KangarooTwelve and TurboSHAKE
draft-irtf-cfrg-kangarootwelve-09
The information below is for an old version of the document.
| Document | Type |
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|---|---|---|---|
| Authors | Benoît Viguier , David Wong , Gilles Van Assche , Quynh Dang , Joan Daemen | ||
| Last updated | 2023-02-17 | ||
| Replaces | draft-viguier-kangarootwelve | ||
| RFC stream | Internet Research Task Force (IRTF) | ||
| Formats | |||
| Additional resources | Mailing list discussion | ||
| Stream | IRTF state | Active RG Document | |
| Consensus boilerplate | Yes | ||
| Document shepherd | Nick Sullivan | ||
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| Send notices to | Nick Sullivan <nick@cloudflare.com> |
draft-irtf-cfrg-kangarootwelve-09
Crypto Forum B. Viguier
Internet-Draft ABN AMRO Bank
Intended status: Informational D. Wong, Ed.
Expires: 21 August 2023 O(1) Labs
G. Van Assche, Ed.
STMicroelectronics
Q. Dang, Ed.
NIST
J. Daemen, Ed.
Radboud University
17 February 2023
KangarooTwelve and TurboSHAKE
draft-irtf-cfrg-kangarootwelve-09
Abstract
This document defines three eXtendable Output Functions (XOF), hash
functions with output of arbitrary length, named TurboSHAKE128,
TurboSHAKE256 and KangarooTwelve.
All three functions provide efficient and secure hashing primitive,
and the later is 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
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
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 21 August 2023.
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Copyright Notice
Copyright (c) 2023 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
extracted from this document must include Revised BSD License text as
described in Section 4.e of the Trust Legal Provisions and are
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 . . . . . . . . . . . . . . . . . . . . . 5
3. KangarooTwelve: Tree hashing over TurboSHAKE128 . . . . . . . 7
3.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Specification . . . . . . . . . . . . . . . . . . . . . . 8
3.3. length_encode( x ) . . . . . . . . . . . . . . . . . . . 10
4. Test vectors . . . . . . . . . . . . . . . . . . . . . . . . 10
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 15
6. Security Considerations . . . . . . . . . . . . . . . . . . . 16
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.1. Normative References . . . . . . . . . . . . . . . . . . 17
7.2. Informative References . . . . . . . . . . . . . . . . . 17
Appendix A. Pseudocode . . . . . . . . . . . . . . . . . . . . . 18
A.1. Keccak-p[1600,n_r=12] . . . . . . . . . . . . . . . . . . 18
A.2. TurboSHAKE128 . . . . . . . . . . . . . . . . . . . . . . 20
A.3. KangarooTwelve . . . . . . . . . . . . . . . . . . . . . 20
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 21
1. Introduction
This document defines the TurboSHAKE128, TurboSHAKE256 [TURBOSHAKE]
and KangarooTwelve [K12] eXtendable Output Functions (XOF), i.e. a
generalization of a hash function 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 SHAKE and SHA-3.
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TurboSHAKE is a sponge function which makes use of Keccak-
p[n_r=12,b=1600], a 12-round-reduced version of the permutation used
in SHA-3. Similarly to SHAKE, it proposes two security strength: 128
bit for TurboSHAKE128 and 256 bits for TurboSHAKE256. The number of
round being halved of SHAKE makes TurboSHAKE roughtly two-times
faster than their SHA-3 equivalent.
The SHA-3 functions process data in a serial manner and are unable to
optimally exploit parallelism available in modern CPU architectures.
Similar to ParallelHash [SP800-185], KangarooTwelve splits the input
message into fragments to exploit available parallelism. It then
applies TurboSHAKE128 on each of them separately before applying
TurboSHAKE128 again on the concatenation of the first fragment and
the digests. It makes use of Sakura coding for ensuring soundness of
the tree hashing mode [SAKURA]. The TurboSHAKE speed-up over SHA-3
directly translates in KangarooTwelve, making it faster than
ParallelHash.
