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Versions: 00

Internet Research Task Force (IRTF)                           B. Viguier
Internet-Draft                                        Radboud University
Intended status: Informational                             June 14, 2017
Expires: December 16, 2017


                             KangarooTwelve
                    draft-viguier-kangarootwelve-00

Abstract

   This document defines the KangarooTwelve eXtendable Output Function
   (XOF), a hash function with arbitrary output length.  It provides an
   efficient and secure hashing primitive, which is able to exploit the
   parallelism of the implementation in a scalable way.  It uses tree
   hashing over a round-reduced version of SHAKE128 as underlying
   primitive.

   This document builds up on the definitions of the permutations and of
   the sponge construction in [FIPS 202], and is meant to serve as a
   stable reference and an implementation guide.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   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 December 16, 2017.

Copyright Notice

   Copyright (c) 2017 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
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents



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   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Conventions . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Specifications  . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Inner function: F . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Tree hashing over F . . . . . . . . . . . . . . . . . . .   5
     2.3.  right_encode( x ) . . . . . . . . . . . . . . . . . . . .   7
   3.  Test vectors  . . . . . . . . . . . . . . . . . . . . . . . .   7
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   9
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  10
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  10
   Appendix A.  Pseudo code  . . . . . . . . . . . . . . . . . . . .  11
     A.1.  Keccak-p[1600] over 12 rounds . . . . . . . . . . . . . .  11
     A.2.  Inner function F  . . . . . . . . . . . . . . . . . . . .  12
     A.3.  KangarooTwelve  . . . . . . . . . . . . . . . . . . . . .  13
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  13

1.  Introduction

   This document defines the KangarooTwelve eXtendable Output Function
   (XOF) [K12], i.e. a generalization of a hash function that can return
   arbitrary output length.  KangarooTwelve is based on a Keccak-p
   permutation specified in [FIPS202] and aims at higher speed than
   SHAKE and SHA-3.

   The SHA-3 functions process data in a serial manner and unable to
   optimally exploit parallelism available in modern CPU architectures.
   KangarooTwelve splits the input message in fragments and applies an
   inner hash function F on each of them separately.  It then applies F
   again on the concatenation of the digests.  It makes use of Sakura
   coding for ensuring soundness of the tree hashing mode [SAKURA].  The
   inner hash function F is a sponge function and uses a round-reduced
   version of the permutation used in Keccak.  Its security builds up on
   the scrutiny that Keccak has received since its publication
   [KECCAK_CRYPTANALYSIS].







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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 bit-string.  For example, `1010101`.

   A 8 bit string `b_0 b_1 b_2 b_3 b_4 b_5 b_6 b_7` is a byte
   represented by an integer value v following the LSB 0 convention,
   i.e.

                     v = sum for i=0..7 of 2^i * b_i

   For example, `11100000` = 7.  The following diagram represents the
   byte "07" with value 7 (decimal).

                       Significance of Bits
                      MSB 7 6 5 4 3 2 1 0 LSB
                         +-+-+-+-+-+-+-+-+
                         |0 0 0 0 0 1 1 1|
                         +-+-+-+-+-+-+-+-+
                      hex:   0       7

   "..."  denotes a string of bytes given in hexadecimal.  For example,
      "0B 80", which can be also be seen as a bit-string : `11010000
      00000001`.

   |s|  denotes the length of a byte string "s".  For example, |"FF FF"|
      = 2.

   `0^b`  denotes the repetition of bit `0` b times.  For example, `0^4`
      = `0000`.

   `0^0`  denotes the empty bit-string.

   `1^b`  denotes the repetition of bit `1` b times.  For example, `1^3`
      = `111`.

   "00^b"  denotes the b times the repetition of byte "00".  For
      example, "00^7" = "00 00 00 00 00 00 00".

   a||b  denotes the concatenation of two strings 'a' and 'b'.  For
      example, `10`||`01` = `1001`





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   s[n:m]  denotes the selection of bytes from n to m exclusive of a
      string 's'.  For example, for s = "A5 C6 D7", s[0:1] = "A5" and
      s[1:3] = "C6 D7".

2.  Specifications

   KangarooTwelve is an eXtendable Output Function (XOF).  It takes as
   an input a pair of byte-strings (M, C) and a positive integer L where

   M  byte-string, is the Message and

   C  byte-string, is a Customization string and

   L  positive integer, the length of the output in bytes.

   The Customization string serves as domain separation.  It is
   typically a short string such as a name or an identifier (e.g.  URI,
   ODI...)

