TurboSHAKE128(M=`FF`, D=`06`, 32):
`8E C9 C6 64 65 ED 0D 4A 6C 35 D1 35 06 71 8D 68
7A 25 CB 05 C7 4C CA 1E 42 50 1A BD 83 87 4A 67`
TurboSHAKE128(M=`FF FF FF`, D=`07`, 32):
`B6 58 57 60 01 CA D9 B1 E5 F3 99 A9 F7 77 23 BB
A0 54 58 04 2D 68 20 6F 72 52 68 2D BA 36 63 ED`
TurboSHAKE128(M=`FF FF FF FF FF FF FF`, D=`0B`, 32):
`8D EE AA 1A EC 47 CC EE 56 9F 65 9C 21 DF A8 E1
12 DB 3C EE 37 B1 81 78 B2 AC D8 05 B7 99 CC 37`
TurboSHAKE128(M=`FF`, D=`30`, 32):
`55 31 22 E2 13 5E 36 3C 32 92 BE D2 C6 42 1F A2
32 BA B0 3D AA 07 C7 D6 63 66 03 28 65 06 32 5B`
TurboSHAKE128(M=`FF FF FF`, D=`7F`, 32):
`16 27 4C C6 56 D4 4C EF D4 22 39 5D 0F 90 53 BD
A6 D2 8E 12 2A BA 15 C7 65 E5 AD 0E 6E AF 26 F9`
TurboSHAKE256(M=`00`^0, D=`1F`, 64):
`36 7A 32 9D AF EA 87 1C 78 02 EC 67 F9 05 AE 13
C5 76 95 DC 2C 66 63 C6 10 35 F5 9A 18 F8 E7 DB
11 ED C0 E1 2E 91 EA 60 EB 6B 32 DF 06 DD 7F 00
2F BA FA BB 6E 13 EC 1C C2 0D 99 55 47 60 0D B0`
TurboSHAKE256(M=`00`^0, D=`1F`, 10032), last 32 bytes:
`AB EF A1 16 30 C6 61 26 92 49 74 26 85 EC 08 2F
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20 72 65 DC CF 2F 43 53 4E 9C 61 BA 0C 9D 1D 75`
TurboSHAKE256(M=ptn(17**0 bytes), D=`1F`, 64):
`3E 17 12 F9 28 F8 EA F1 05 46 32 B2 AA 0A 24 6E
D8 B0 C3 78 72 8F 60 BC 97 04 10 15 5C 28 82 0E
90 CC 90 D8 A3 00 6A A2 37 2C 5C 5E A1 76 B0 68
2B F2 2B AE 74 67 AC 94 F7 4D 43 D3 9B 04 82 E2`
TurboSHAKE256(M=ptn(17**1 bytes), D=`1F`, 64):
`B3 BA B0 30 0E 6A 19 1F BE 61 37 93 98 35 92 35
78 79 4E A5 48 43 F5 01 10 90 FA 2F 37 80 A9 E5
CB 22 C5 9D 78 B4 0A 0F BF F9 E6 72 C0 FB E0 97
0B D2 C8 45 09 1C 60 44 D6 87 05 4D A5 D8 E9 C7`
TurboSHAKE256(M=ptn(17**2 bytes), D=`1F`, 64):
`66 B8 10 DB 8E 90 78 04 24 C0 84 73 72 FD C9 57
10 88 2F DE 31 C6 DF 75 BE B9 D4 CD 93 05 CF CA
E3 5E 7B 83 E8 B7 E6 EB 4B 78 60 58 80 11 63 16
FE 2C 07 8A 09 B9 4A D7 B8 21 3C 0A 73 8B 65 C0`
TurboSHAKE256(M=ptn(17**3 bytes), D=`1F`, 64):
`C7 4E BC 91 9A 5B 3B 0D D1 22 81 85 BA 02 D2 9E
F4 42 D6 9D 3D 42 76 A9 3E FE 0B F9 A1 6A 7D C0
CD 4E AB AD AB 8C D7 A5 ED D9 66 95 F5 D3 60 AB
E0 9E 2C 65 11 A3 EC 39 7D A3 B7 6B 9E 16 74 FB`
TurboSHAKE256(M=ptn(17**4 bytes), D=`1F`, 64):
`02 CC 3A 88 97 E6 F4 F6 CC B6 FD 46 63 1B 1F 52
07 B6 6C 6D E9 C7 B5 5B 2D 1A 23 13 4A 17 0A FD
AC 23 4E AB A9 A7 7C FF 88 C1 F0 20 B7 37 24 61
8C 56 87 B3 62 C4 30 B2 48 CD 38 64 7F 84 8A 1D`
TurboSHAKE256(M=ptn(17**5 bytes), D=`1F`, 64):
`AD D5 3B 06 54 3E 58 4B 58 23 F6 26 99 6A EE 50
FE 45 ED 15 F2 02 43 A7 16 54 85 AC B4 AA 76 B4
FF DA 75 CE DF 6D 8C DC 95 C3 32 BD 56 F4 B9 86
