Crypto Forum
Internet Research Task Force (IRTF) B. Viguier
Internet-Draft
Request for Comments: 9861 ABN AMRO Bank
Intended status:
Category: Informational D. Wong, Ed.
Expires: 25 August 2025
ISSN: 2070-1721 zkSecurity
G. Van Assche, Ed.
STMicroelectronics
Q. Dang, Ed.
NIST
J. Daemen, Ed.
Radboud University
21 February
September 2025
KangarooTwelve and TurboSHAKE
draft-irtf-cfrg-kangarootwelve-17
Abstract
This document defines four eXtendable Output eXtendable-Output Functions (XOF), (XOFs), hash
functions with output of arbitrary length, named TurboSHAKE128,
TurboSHAKE256, KT128 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 is a product of the Crypto Forum Research Group. It
builds up on the definitions of the permutations and of the sponge
construction in [FIPS 202], NIST FIPS 202 and is meant to serve as a stable
reference and an implementation guide.
Status of This Memo
This Internet-Draft document is submitted in full conformance with not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the
provisions Internet Research Task Force
(IRTF). The IRTF publishes the results of BCP 78 Internet-related research
and BCP 79.
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deployment. This RFC represents the consensus of the Crypto Forum
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approved for publication by the IRSG are draft documents valid not candidates for a maximum any level
of Internet Standard; see Section 2 of RFC 7841.
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This Internet-Draft will expire on 25 August 2025.
https://www.rfc-editor.org/info/rfc9861.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Conventions . . . . . . . . . . . . . . . . . . . . . . . 4
2. TurboSHAKE . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. Specifications . . . . . . . . . . . . . . . . . . . . . 6
3. KangarooTwelve: Tree hashing Hashing over TurboSHAKE . . . . . . . . 8
3.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2. Specification of KT128 . . . . . . . . . . . . . . . . . 8
3.3. length_encode( x ) . . . . . . . . . . . . . . . . . . . 11
3.4. Specification of KT256 . . . . . . . . . . . . . . . . . 11
4. Message authentication codes . . . . . . . . . . . . . . . . 11 Authentication Codes
5. Test vectors . . . . . . . . . . . . . . . . . . . . . . . . 12 Vectors
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 20
7. Security Considerations . . . . . . . . . . . . . . . . . . . 21
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 22
8.1. Normative References . . . . . . . . . . . . . . . . . . 22
8.2. Informative References . . . . . . . . . . . . . . . . . 23
Appendix A. Pseudocode . . . . . . . . . . . . . . . . . . . . . 24
A.1. Keccak-p[1600,n_r=12] . . . . . . . . . . . . . . . . . . 24
A.2. TurboSHAKE128 . . . . . . . . . . . . . . . . . . . . . . 25
A.3. TurboSHAKE256 . . . . . . . . . . . . . . . . . . . . . . 26
A.4. KT128 . . . . . . . . . . . . . . . . . . . . . . . . . . 27
A.5. KT256 . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 29
1. Introduction
This document defines the TurboSHAKE128, TurboSHAKE256 [TURBOSHAKE],
KT128
KT128, and KT256 [KT] eXtendable Output eXtendable-Output Functions (XOF), (XOFs), i.e., a hash
function generalization generalizations 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.
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 two times 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 KT128, and KT256 builds
on the public scrutiny that Keccak has received since its publication
[KECCAK_CRYPTANALYSIS][TURBOSHAKE].
[KECCAK_CRYPTANALYSIS] [TURBOSHAKE].
With respect to functions defined in [FIPS202] and [SP800-185] functions, [SP800-185],
TurboSHAKE128, TurboSHAKE256, KT128 KT128, and KT256 feature the following
advantages:
* Unlike SHA3-224, SHA3-256, SHA3-384, and SHA3-512, the TurboSHAKE
and KangarooTwelve functions have an extendable output.
* Unlike any [FIPS202] defined function, similarly functions in [FIPS202], and similar to functions
defined in
[SP800-185], KT128 and KT256 allow the use of a customization
string.