The security of both TurboSHAKE128, TurboSHAKE256 and KangarooTwelve
builds up on the scrutiny that Keccak has received since its
publication [KECCAK_CRYPTANALYSIS].
With respect to [FIPS202] and [SP800-185] functions, TurboSHAKE128,
TurboSHAKE256 and KangarooTwelve feature the following advantages:
* Unlike SHA3-224, SHA3-256, SHA3-384, SHA3-512; TurboSHAKE and
KangarooTwelve have an extendable output.
* Unlike any [FIPS202] defined function, similarly to functions
defined in [SP800-185], KangarooTwelve allows the use of a
customization string.
* Unlike any [FIPS202] and [SP800-185] functions but ParallelHash,
KangarooTwelve splits the input message into fragments to exploit
available parallelism.
* Unlike ParallelHash, KangarooTwelve does not have overhead when
processing short messages.
* The permutation in TurboSHAKE is Keccak-p[n_r=12] and hence has
half the number of rounds of the one used in SHA3, making it
faster than any function defined in [FIPS202]. KangarooTwelve
immediately benefits from this speeds up, improving over [FIPS202]
and [SP800-185].
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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
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.
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2. TurboSHAKE
2.1. Interface
TurboSHAKE is a family of eXtendable Output Functions (XOF). It
takes as input 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, the requested number of output bytes.
By default, the Domain separation byte is `01`. For an API that does
not support a domain separation byte, D MUST be the `01`.
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 instances 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 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 message M is appended with the domain separation byte D,
forming the input.
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* Non-multiple of 168-bytes-length inputs are padded with zeroes to
the next multiple of 168 bytes while inputs multiple of 168 bytes
are kept as is. Then a byte `80` is XORed to the last byte of the
padded message and the resulting string is split into a sequence
of 168-byte blocks.
* Inputs of length 0 bytes do not happen 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 input 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-bytes
blocks with respect to padding, absorbing, and squeezing phases.
The definition of the function TurboSHAKE equivalently implements the
pad10*1 rule. While M can be empty, the D byte 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
[K12].
A pseudocode version is available as follows:
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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
end
3. KangarooTwelve: Tree hashing over TurboSHAKE128
3.1. Interface
KangarooTwelve is an eXtendable Output Function (XOF). It takes as
input two byte-strings (M, C) and a positive integer L where
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...)
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By default, the Customization string is the empty string. For an API
that does not support a customization string input, C MUST be the
empty string.
3.2. Specification
On top of the sponge function TurboSHAKE128, KangarooTwelve 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
SHOULD 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:
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, KangarooTwelve output is retrieved:
* If |S| <= 8192 bytes, from TurboSHAKE128( FinalNode, `07`, L )
KangarooTwelve( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L )
* Otherwise from TurboSHAKE128( FinalNode, `06`, L )
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KangarooTwelve( M, C, L ) = TurboSHAKE128( FinalNode, `06`, L )
The following figure illustrates the computation flow of
KangarooTwelve for |S| <= 8192 bytes:
+--------------+ TurboSHAKE128(.., `07`, L)
| S |-----------------------------> output
+--------------+
The following figure illustrates the computation flow of
KangarooTwelve for |S| > 8192 bytes and where TurboSHAKE128 and
length_encode( x ) are abbreviated as respectively 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.3.
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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` |
+--------------------+------------------+
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 from i=0..n-1 of 256**i * x_i
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.
length_encode(x):
S = `00`^0
while x > 0
S = x mod 256 || S
x = x / 256
S = S || length(S)
return S
end
4. Test vectors
Test vectors are based on the repetition of the pattern `00 01 .. FA`
with a specific length. ptn(n) defines a string by repeating the
pattern `00 01 .. FA` as many times as necessary and truncated to n
bytes e.g.