B5 8B B1 7D 17 78 BF C1 B1 A9 75 45 CD F4 EC 9F`
TurboSHAKE256(M=ptn(17**6 bytes), D=`1F`, 64):
`9E 11 BC 59 C2 4E 73 99 3C 14 84 EC 66 35 8E F7
1D B7 4A EF D8 4E 12 3F 78 00 BA 9C 48 53 E0 2C
FE 70 1D 9E 6B B7 65 A3 04 F0 DC 34 A4 EE 3B A8
2C 41 0F 0D A7 0E 86 BF BD 90 EA 87 7C 2D 61 04`
TurboSHAKE256(M=`FF FF FF`, D=`01`, 64):
`D2 1C 6F BB F5 87 FA 22 82 F2 9A EA 62 01 75 FB
02 57 41 3A F7 8A 0B 1B 2A 87 41 9C E0 31 D9 33
AE 7A 4D 38 33 27 A8 A1 76 41 A3 4F 8A 1D 10 03
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AD 7D A6 B7 2D BA 84 BB 62 FE F2 8F 62 F1 24 24`
TurboSHAKE256(M=`FF`, D=`06`, 64):
`73 8D 7B 4E 37 D1 8B 7F 22 AD 1B 53 13 E3 57 E3
DD 7D 07 05 6A 26 A3 03 C4 33 FA 35 33 45 52 80
F4 F5 A7 D4 F7 00 EF B4 37 FE 6D 28 14 05 E0 7B
E3 2A 0A 97 2E 22 E6 3A DC 1B 09 0D AE FE 00 4B`
TurboSHAKE256(M=`FF FF FF`, D=`07`, 64):
`18 B3 B5 B7 06 1C 2E 67 C1 75 3A 00 E6 AD 7E D7
BA 1C 90 6C F9 3E FB 70 92 EA F2 7F BE EB B7 55
AE 6E 29 24 93 C1 10 E4 8D 26 00 28 49 2B 8E 09
B5 50 06 12 B8 F2 57 89 85 DE D5 35 7D 00 EC 67`
TurboSHAKE256(M=`FF FF FF FF FF FF FF`, D=`0B`, 64):
`BB 36 76 49 51 EC 97 E9 D8 5F 7E E9 A6 7A 77 18
FC 00 5C F4 25 56 BE 79 CE 12 C0 BD E5 0E 57 36
D6 63 2B 0D 0D FB 20 2D 1B BB 8F FE 3D D7 4C B0
08 34 FA 75 6C B0 34 71 BA B1 3A 1E 2C 16 B3 C0`
TurboSHAKE256(M=`FF`, D=`30`, 64):
`F3 FE 12 87 3D 34 BC BB 2E 60 87 79 D6 B7 0E 7F
86 BE C7 E9 0B F1 13 CB D4 FD D0 C4 E2 F4 62 5E
14 8D D7 EE 1A 52 77 6C F7 7F 24 05 14 D9 CC FC
3B 5D DA B8 EE 25 5E 39 EE 38 90 72 96 2C 11 1A`
TurboSHAKE256(M=`FF FF FF`, D=`7F`, 64):
`AB E5 69 C1 F7 7E C3 40 F0 27 05 E7 D3 7C 9A B7
E1 55 51 6E 4A 6A 15 00 21 D7 0B 6F AC 0B B4 0C
06 9F 9A 98 28 A0 D5 75 CD 99 F9 BA E4 35 AB 1A
CF 7E D9 11 0B A9 7C E0 38 8D 07 4B AC 76 87 76`
KT128(M=`00`^0, C=`00`^0, 32):
`1A C2 D4 50 FC 3B 42 05 D1 9D A7 BF CA 1B 37 51
3C 08 03 57 7A C7 16 7F 06 FE 2C E1 F0 EF 39 E5`
KT128(M=`00`^0, C=`00`^0, 64):
`1A C2 D4 50 FC 3B 42 05 D1 9D A7 BF CA 1B 37 51
3C 08 03 57 7A C7 16 7F 06 FE 2C E1 F0 EF 39 E5
42 69 C0 56 B8 C8 2E 48 27 60 38 B6 D2 92 96 6C
C0 7A 3D 46 45 27 2E 31 FF 38 50 81 39 EB 0A 71`
KT128(M=`00`^0, C=`00`^0, 10032), last 32 bytes:
`E8 DC 56 36 42 F7 22 8C 84 68 4C 89 84 05 D3 A8
34 79 91 58 C0 79 B1 28 80 27 7A 1D 28 E2 FF 6D`
KT128(M=ptn(1 bytes), C=`00`^0, 32):
`2B DA 92 45 0E 8B 14 7F 8A 7C B6 29 E7 84 A0 58
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EF CA 7C F7 D8 21 8E 02 D3 45 DF AA 65 24 4A 1F`
KT128(M=ptn(17 bytes), C=`00`^0, 32):