* Unlike any functions in [FIPS202] and [SP800-185] functions but except for
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].
With respect to SHA-256 and SHA-512 SHA-256, SHA-512, and other [FIPS180] functions, functions defined in
[FIPS180], TurboSHAKE128, TurboSHAKE256, KT128 KT128, and KT256 feature the
following advantages:
* Unlike [FIPS180] functions, any functions in [FIPS180], 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, when used in a mask
generation function (MGF) construction, produce output half as
fast as they process input.
* Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128,
TurboSHAKE256, KT128 KT128, and KT256 do not suffer from the length
extension weakness.
* Unlike any [FIPS180] functions, functions in [FIPS180], TurboSHAKE128, TurboSHAKE256,
KT128
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.
This document represents the consensus of the Crypto Forum Research
Group (CFRG) in the IRTF. It is not an IETF product and is not a
standard.
1.1. Conventions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
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. byte string.
* a||b denotes the concatenation of two strings strings, a and b. For
example, `10`||`F1` = `10 F1` 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 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
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 the remainder 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 eXtendable-Output Functions (XOF). (XOFs).
Internally, it makes use of the sponge construction, parameterized by
two integers, the rate and the capacity, that sum to the permutation
width (here, 1600 bits). The rate gives the number of bits processed
or produced per call to the permutation, whereas the capacity
determines the security level, level; see [FIPS202] for more details. This
document focuses on only two instances, namely, namely TurboSHAKE128 and
TurboSHAKE256. (Note that the original definition includes a wider
range of instances parameterized by their capacity [TURBOSHAKE].)
An instance of
A TurboSHAKE instance takes as input parameters a byte-string byte string M, an OPTIONAL byte D D, and
a positive integer L where as input parameters, where:
* M byte-string, byte string is the Message and Message,
* D byte in the range [`01`, `02`, .. , `7F`], `7F`] is an OPTIONAL Domain domain
separation byte byte, and
* L positive integer, integer is the requested number of output bytes.
Conceptually, a an XOF can be viewed as a hash function with an
infinitely long output truncated to L bytes. This means that calling
a
an 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).
By default, the Domain 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 as specified in FIPS 202, 202; see Sections 3.3 and 3.4 of
[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, bits and has a capacity of 512 bits or 64
bytes.
+-------------+--------------+
+---------------+===========+==========+
| | Rate | Capacity |
+----------------+-------------+--------------+
+===============+===========+==========+
| TurboSHAKE128 | 168 Bytes | 32 Bytes |
| | | |
+===============+-----------+----------+
| TurboSHAKE256 | 136 Bytes | 64 Bytes |
+----------------+-------------+--------------+
+===============+-----------+----------+
Table 1
We now describe the operations inside TurboSHAKE128.
* First First, the input M' is formed by appending the domain separation
byte D to the message M.
* If the length of M' is not a multiple of 168 bytes bytes, then it is
padded with zeros at the end to make it a multiple of 168 bytes.
If M' is already a multiple of 168 bytes bytes, then no padding is
added.
Then 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 phase, which
processes the padded input M' M', and the squeezing phase that phase, which
produces the output.
* In the absorbing phase phase, the state is initialized to all-zero. 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 phase, the output is formed by taking the first
168 bytes of the state, applying KP to the state, and repeating as
many times as is necessary.
TurboSHAKE256 performs the same steps but makes use of 136-byte
blocks with respect to the 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 (hence,
it cannot be `00`). Additionally, it must leave room for the second
bit of padding (hence (hence, it cannot have the MSB most significant bit (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 Appendices A.2 and Appendix A.3. A.3, respectively.
3. KangarooTwelve: Tree hashing Hashing over TurboSHAKE
3.1. Interface
KangarooTwelve is a family of eXtendable Output eXtendable-Output Functions (XOF) (XOFs)
consisting of the KT128 and KT256 instances. A KangarooTwelve
instance takes as input parameters two byte-strings byte strings (M, C) and a positive integer L where as
input parameters, where:
* M byte-string, byte string is the Message and Message,
* C byte-string, byte string is an OPTIONAL Customization string string, and
* L positive integer, integer is 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. (e.g., URI,
ODI...).