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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=`07`, 32):
`5A 22 3A D3 0B 3B 8C 66 A2 43 04 8C FC ED 43 0F
54 E7 52 92 87 D1 51 50 B9 73 13 3A DF AC 6A 2F`
TurboSHAKE128(M=`00`^0, D=`07`, 64):
`5A 22 3A D3 0B 3B 8C 66 A2 43 04 8C FC ED 43 0F
54 E7 52 92 87 D1 51 50 B9 73 13 3A DF AC 6A 2F
FE 27 08 E7 30 61 E0 9A 40 00 16 8B A9 C8 CA 18
13 19 8F 7B BE D4 98 4B 41 85 F2 C2 58 0E E6 23`
TurboSHAKE128(M=`00`^0, D=`07`, 10032), last 32 bytes:
`75 93 A2 80 20 A3 C4 AE 0D 60 5F D6 1F 5E B5 6E
CC D2 7C C3 D1 2F F0 9F 78 36 97 72 A4 60 C5 5D`
TurboSHAKE128(M=ptn(1 bytes), D=`07`, 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`
TurboSHAKE128(M=ptn(17 bytes), D=`07`, 32):
`AC BD 4A A5 75 07 04 3B CE E5 5A D3 F4 85 04 D8
15 E7 07 FE 82 EE 3D AD 6D 58 52 C8 92 0B 90 5E`
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TurboSHAKE128(M=ptn(17**2 bytes), D=`07`, 32):
`7A 4D E8 B1 D9 27 A6 82 B9 29 61 01 03 F0 E9 64
55 9B D7 45 42 CF AD 74 0E E3 D9 B0 36 46 9E 0A`
TurboSHAKE128(M=ptn(17**3 bytes), D=`07`, 32):
`74 52 ED 0E D8 60 AA 8F E8 E7 96 99 EC E3 24 F8
D9 32 71 46 36 10 DA 76 80 1E BC EE 4F CA FE 42`
TurboSHAKE128(M=ptn(17**4 bytes), D=`07`, 32):
`CA 5F 1F 3E EA C9 92 CD C2 AB EB CA 0E 21 67 65
DB F7 79 C3 C1 09 46 05 5A 94 AB 32 72 57 35 22`
TurboSHAKE128(M=ptn(17**5 bytes), D=`07`, 32):
`E9 88 19 3F B9 11 9F 11 CD 34 46 79 14 E2 A2 6D
A9 BD F9 6C 8B EF 07 6A EE AD 1A 89 7B 86 63 83`
TurboSHAKE128(M=ptn(17**6 bytes), D=`07`, 32):
`9C 0F FB 98 7E EE ED AD FA 55 94 89 87 75 6D 09
0B 67 CC B6 12 36 E3 06 AC 8A 24 DE 1D 0A F7 74`
TurboSHAKE128(M=`00`^0, D=`06`, 32):
`C7 90 29 30 6B FA 2F 17 83 6A 3D 65 16 D5 56 63
40 FE A6 EB 1A 11 39 AD 90 0B 41 24 3C 49 4B 37`
TurboSHAKE128(M=`00`^0, D=`0B`, 32):
`8B 03 5A B8 F8 EA 7B 41 02 17 16 74 58 33 2E 46
F5 4B E4 FF 83 54 BA F3 68 71 04 A6 D2 4B 0E AB`
TurboSHAKE128(M=`00`^0, D=`06`, 32):
`C7 90 29 30 6B FA 2F 17 83 6A 3D 65 16 D5 56 63
40 FE A6 EB 1A 11 39 AD 90 0B 41 24 3C 49 4B 37`
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=`06`, 32):
`3D 03 98 8B B5 9E 68 18 51 A1 92 F4 29 AE 03 98
8E 8F 44 4B C0 60 36 A3 F1 A7 D2 CC D7 58 D1 74`
TurboSHAKE128(M=`FF FF FF FF FF FF FF`, D=`06`, 32):
`05 D9 AE 67 3D 5F 0E 48 BB 2B 57 E8 80 21 A1 A8
3D 70 BA 85 92 3A A0 4C 12 E8 F6 5B A1 F9 45 95`
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TurboSHAKE256(M=`00`^0, D=`07`, 64):
`4A 55 5B 06 EC F8 F1 53 8C CF 5C 95 15 D0 D0 49
70 18 15 63 A6 23 81 C7 F0 C8 07 A6 D1 BD 9E 81
97 80 4B FD E2 42 8B F7 29 61 EB 52 B4 18 9C 39
1C EF 6F EE 66 3A 3C 1C E7 8B 88 25 5B C1 AC C3`
TurboSHAKE256(M=`00`^0, D=`07`, 10032), last 32 bytes:
`40 22 1A D7 34 F3 ED C1 B1 06 BA D5 0A 72 94 93
15 B3 52 BA 39 AD 98 B5 B3 C2 30 11 63 AD AA D0`
TurboSHAKE256(M=`00`^0, D=`07`, 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`
TurboSHAKE256(M=ptn(17 bytes), D=`07`, 64):
`66 D3 78 DF E4 E9 02 AC 4E B7 8F 7C 2E 5A 14 F0
2B C1 C8 49 E6 21 BA E6 65 79 6F B3 34 6E 6C 79