`6B F7 5F A2 23 91 98 DB 47 72 E3 64 78 F8 E1 9B
0F 37 12 05 F6 A9 A9 3A 27 3F 51 DF 37 12 28 88`
KT128(M=ptn(17**2 bytes), C=`00`^0, 32):
`0C 31 5E BC DE DB F6 14 26 DE 7D CF 8F B7 25 D1
E7 46 75 D7 F5 32 7A 50 67 F3 67 B1 08 EC B6 7C`
KT128(M=ptn(17**3 bytes), C=`00`^0, 32):
`CB 55 2E 2E C7 7D 99 10 70 1D 57 8B 45 7D DF 77
2C 12 E3 22 E4 EE 7F E4 17 F9 2C 75 8F 0D 59 D0`
KT128(M=ptn(17**4 bytes), C=`00`^0, 32):
`87 01 04 5E 22 20 53 45 FF 4D DA 05 55 5C BB 5C
3A F1 A7 71 C2 B8 9B AE F3 7D B4 3D 99 98 B9 FE`
KT128(M=ptn(17**5 bytes), C=`00`^0, 32):
`84 4D 61 09 33 B1 B9 96 3C BD EB 5A E3 B6 B0 5C
C7 CB D6 7C EE DF 88 3E B6 78 A0 A8 E0 37 16 82`
KT128(M=ptn(17**6 bytes), C=`00`^0, 32):
`3C 39 07 82 A8 A4 E8 9F A6 36 7F 72 FE AA F1 32
55 C8 D9 58 78 48 1D 3C D8 CE 85 F5 8E 88 0A F8`
KT128(`00`^0, C=ptn(1 bytes), 32):
`FA B6 58 DB 63 E9 4A 24 61 88 BF 7A F6 9A 13 30
45 F4 6E E9 84 C5 6E 3C 33 28 CA AF 1A A1 A5 83`
KT128(`FF`, C=ptn(41 bytes), 32):
`D8 48 C5 06 8C ED 73 6F 44 62 15 9B 98 67 FD 4C
20 B8 08 AC C3 D5 BC 48 E0 B0 6B A0 A3 76 2E C4`
KT128(`FF FF FF`, C=ptn(41**2 bytes), 32):
`C3 89 E5 00 9A E5 71 20 85 4C 2E 8C 64 67 0A C0
13 58 CF 4C 1B AF 89 44 7A 72 42 34 DC 7C ED 74`
KT128(`FF FF FF FF FF FF FF`, C=ptn(41**3 bytes), 32):
`75 D2 F8 6A 2E 64 45 66 72 6B 4F BC FC 56 57 B9
DB CF 07 0C 7B 0D CA 06 45 0A B2 91 D7 44 3B CF`
KT128(M=ptn(8191 bytes), C=`00`^0, 32):
`1B 57 76 36 F7 23 64 3E 99 0C C7 D6 A6 59 83 74
36 FD 6A 10 36 26 60 0E B8 30 1C D1 DB E5 53 D6`
KT128(M=ptn(8192 bytes), C=`00`^0, 32):
`48 F2 56 F6 77 2F 9E DF B6 A8 B6 61 EC 92 DC 93
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B9 5E BD 05 A0 8A 17 B3 9A E3 49 08 70 C9 26 C3`
KT128(M=ptn(8192 bytes), C=ptn(8189 bytes), 32):
`3E D1 2F 70 FB 05 DD B5 86 89 51 0A B3 E4 D2 3C
6C 60 33 84 9A A0 1E 1D 8C 22 0A 29 7F ED CD 0B`
KT128(M=ptn(8192 bytes), C=ptn(8190 bytes), 32):
`6A 7C 1B 6A 5C D0 D8 C9 CA 94 3A 4A 21 6C C6 46
04 55 9A 2E A4 5F 78 57 0A 15 25 3D 67 BA 00 AE`
KT256(M=`00`^0, C=`00`^0, 64):
`B2 3D 2E 9C EA 9F 49 04 E0 2B EC 06 81 7F C1 0C
E3 8C E8 E9 3E F4 C8 9E 65 37 07 6A F8 64 64 04
E3 E8 B6 81 07 B8 83 3A 5D 30 49 0A A3 34 82 35
3F D4 AD C7 14 8E CB 78 28 55 00 3A AE BD E4 A9`
KT256(M=`00`^0, C=`00`^0, 128):
`B2 3D 2E 9C EA 9F 49 04 E0 2B EC 06 81 7F C1 0C
E3 8C E8 E9 3E F4 C8 9E 65 37 07 6A F8 64 64 04
E3 E8 B6 81 07 B8 83 3A 5D 30 49 0A A3 34 82 35
3F D4 AD C7 14 8E CB 78 28 55 00 3A AE BD E4 A9
B0 92 53 19 D8 EA 1E 12 1A 60 98 21 EC 19 EF EA
89 E6 D0 8D AE E1 66 2B 69 C8 40 28 9F 18 8B A8
