Internet-Draft KangarooTwelve February 2023
Viguier, et al. Expires 21 August 2023 [Page]
Workgroup:
Crypto Forum
Internet-Draft:
draft-irtf-cfrg-kangarootwelve-09
Published:
Intended Status:
Informational
Expires:
Authors:
B. Viguier
ABN AMRO Bank
D. Wong, Ed.
O(1) Labs
G. Van Assche, Ed.
STMicroelectronics
Q. Dang, Ed.
NIST
J. Daemen, Ed.
Radboud University

KangarooTwelve and TurboSHAKE

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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Table of Contents

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.

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:

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.

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.

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:

  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...)

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.

            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:

      KangarooTwelve( M, C, L ) = TurboSHAKE128( FinalNode, `07`, L )

      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.

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.

    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`

  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`

  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
     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`

  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.

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:

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:

   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, , <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, .
[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, .

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.
[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, .
[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, .
[KECCAK_CRYPTANALYSIS]
Keccak Team, "Summary of Third-party cryptanalysis of Keccak", WWW 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, .
[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, .

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`
  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

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 

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
David Wong (editor)
O(1) Labs
Gilles Van Assche (editor)
STMicroelectronics
Quynh Dang (editor)
National Institute of Standards and Technology
Joan Daemen (editor)
Radboud University