2.1.  Inner function: F

   The inner function F makes use of the permutation Keccak-
   p[1600,n_r=12], i.e., a version of the one used in SHAKE and SHA-3
   instances reduced to n_r=12 rounds and specified in FIPS 202
   [FIPS202].  F is a sponge function calling this permutation, multi-
   rate padding pad10*1 and with a rate of 168 bytes (= 1344 bits):

             F = Sponge[Keccak-p[1600,n_r=12], pad10*1, r=1344]

   It follows that F has a capacity of 1600 - 1344 = 256 bits.

   The sponge function F takes as an input a bit-string S and a positive
   integer L where

   S  bit-string, is the input String and

   L  positive integer, the Length of the output in bytes

   The input string S SHOULD be represented as a pair (Sbytes, dS),
   where Sbytes contains only bytes and where dS is the delimited suffix
   representing the trailing bits.

   First, let S = Sbytes || Sbits, where Sbytes contains only bytes and
   Sbits contains at most 7 bits.  Then, convert Sbits into the
   delimited suffix dS by appending a bit `1` and as many bits `0` as
   necessary so that dS is a byte.  The numerical value of dS is thus:

             dS = 2^|Sbits| + sum for i=0..|Sbits|-1 of 2^i*Sbits_i



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   Notice that the most significant bit `1` of dS coincides with the
   first bit of padding in the multi-rate padding rule pad10*1.  The
   implementation of F therefore SHOULD add dS to the state and then the
   second bit of padding.  Appendix A.2 provides a pseudo code version.

   In the table below, here are some examples of values, including those
   that are used in this document:

   +---------+---------------+---------------+-------------------------+
   |  Sbits  |   bit-string  |   value (dec) |  delimited Suffix (dS)  |
   +---------+---------------+---------------+-------------------------+
   |  ``     |  `10000000`   |       1       |           "01"          |
   |         |               |               |                         |
   |  `01`   |  `01100000`   |       6       |           "06"          |
   |         |               |               |                         |
   |  `11`   |  `11100000`   |       7       |           "07"          |
   |         |               |               |                         |
   |  `110`  |  `11010000`   |       11      |           "0B"          |
   +---------+---------------+---------------+-------------------------+

2.2.  Tree hashing over F

   On top of the sponge function F, KangarooTwelve uses a Sakura-
   compatible tree hash mode [SAKURA].  First, merge M and C to a single
   input string S in a reversible way.  right_encode( |C| ) gives the
   length in bytes of C as a byte-string.  See Section 2.3.

             S = M || C || right_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-bytes hashes CV_0 .. CV_n-2.  This
   computation SHOULD exploit the parallelism available on the platform
   in order to be optimally efficient.

             Node_i  = S_i+1 || `110`
             CV_i    = F( Node_i, 32 )

   Compute the final node: Node*.

   o  If |S| <= 8192 bytes, then Node* = S || `11`

   o  Otherwise compute Node* as follow:




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             Node* = S_0 || "03 00 00 00 00 00 00 00"
             Node* = Node* || CV_0
                   ..
             Node* = Node* ||  CV_n-2
             Node* = Node* || right_encode(n-1)
             Node* = Node* || "FF FF" || `01`

   Finally, KangarooTwelve output is retrieved from F( Node* ).

            KangarooTwelve( M, C, L ) = F( Node*, L )

   For |S| > 8192 bytes, KangarooTwelve computation flow is as follow:

                                 +--------------+
                                 |      S_0     |
                                 +--------------+
                                        ||
                                 +--------------+
                                 | `11`||`0^62` |
                                 +--------------+
                                        ||
     +-------------------+   F   +--------------+
     |    S_1   || `110` |------>|     CV_0     |
     +-------------------+       +--------------+
                                        ||
     +-------------------+   F   +--------------+
     |    S_2   || `110` |------>|     CV_1     |
     +-------------------+       +--------------+
                                        ||
             ...                       ...
                                        ||
     +-------------------+   F   +--------------+
     |   S_n-1  || `110` |------>|    CV_n-2    |
     +-------------------+       +--------------+
                                        ||
                                 +--------------+
                                 |   r_e(n-1)   |
                                 +--------------+
                                        ||
                                 +------------------+     F
                                 |  "FF FF" || `01` |---------->  output
                                 +------------------+

   We provide a pseudo code version in Appendix A.3.