60 F5 57 60 B6 1F 82 11 4C 03 0C 97 E5 17 84 49
60 8C CD 2C D2 D9 19 FC 78 29 FF 69 93 1A C4 D0`
KT256(M=`00`^0, C=`00`^0, 10064), last 64 bytes:
`AD 4A 1D 71 8C F9 50 50 67 09 A4 C3 33 96 13 9B
44 49 04 1F C7 9A 05 D6 8D A3 5F 1E 45 35 22 E0
56 C6 4F E9 49 58 E7 08 5F 29 64 88 82 59 B9 93
27 52 F3 CC D8 55 28 8E FE E5 FC BB 8B 56 30 69`
KT256(M=ptn(1 bytes), C=`00`^0, 64):
`0D 00 5A 19 40 85 36 02 17 12 8C F1 7F 91 E1 F7
13 14 EF A5 56 45 39 D4 44 91 2E 34 37 EF A1 7F
82 DB 6F 6F FE 76 E7 81 EA A0 68 BC E0 1F 2B BF
81 EA CB 98 3D 72 30 F2 FB 02 83 4A 21 B1 DD D0`
KT256(M=ptn(17 bytes), C=`00`^0, 64):
`1B A3 C0 2B 1F C5 14 47 4F 06 C8 97 99 78 A9 05
6C 84 83 F4 A1 B6 3D 0D CC EF E3 A2 8A 2F 32 3E
1C DC CA 40 EB F0 06 AC 76 EF 03 97 15 23 46 83
7B 12 77 D3 E7 FA A9 C9 65 3B 19 07 50 98 52 7B`
KT256(M=ptn(17**2 bytes), C=`00`^0, 64):
`DE 8C CB C6 3E 0F 13 3E BB 44 16 81 4D 4C 66 F6
91 BB F8 B6 A6 1E C0 A7 70 0F 83 6B 08 6C B0 29
D5 4F 12 AC 71 59 47 2C 72 DB 11 8C 35 B4 E6 AA
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21 3C 65 62 CA AA 9D CC 51 89 59 E6 9B 10 F3 BA`
KT256(M=ptn(17**3 bytes), C=`00`^0, 64):
`64 7E FB 49 FE 9D 71 75 00 17 1B 41 E7 F1 1B D4
91 54 44 43 20 99 97 CE 1C 25 30 D1 5E B1 FF BB
59 89 35 EF 95 45 28 FF C1 52 B1 E4 D7 31 EE 26
83 68 06 74 36 5C D1 91 D5 62 BA E7 53 B8 4A A5`
KT256(M=ptn(17**4 bytes), C=`00`^0, 64):
`B0 62 75 D2 84 CD 1C F2 05 BC BE 57 DC CD 3E C1
FF 66 86 E3 ED 15 77 63 83 E1 F2 FA 3C 6A C8 F0
8B F8 A1 62 82 9D B1 A4 4B 2A 43 FF 83 DD 89 C3
CF 1C EB 61 ED E6 59 76 6D 5C CF 81 7A 62 BA 8D`
KT256(M=ptn(17**5 bytes), C=`00`^0, 64):
`94 73 83 1D 76 A4 C7 BF 77 AC E4 5B 59 F1 45 8B
16 73 D6 4B CD 87 7A 7C 66 B2 66 4A A6 DD 14 9E
60 EA B7 1B 5C 2B AB 85 8C 07 4D ED 81 DD CE 2B
40 22 B5 21 59 35 C0 D4 D1 9B F5 11 AE EB 07 72`
KT256(M=ptn(17**6 bytes), C=`00`^0, 64):
`06 52 B7 40 D7 8C 5E 1F 7C 8D CC 17 77 09 73 82
76 8B 7F F3 8F 9A 7A 20 F2 9F 41 3B B1 B3 04 5B
31 A5 57 8F 56 8F 91 1E 09 CF 44 74 6D A8 42 24
A5 26 6E 96 A4 A5 35 E8 71 32 4E 4F 9C 70 04 DA`
KT256(`00`^0, C=ptn(1 bytes), 64):
`92 80 F5 CC 39 B5 4A 5A 59 4E C6 3D E0 BB 99 37
1E 46 09 D4 4B F8 45 C2 F5 B8 C3 16 D7 2B 15 98
11 F7 48 F2 3E 3F AB BE 5C 32 26 EC 96 C6 21 86
DF 2D 33 E9 DF 74 C5 06 9C EE CB B4 DD 10 EF F6`
KT256(`FF`, C=ptn(41 bytes), 64):
`47 EF 96 DD 61 6F 20 09 37 AA 78 47 E3 4E C2 FE
AE 80 87 E3 76 1D C0 F8 C1 A1 54 F5 1D C9 CC F8
45 D7 AD BC E5 7F F6 4B 63 97 22 C6 A1 67 2E 3B
F5 37 2D 87 E0 0A FF 89 BE 97 24 07 56 99 88 53`
KT256(`FF FF FF`, C=ptn(41**2 bytes), 64):