Original Dialog Identifier (ODI), etc.). It can serve the same
purpose as TurboSHAKE's D input parameter (see Section 2.1), 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 the input
and/or output provided incrementally incrementally, 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. 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 platform, such as SIMD single
instruction, multiple data (SIMD) instructions.
CV_i = TurboSHAKE128( S_i, `0B`, 32 )
Compute the final node: FinalNode.
* If |S| <= 8192 bytes, FinalNode = S S.
* Otherwise Otherwise, compute FinalNode as follows:
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 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 as TSHK128 and l_e( x ) :
+--------------+
| 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` |
+--------------------+------------------+
+------------------+------+
Table 2
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
For example, length_encode(0) = `00`, length_encode(12) = `0C 01` 01`,
and length_encode(65538) = `01 00 02 03` 03`.
A pseudocode version is as follows 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 64 bytes 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 Authentication Codes
Implementing a MAC Message Authentication Code (MAC) with KT128 or KT256
MAY use a hash-then-MAC construction. This document defines and
recommends a method called HopMAC:
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, Hashed Message Authentication Code (HMAC), HopMAC
consists of two calls: an inner call compressing the message M and
the optional customization string C to a digest, 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). (SCAs). Consequently, in an implementation that has to
protect the HopMAC key against SCA an SCA, only the outer call does need needs
protection, and this amounts to a single execution of the underlying
permutation (assuming the key length is at most 69 bytes).
In any case, TurboSHAKE128, TurboSHAKE256, KT128 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 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. bytes, for example:
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`
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`
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
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
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
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
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
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
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. IANA Considerations
In the Named "Named Information Hash Algorithm Registry, Registry", k12-256 refers to
the hash function obtained by evaluating KT128 on the input message
with default C (the empty string) and L = 32 bytes (256 bits).
Similarly, k12-512 refers to the hash function obtained by evaluating
KT256 on the input message with default C (the empty string) and L =
64 bytes (512 bits).
In the COSE Algorithms "COSE Algorithms" registry, IANA has added the following
entries are assigned
to for TurboSHAKE and KangarooTwelve:
+---------------+-------+-------------------+--------------+
+===============+=======+===================+==============+
| Name | Value | Description | Capabilities |
+---------------+-------+-------------------+--------------+
+===============+=======+===================+==============+
| TurboSHAKE128 | -261 | TurboSHAKE128 XOF | [kty] |
| | | | |
+---------------+-------+-------------------+--------------+
| TurboSHAKE256 | -262 | TurboSHAKE256 XOF | [kty] |
| | | | |
+---------------+-------+-------------------+--------------+
| KT128 | -263 | KT128 XOF | [kty] |
| | | | |
+---------------+-------+-------------------+--------------+
| KT256 | -264 | KT256 XOF | [kty] |
+---------------+-------+-------------------+--------------+
Table 3
7. Security Considerations
This document is meant to serve as a stable reference and an
implementation guide for the KangarooTwelve and TurboSHAKE eXtendable
Output
eXtendable-Output Functions. The security assurance of these
functions relies on the cryptanalysis of reduced-round versions of Keccak
Keccak, and they have the same claimed security strength as their
corresponding SHAKE functions.
+-------------------------------+
+---------------+=============================+
| security claim |
+-----------------+-------------------------------+ 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) |
+-----------------+-------------------------------+
+===============+-----------------------------+
Table 4
To be more precise, KT128 is made of two layers:
* 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
the 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 security, the output should be at least 128
bits,
bits; for 128 bits of security against multi-target preimage attacks
with T targets targets, the output should be at least 128+log_2(T) bits bits; and
for 128-bit collision security 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 security, the output
should be at least 256 bits, bits; for 256 bits of security against multi-
target preimage attacks with T targets targets, the output should be at least
256+log_2(T) bits bits; and for 256-bit collision security 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].