75 70 5B B9 3C 00 F3 CA 8F 83 BC A4 79 F0 69 77
AB 3A 60 F3 97 96 B1 36 53 8A AA E8 BC AC 85 44`
TurboSHAKE256(M=ptn(17**2 bytes), D=`07`, 64):
`C5 21 74 AB F2 82 95 E1 5D FB 37 B9 46 AC 36 BD
3A 6B CC 98 C0 74 FC 25 19 9E 05 30 42 5C C5 ED
D4 DF D4 3D C3 E7 E6 49 1A 13 17 98 30 C3 C7 50
C9 23 7E 83 FD 9A 3F EC 46 03 FF 57 E4 22 2E F2`
TurboSHAKE256(M=ptn(17**3 bytes), D=`07`, 64):
`62 A5 A0 BF F0 64 26 D7 1A 7A 3E 9E 3F 2F D6 E2
52 FF 3F C1 88 A6 A5 36 EC A4 5A 49 A3 43 7C B3
BC 3A 0F 81 49 C8 50 E6 E7 F4 74 7A 70 62 7F D2
30 30 41 C6 C3 36 30 F9 43 AD 92 F8 E1 FF 43 90`
TurboSHAKE256(M=ptn(17**4 bytes), D=`07`, 64):
`52 3C 06 47 18 2D 89 41 F0 DD 5C 5C 0A B6 2D 4F
C2 95 61 61 53 96 BB 5B 9A 9D EB 02 2B 80 C5 BF
2D 83 A3 BB 36 FF C0 4F AC 58 CF 11 49 C6 6D EC
4A 59 52 6E 51 F2 95 96 D8 24 42 1A 4B 84 B4 4D`
TurboSHAKE256(M=ptn(17**5 bytes), D=`07`, 64):
`D1 14 A1 C1 A2 08 FF 05 FD 49 D0 9E E0 35 46 5D
86 54 7E BA D8 E9 AF 4F 8E 87 53 70 57 3D 6B 7B
B2 0A B9 60 63 5A B5 74 E2 21 95 EF 9D 17 1C 9A
28 01 04 4B 6E 2E DF 27 2E 23 02 55 4B 3A 77 C9`
TurboSHAKE256(M=ptn(17**6 bytes), D=`07`, 64):
`1E 51 34 95 D6 16 98 75 B5 94 53 A5 94 E0 8A E2
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71 CA 20 E0 56 43 C8 8A 98 7B 5B 6A B4 23 ED E7
24 0F 34 F2 B3 35 FA 94 BC 4B 0D 70 E3 1F B6 33
B0 79 84 43 31 FE A4 2A 9C 4D 79 BB 8C 5F 9E 73`
TurboSHAKE256(M=`00`^0, D=`0B`, 64):
`4C FB 3C A1 0E 97 D3 51 1C F6 1F C5 00 D0 BF 7D
0E 0B 7E 6C 2E 6E F6 58 8F 96 24 8E 97 1C 50 26
35 59 04 87 8C 01 D4 AD 64 4A 43 31 B2 BB 17 F1
B9 63 C7 79 03 1A 7C B3 EE FB 02 66 9B 37 4C 2A`
TurboSHAKE256(M=`00`^0, D=`06`, 64):
`FF 23 DC CD 62 16 8F 5A 44 46 52 49 A8 6D C1 0E
8A AB 4B D2 6A 22 DE BF 23 48 02 0A 83 1C DB E1
2C DD 36 A7 DD D3 1E 71 C0 1F 7C 97 A0 D4 C3 A0
CC 1B 21 21 E6 B7 CE AB 38 87 A4 C9 A5 AF 8B 03`
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=`06`, 64):
`E5 53 8C DD 28 30 2A 2E 81 E4 1F 65 FD 2A 40 52
01 4D 0C D4 63 DF 67 1D 1E 51 0A 9D 95 C3 7D 71
35 EF 27 28 43 0A 9E 31 70 04 F8 36 C9 A2 38 EF
35 37 02 80 D0 3D CE 7F 06 12 F0 31 5B 3C BF 63`
TurboSHAKE256(M=`FF FF FF FF FF FF FF`, D=`06`, 64):
`B3 8B 8C 15 F4 A6 E8 0C D3 EC 64 5F 99 9F 64 98
AA D7 A5 9A 48 9C 1D EE 29 70 8B 4F 8A 59 E1 24
99 A9 6F 89 37 22 56 FE 52 2B 1B 97 47 2A DD 73
69 15 BD 4D F9 3B 21 FF E5 97 21 7E B3 C2 C6 D9`
KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(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`
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KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(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`
KangarooTwelve(M=`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`
KangarooTwelve(M=`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`
KangarooTwelve(M=`FF FF FF`, C=ptn(41**2), 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`
KangarooTwelve(M=`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`
5. IANA Considerations
None.