`3B 48 66 7A 50 51 C5 96 6C 53 C5 D4 2B 95 DE 45
1E 05 58 4E 78 06 E2 FB 76 5E DA 95 90 74 17 2C
B4 38 A9 E9 1D DE 33 7C 98 E9 C4 1B ED 94 C4 E0
AE F4 31 D0 B6 4E F2 32 4F 79 32 CA A6 F5 49 69`
KT256(`FF FF FF FF FF FF FF`, C=ptn(41**3 bytes), 64):
`E0 91 1C C0 00 25 E1 54 08 31 E2 66 D9 4A DD 9B
98 71 21 42 B8 0D 26 29 E6 43 AA C4 EF AF 5A 3A
30 A8 8C BF 4A C2 A9 1A 24 32 74 30 54 FB CC 98
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97 67 0E 86 BA 8C EC 2F C2 AC E9 C9 66 36 97 24`
KT256(M=ptn(8191 bytes), C=`00`^0, 64):
`30 81 43 4D 93 A4 10 8D 8D 8A 33 05 B8 96 82 CE
BE DC 7C A4 EA 8A 3C E8 69 FB B7 3C BE 4A 58 EE
F6 F2 4D E3 8F FC 17 05 14 C7 0E 7A B2 D0 1F 03
81 26 16 E8 63 D7 69 AF B3 75 31 93 BA 04 5B 20`
KT256(M=ptn(8192 bytes), C=`00`^0, 64):
`C6 EE 8E 2A D3 20 0C 01 8A C8 7A AA 03 1C DA C2
21 21 B4 12 D0 7D C6 E0 DC CB B5 34 23 74 7E 9A
1C 18 83 4D 99 DF 59 6C F0 CF 4B 8D FA FB 7B F0
2D 13 9D 0C 90 35 72 5A DC 1A 01 B7 23 0A 41 FA`
KT256(M=ptn(8192 bytes), C=ptn(8189 bytes), 64):
`74 E4 78 79 F1 0A 9C 5D 11 BD 2D A7 E1 94 FE 57
E8 63 78 BF 3C 3F 74 48 EF F3 C5 76 A0 F1 8C 5C
AA E0 99 99 79 51 20 90 A7 F3 48 AF 42 60 D4 DE
3C 37 F1 EC AF 8D 2C 2C 96 C1 D1 6C 64 B1 24 96`
KT256(M=ptn(8192 bytes), C=ptn(8190 bytes), 64):
`F4 B5 90 8B 92 9F FE 01 E0 F7 9E C2 F2 12 43 D4
1A 39 6B 2E 73 03 A6 AF 1D 63 99 CD 6C 7A 0A 2D
D7 C4 F6 07 E8 27 7F 9C 9B 1C B4 AB 9D DC 59 D4
B9 2D 1F C7 55 84 41 F1 83 2C 32 79 A4 24 1B 8B`
6. Security Considerations
This document is meant to serve as a stable reference and an
implementation guide for the KangarooTwelve and TurboSHAKE eXtendable
Output Functions. The security assurance of these functions relies
on the cryptanalysis of reduced-round versions of Keccak and they
have the same claimed security strength as their corresponding SHAKE
functions.
+-------------------------------+
| security claim |
+-----------------+-------------------------------+
| TurboSHAKE128 | 128 bits (same as SHAKE128) |
| | |
| KT128 | 128 bits (same as SHAKE128) |
| | |
| TurboSHAKE256 | 256 bits (same as SHAKE256) |
| | |
| KT256 | 256 bits (same as SHAKE256) |
+-----------------+-------------------------------+
To be more precise, KT128 is made of two layers:
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* The inner function TurboSHAKE128. The security assurance of this
layer relies on cryptanalysis. The TurboSHAKE128 function is
exactly Keccak[r=1344, c=256] (as in SHAKE128) reduced to 12
rounds. Any cryptanalysis of reduced-round Keccak is also