Unlike the SHA-256 and SHA-512 functions, TurboSHAKE128,
TurboSHAKE256, KT128 KT128, and KT256 do not suffer from the length
extension weakness, weakness and therefore do not require the use of the HMAC
construction
construction, for instance 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 Elliptic Curve
Diffie-Hellman (ECDH) protocol, but it needs to have sufficient min-entropy. 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.
8. References
8.1. 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>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[FIPS202] National Institute of Standards and Technology, "FIPS PUB
202 - SHA-3 NIST, "SHA-3 Standard: Permutation-Based Hash and
Extendable-Output Functions",
WWW http://dx.doi.org/10.6028/NIST.FIPS.202, NIST FIPS 202,
DOI 10.6028/NIST.FIPS.202, August 2015. 2015,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.202.pdf>.
[SP800-185]
National Institute of Standards
Kelsey, J., Chang, S., and Technology, "NIST
Special Publication 800-185 SHA-3 R. Perlner, "SHA-3 Derived
Functions: cSHAKE, KMAC, TupleHash and ParallelHash",
WWW https://doi.org/10.6028/NIST.SP.800-185,
National Institute of Standards and Technology, NIST
SP 800-185, DOI 10.6028/NIST.SP.800-185, December
2016. 2016,
<https://doi.org/10.6028/NIST.SP.800-185>.
8.2. 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,
Cryptology ePrint Archive, Paper 2023/342, March 2023. 2023,
<http://eprint.iacr.org/2023/342>.
[KT] Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., Van
Keer, R., and B. Viguier, "KangarooTwelve: fast hashing
based 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. Applied Cryptography and Network
Security (ACNS 2018), Lecture Notes in Computer Science,
vol. 10892, pp. 400-418, DOI 10.1007/978-3-319-93387-0_21,
June 2018, <https://link.springer.com/
chapter/10.1007/978-3-319-93387-0_21>.
[SAKURA] Bertoni, G., Daemen, J., Peeters, M., and G. Van Assche,
"Sakura: a flexible coding 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. Tree Hashing", Applied
Cryptography and Network Security (ACNS 2014), Lecture
Notes in Computer Science, vol. 8479, pp. 217-234,
DOI 10.1007/978-3-319-07536-5_14, 2014,
<https://link.springer.com/
chapter/10.1007/978-3-319-07536-5_14>.
[KECCAK_CRYPTANALYSIS]
Keccak Team, "Summary of Third-party cryptanalysis of
Keccak", WWW https://www.keccak.team/third_party.html,
2022. <https://www.keccak.team/third_party.html>.
[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. 2022,
<https://github.com/XKCP/XKCP>.
[NISTPQ] National Institute of Standards and Technology, NIST, "Submission Requirements and Evaluation Criteria for
the Post-Quantum Cryptography Standardization Process", WWW
https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-
<https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-
Cryptography/documents/call-for-proposals-final-dec-
2016.pdf, December 2016.
2016.pdf>.
[FIPS180] National Institute of Standards and Technology (NIST), NIST, "Secure Hash Standard (SHS)", Standard", NIST FIPS PUB 180-4,
WWW https://doi.org/10.6028/NIST.FIPS.180-4,
DOI 10.6028/NIST.FIPS.180-4, August 2015. 2015,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.180-4.pdf>.
[FIPS198] National Institute of Standards and Technology (NIST), NIST, "The Keyed-Hash Message Authentication Code (HMAC)",
NIST FIPS
PUB 198-1, WWW https://doi.org/10.6028/NIST.FIPS.198-1, DOI 10.6028/NIST.FIPS.198-1, July 2008. 2008,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.198-1.pdf>.
Appendix A. Pseudocode
The sub-sections subsections of this appendix contain pseudocode definitions of
TurboSHAKE128, TurboSHAKE256 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]
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
lanes[0][0] ^= RC[round]
state = `00`^0
for y from 0 to 4
for x 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 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
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
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
Authors' Addresses
Benoît Viguier
ABN AMRO Bank
Groenelaan 2
Amstelveen
Netherlands
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