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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. It relies on the cryptanalysis of Keccak and
provides with the same security strength as their respective SHA-3
functions.
+-------------------------------+
| security claim |
+-----------------+-------------------------------+
| TurboSHAKE128 | 128 bits (same as SHAKE128) |
| | |
| KangarooTwelve | 128 bits (same as SHAKE128) |
| | |
| TurboSHAKE256 | 256 bits (same as SHAKE256) |
+-----------------+-------------------------------+
To be more precise, KangarooTwelve is made of two layers:
* The inner function TurboSHAKE128. This layer relies on
cryptanalysis. TurboSHAKE128 function is exactly Keccak[r=1344,
c=256] (as in SHAKE128) reduced to 12 rounds. Any reduced-round
cryptanalysis on Keccak is also a reduced-round cryptanalysis of
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 [K12].
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-bit 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,
KangarooTwelve achieves NIST's post-quantum security level 2
[NISTPQ].
Implementing a MAC with KangarooTwelve SHOULD use a HASH-then-MAC
construction. This document recommends a method called HopMAC,
defined as follows:
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HopMAC(Key, M, C, L) = K12(Key, K12(M, C, 32), 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, KangarooTwelve 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 KangarooTwelve with
the key as the customization string, i.e., MAC = K12(M, Key, L).
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/TO APPEAR.
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[K12] 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,
2017.
[XKCP] Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., and
R. Van Keer, "eXtended Keccak Code Package",
WWW https://github.com/XKCP/XKCP, September 2018.
[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.
Appendix A. Pseudocode
The sub-sections of this appendix contain pseudocode definitions of
KangarooTwelve. A standalone Python version is also available in the
Keccak Code Package [XKCP] and in [K12]
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`
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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 x from 0 to 4
for y from 0 to 4
state = state || lanes[x][y]
return state
end
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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. KangarooTwelve
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KangarooTwelve(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
Authors' Addresses
Benoît Viguier
ABN AMRO Bank
Groenelaan 2
Amstelveen
Email: cs.ru.nl@viguier.nl
David Wong (editor)
O(1) Labs
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
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Joan Daemen (editor)
Radboud University
Email: joan@cs.ru.nl
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