cryptanalysis of reduced-round TurboSHAKE128 (provided the number
of rounds attacked is not higher than 12).
* The tree hashing over TurboSHAKE128. This layer is a mode on top
of TurboSHAKE128 that does not introduce any vulnerability thanks
to the use of Sakura coding proven secure in [SAKURA].
This reasoning is detailed and formalized in [KT].
KT256 is structured as KT128, except that it uses TurboSHAKE256 as
inner function. The TurboSHAKE256 function is exactly Keccak[r=1088,
c=512] (as in SHAKE256) reduced to 12 rounds, and the same reasoning
on cryptanalysis applies.
TurboSHAKE128 and KT128 aim at 128-bit security. To achieve 128-bit
security strength, the output L must be chosen long enough so that
there are no generic attacks that violate 128-bit security. So for
128-bit (second) preimage security the output should be at least 128
bits, for 128 bits of security against multi-target preimage attacks
with T targets the output should be at least 128+log_2(T) bits and
for 128-bit collision security the output should be at least 256
bits. Furthermore, when the output length is at least 256 bits,
TurboSHAKE128 and KT128 achieve NIST's post-quantum security level 2
[NISTPQ].
Similarly, TurboSHAKE256 and KT256 aim at 256-bit security. To
achieve 256-bit security strength, the output L must be chosen long
enough so that there are no generic attacks that violate 256-bit
security. So for 256-bit (second) preimage security the output
should be at least 256 bits, for 256 bits of security against multi-
target preimage attacks with T targets the output should be at least
256+log_2(T) bits and for 256-bit collision security the output
should be at least 512 bits. Furthermore, when the output length is
at least 512 bits, TurboSHAKE256 and KT256 achieve NIST's post-
quantum security level 5 [NISTPQ].
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Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128,
TurboSHAKE256, KT128 and KT256 do not suffer from the length
extension weakness, and therefore do not require the use of the HMAC
construction for instance when used for MAC computation [FIPS198].
Also, they can naturally be used as a key derivation function. The
input must be an injective encoding of secret and diversification
material, and the output can be taken as the derived key(s). The
input does not need to be uniformly distributed, e.g., it can be a
shared secret produced by the Diffie-Hellman or ECDH protocol, but it
needs to have sufficient min-entropy.