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2.3.  right_encode( x )

   The function right_encode takes as inputs a non negative integer x <
   256^255 and outputs a string of bytes x_n || .. || x_0 || n where

                x = sum from i=0..n of 256^i * x_i

   A pseudo code version is as follow.

     right_encode(x):
       S = 0^0

       while x > 0
           S = x % 256 || S
           x = x / 256

       S = S || length(S)

       return S
       end

3.  Test vectors

   Test vectors are based on the repetition of pattern the "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"




















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       Pattern for a length of 17^2 bytes:
       ptn(17^2) =
         "00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
          10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
          20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F
          30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F
          40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F
          50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F
          60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F
          70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F
          80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F
          90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F
          A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF
          B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE BF
          C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF
          D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF
          E0 E1 E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF
          F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA
          00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
          10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
          20 21 22 23 24 25"

     KangarooTwelve(M=0^0, C=0^0, 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=0^0, C=0^0, 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=0^0, C=0^0, 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=0^0, 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=0^0, 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=0^0, 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"




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     KangarooTwelve(M=ptn(17^3 bytes), C=0^0, 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=0^0, 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=0^0, 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=0^0, 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=0^0, 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=0xff, 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=0xff 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=0xff 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"

4.  IANA Considerations

   None.

5.  Security Considerations

   This document is meant to serve as a stable reference and an
   implementation guide for the KangarooTwelve eXtendable Output
   Function.  It makes no assertion to its security and relies on the
   cryptanalysis of Keccak [KECCAK_CRYPTANALYSIS].

6.  References







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6.1.  Normative References

   [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.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

6.2.  Informative References

   [K12]      Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., and
              R. Van Keer, "KangarooTwelve: fast hashing based on
              Keccak-p", WWW http://eprint.iacr.org/2016/770.pdf, August
              2016.

   [KECCAK_CRYPTANALYSIS]
              Keccak Team, "Summary of Third-party cryptanalysis of
              Keccak", WWW https://www.keccak.team/third_party.html,
              2017.

   [SAKURA]   Bertoni, G., Daemen, J., Peeters, M., and G. Van Assche,
              "Sakura: a flexible coding for tree hashing",
              WWW http://eprint.iacr.org/2013/231.pdf, April 2013.
























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Appendix A.  Pseudo code

   The sub-sections of this appendix contain pseudo code definitions of
   KangarooTwelve.

A.1.  Keccak-p[1600] over 12 rounds

     Keccak-p_1600_12(state):
       R = "D5"

       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 12 to 23
         # 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)%5] ^ ROL64(C[(x+1)%5], 1)
         for y from 0 to 4
           for x from 0 to 4
             lanes = 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)%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)%5]) & T[(x+2)%5])

         # iota
         for j from 0 to 6
           R = ((R << 1) ^ ((R >> 7)* "71")) % 256
           if (R & 2)
             lanes[0][0] = lanes[0][0] ^ (1 << ((1<<j)-1))



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       state = 0^0
       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' bits.

A.2.  Inner function F

     F(inputBytes, Suffix, outputByteLen):
       state = "00^200"
       blockSize = 0
       offset = 0

       # === Absorb inputBytes ===
       while offset < |inputBytes|
           blockSize = min( |inputBytes| - offset, 168)
           state ^= inputBytes[offset : offset + blockSize]
           offset = offset + blockSize

           if blockSize = 168
               state = Keccak-p_1600_12(state)
               blockSize = 0

       # === Absorb Suffix ===
       state ^= "00^blockSize" || Suffix
       if (Suffix & "80") != 0 and blockSize == 167
           state = Keccak-p_1600_12(state)
       state ^= "00^167" || "80"

       state = Keccak-p_1600_12(state)

       # === Squeeze ===
       while outputByteLen > 0
           blockSize = min(outputByteLen, 168)
           outputBytes = outputBytes || state[0:blockSize]
           outputByteLen = outputByteLen - blockSize

           if outputByteLen > 0
               state = Keccak-p_1600_12(state)

       return outputBytes
       end




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A.3.  KangarooTwelve

   KangarooTwelve(inputMessage, customString, outputByteLen):
     S = inputMessage || customString
     S = S || right_encode( |customString| )

     if |S| <= 8192
         return F(S, "07", outputByteLen)
     else
         # === Kangaroo hopping ===
         Node* = S[0:8192] || "03 00^7"
         offset = 8192
         while offset < |inputBytes|
             blockSize = min( |inputBytes| - offset, 8192)
             CV = F(inputBytes[offset : offset + blockSize], "0B", 32)
             Node* = Node* || CV
             offset = offset + blockSize

         Node* = Node* || right_encode( |S| / 8192 ) || "FF FF"
         return F(Node*, "06", outputByteLen)
     end

Author's Address

   Benoit Viguier
   Radboud University
   Toernooiveld 212
   Nijmegen
   The Netherlands

   EMail: b.viguier@cs.ru.nl




















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