Lastly, as KT128 and KT256 use TurboSHAKE with three values for D,
namely 0x06, 0x07, and 0x0B. Protocols that use both KT128 and
TurboSHAKE128, or both KT256 and TurboSHAKE256, SHOULD avoid using
these three values for D.
7. References
7.1. Normative References
[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>.
[FIPS202] National Institute of Standards and Technology, "FIPS PUB
202 - SHA-3 Standard: Permutation-Based Hash and
Extendable-Output Functions",
WWW http://dx.doi.org/10.6028/NIST.FIPS.202, August 2015.
[SP800-185]
National Institute of Standards and Technology, "NIST
Special Publication 800-185 SHA-3 Derived Functions:
cSHAKE, KMAC, TupleHash and ParallelHash",
WWW https://doi.org/10.6028/NIST.SP.800-185, December
2016.
7.2. Informative References
[TURBOSHAKE]
Bertoni, G., Daemen, J., Hoffert, S., Peeters, M., Van
Assche, G., Van Keer, R., and B. Viguier, "TurboSHAKE",
WWW http://eprint.iacr.org/2023/342, March 2023.
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[KT] Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., Van
Keer, R., and B. Viguier, "KangarooTwelve: fast hashing
based on Keccak-p", WWW https://link.springer.com/
chapter/10.1007/978-3-319-93387-0_21,
WWW http://eprint.iacr.org/2016/770.pdf, July 2018.
[SAKURA] Bertoni, G., Daemen, J., Peeters, M., and G. Van Assche,
"Sakura: a flexible coding for tree hashing", WWW
https://link.springer.com/
chapter/10.1007/978-3-319-07536-5_14,
WWW http://eprint.iacr.org/2013/231.pdf, June 2014.
[KECCAK_CRYPTANALYSIS]
Keccak Team, "Summary of Third-party cryptanalysis of
Keccak", WWW https://www.keccak.team/third_party.html,
2022.
[XKCP] Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., and
R. Van Keer, "eXtended Keccak Code Package",
WWW https://github.com/XKCP/XKCP, December 2022.
[NISTPQ] National Institute of Standards and Technology,
"Submission Requirements and Evaluation Criteria for the
Post-Quantum Cryptography Standardization Process", WWW
https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-
Cryptography/documents/call-for-proposals-final-dec-
2016.pdf, December 2016.
[FIPS180] National Institute of Standards and Technology (NIST),
"Secure Hash Standard (SHS)", FIPS PUB 180-4,
WWW https://doi.org/10.6028/NIST.FIPS.180-4, August 2015.
[FIPS198] National Institute of Standards and Technology (NIST),
"The Keyed-Hash Message Authentication Code (HMAC)", FIPS
PUB 198-1, WWW https://doi.org/10.6028/NIST.FIPS.198-1,
July 2008.
Appendix A. Pseudocode
The sub-sections of this appendix contain pseudocode definitions of
TurboSHAKE128, TurboSHAKE256 and KangarooTwelve. Standalone Python
versions are also available in the Keccak Code Package [XKCP] and in
[KT]
A.1. Keccak-p[1600,n_r=12]
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KP(state):
RC[0] = `8B 80 00 80 00 00 00 00`
RC[1] = `8B 00 00 00 00 00 00 80`
RC[2] = `89 80 00 00 00 00 00 80`
RC[3] = `03 80 00 00 00 00 00 80`
RC[4] = `02 80 00 00 00 00 00 80`
RC[5] = `80 00 00 00 00 00 00 80`
RC[6] = `0A 80 00 00 00 00 00 00`
RC[7] = `0A 00 00 80 00 00 00 80`
RC[8] = `81 80 00 80 00 00 00 80`
RC[9] = `80 80 00 00 00 00 00 80`
RC[10] = `01 00 00 80 00 00 00 00`
RC[11] = `08 80 00 80 00 00 00 80`
for x from 0 to 4
for y from 0 to 4
lanes[x][y] = state[8*(x+5*y):8*(x+5*y)+8]
for round from 0 to 11
# theta
for x from 0 to 4
C[x] = lanes[x][0]
C[x] ^= lanes[x][1]
C[x] ^= lanes[x][2]
C[x] ^= lanes[x][3]
C[x] ^= lanes[x][4]
for x from 0 to 4
D[x] = C[(x+4) mod 5] ^ ROL64(C[(x+1) mod 5], 1)
for y from 0 to 4
for x from 0 to 4
lanes[x][y] = lanes[x][y]^D[x]
# rho and pi
(x, y) = (1, 0)
current = lanes[x][y]
for t from 0 to 23
(x, y) = (y, (2*x+3*y) mod 5)
(current, lanes[x][y]) =
(lanes[x][y], ROL64(current, (t+1)*(t+2)/2))
# chi
for y from 0 to 4
for x from 0 to 4
T[x] = lanes[x][y]
for x from 0 to 4
lanes[x][y] = T[x] ^((not T[(x+1) mod 5]) & T[(x+2) mod 5])
# iota
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lanes[0][0] ^= RC[round]
state = `00`^0
for x from 0 to 4
for y from 0 to 4
state = state || lanes[x][y]
return state
end
where ROL64(x, y) is a rotation of the 'x' 64-bit word toward the
bits with higher indexes by 'y' positions. The 8-bytes byte-string x
is interpreted as a 64-bit word in little-endian format.
A.2. TurboSHAKE128
TurboSHAKE128(message, separationByte, outputByteLen):
offset = 0
state = `00`^200
input = message || separationByte
# === Absorb complete blocks ===
while offset < |input| - 168
state ^= input[offset : offset + 168] || `00`^32
state = KP(state)
offset += 168
# === Absorb last block and treatment of padding ===
LastBlockLength = |input| - offset
state ^= input[offset:] || `00`^(200-LastBlockLength)
state ^= `00`^167 || `80` || `00`^32
state = KP(state)
# === Squeeze ===
output = `00`^0
while outputByteLen > 168
output = output || state[0:168]
outputByteLen -= 168
state = KP(state)
output = output || state[0:outputByteLen]
return output
A.3. TurboSHAKE256
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TurboSHAKE256(message, separationByte, outputByteLen):
offset = 0
state = `00`^200
input = message || separationByte
# === Absorb complete blocks ===
while offset < |input| - 136
state ^= input[offset : offset + 136] || `00`^64
state = KP(state)
offset += 136
# === Absorb last block and treatment of padding ===
LastBlockLength = |input| - offset
state ^= input[offset:] || `00`^(200-LastBlockLength)
state ^= `00`^135 || `80` || `00`^64
state = KP(state)
# === Squeeze ===
output = `00`^0
while outputByteLen > 136
output = output || state[0:136]
outputByteLen -= 136
state = KP(state)
output = output || state[0:outputByteLen]
return output
A.4. KT128
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KT128(inputMessage, customString, outputByteLen):
S = inputMessage || customString
S = S || length_encode( |customString| )
if |S| <= 8192
return TurboSHAKE128(S, `07`, outputByteLen)
else
# === Kangaroo hopping ===
FinalNode = S[0:8192] || `03` || `00`^7
offset = 8192
numBlock = 0
while offset < |S|
blockSize = min( |S| - offset, 8192)
CV = TurboSHAKE128(S[offset : offset + blockSize], `0B`, 32)
FinalNode = FinalNode || CV
numBlock += 1
offset += blockSize
FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`
return TurboSHAKE128(FinalNode, `06`, outputByteLen)
end
A.5. KT256
KT256(inputMessage, customString, outputByteLen):
S = inputMessage || customString
S = S || length_encode( |customString| )
if |S| <= 8192
return TurboSHAKE256(S, `07`, outputByteLen)
else
# === Kangaroo hopping ===
FinalNode = S[0:8192] || `03` || `00`^7
offset = 8192
numBlock = 0
while offset < |S|
blockSize = min( |S| - offset, 8192)
CV = TurboSHAKE256(S[offset : offset + blockSize], `0B`, 64)
FinalNode = FinalNode || CV
numBlock += 1
offset += blockSize
FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`
return TurboSHAKE256(FinalNode, `06`, outputByteLen)
end
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Authors' Addresses
Benoît Viguier
ABN AMRO Bank
Groenelaan 2
Amstelveen
Email: cs.ru.nl@viguier.nl
David Wong (editor)
zkSecurity
Email: davidwong.crypto@gmail.com
Gilles Van Assche (editor)
STMicroelectronics
Email: gilles.vanassche@st.com
Quynh Dang (editor)
National Institute of Standards and Technology
Email: quynh.dang@nist.gov
Joan Daemen (editor)
Radboud University
Email: joan@cs.ru.nl
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