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Versions: 00 01 02

Internet Research Task Force (IRTF)                           B. Viguier
Internet-Draft                                        Radboud University
Intended status: Informational                         December 14, 2017
Expires: June 17, 2018


                             KangarooTwelve
                    draft-viguier-kangarootwelve-01

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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   This Internet-Draft will expire on June 17, 2018.

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
   (https://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.  length_encode( x )  . . . . . . . . . . . . . . . . . . .   8
   3.  Test vectors  . . . . . . . . . . . . . . . . . . . . . . . .   8
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .  10
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     6.2.  Informative References  . . . . . . . . . . . . . . . . .  11
   Appendix A.  Pseudo code  . . . . . . . . . . . . . . . . . . . .  12
     A.1.  Keccak-p[1600,n_r=12] . . . . . . . . . . . . . . . . . .  12
     A.2.  KangarooTwelve  . . . . . . . . . . . . . . . . . . . . .  13
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  14

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 are 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 Keccak-f used in SHA-3.  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 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 to m exclusive of a
      string s.  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 x multiplied by itself y times.








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2.  Specifications

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

   M  byte-string, is the Message and

   C  byte-string, is a OPTIONAL Customization string and

   L  positive integer, the number of output bytes requested.

   The Customization string MAY serves 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
   does that not support a customization string input, C MUST be the
   empty string.

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 permutation Keccak-f[1600]
   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.

   F is a sponge function calling this permutation KP with a rate of 168
   bytes or 1344 bits.  It follows that F has a capacity of 1600 - 1344
   = 256 bits or 32 bytes.

   The sponge function F takes:

   input  byte-string, the input bytes and

   outputByteLen  positive integer, the Length of the output in bytes

   First the message is padded with zeroes to the closest multiple of
   168 bytes.  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.

   As defined by the sponge construction, the process operates on a
   state and consists of two phases.






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   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.

   This definition of the sponge construction assumes a at least one-
   byte-long input where the last byte is in the `01`-`7F` range.  This
   is the case in KangarooTwelve.

   A pseudo-code version is available as follows:

     F(input, outputByteLen):
       offset = 0
       state = `00`^200

       # === Absorb complete blocks ===
       while offset < |input| - 168
           state ^= inputBytes[offset : offset + 168] || `00`^32
           state = KP(state)
           offset += 168

       # === Absorb last block and treatment of padding ===
       LastBlockLength = |input| - offset
       state ^= inputBytes[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

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 the OPTIONAL




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   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 2.3.

             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-bytes Chaining Values CV_1 .. CV_n-
   1.  This computation SHOULD exploit the parallelism available on the
   platform in order to be optimally efficient.

                CV_i    = F( S_i||`0B`, 32 )

   Compute the final node: FinalNode.

   o  If |S| <= 8192 bytes, FinalNode = S

   o  Otherwise compute FinalNode as follow:

             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:

   o  If |S| <= 8192 bytes, from F( FinalNode||`07`, L )

         KangarooTwelve( M, C, L ) = F( FinalNode||`07`, L )

   o  Otherwise from F( FinalNode||`06`, L )

         KangarooTwelve( M, C, L ) = F( FinalNode||`06`, L )

   The following figure illustrates the computation flow of
   KangarooTwelve for |S| <= 8192 bytes:

             +--------------+  F(..||`07`, L)
             |      S       |----------------->  output
             +--------------+





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   The following figure illustrates the computation flow of
   KangarooTwelve for |S| > 8192 bytes:

                                +--------------+
                                |     S_0      |
                                +--------------+
                                      ||
                                +--------------+
                                | `03`||`00`^7 |
                                +--------------+
                                      ||
   +---------+  F(..||`0B`,32)  +--------------+
   |   S_1   |----------------->|     CV_1     |
   +---------+                  +--------------+
                                      ||
   +---------+  F(..||`0B`,32)  +--------------+
   |   S_2   |----------------->|     CV_2     |
   +---------+                  +--------------+
                                      ||
             ...                      ...
                                      ||
   +---------+  F(..||`0B`,32)  +--------------+
   |  S_n-1  |----------------->|    CV_n-1    |
   +---------+                  +--------------+
                                      ||
                                +--------------+
                                |   l_e(n-1)   |
                                +--------------+
                                      ||
                                +------------+  F(..||`06`, L)
                                |   `FF FF`  |----------------->  output
                                +------------+

   We provide a pseudo code version in Appendix A.2.

   In the table below are gathered the values of the domain separation
   bytes used by the tree hash mode:

           +--------------------+------------------+
           |   Type             |       Byte       |
           +--------------------+------------------+
           |  SingleNode        |       `07`       |
           |                    |                  |
           |  IntermediateNode  |       `0B`       |
           |                    |                  |
           |  FinalNode         |       `06`       |
           +--------------------+------------------+




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2.3.  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 pseudo code version is as follow.

     length_encode(x):
       S = `00`^0

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

       S = S || length(S)

       return S
       end

3.  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`














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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=`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`




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     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`

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,
              <https://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.

   [KCP]      Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., and
              R. Van Keer, "Keccak Code Package",
              WWW https://github.com/KeccakTeam/KeccakCodePackage,
              December 2017.

   [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 standalone Python version is also available in the
   Keccak Code Package [KCP] 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))




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       # 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.  KangarooTwelve

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

     if |S| <= 8192
         return F(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 = F(S[offset : offset + blockSize] || `0B`, 32)
             FinalNode = FinalNode || CV
             numBlock += 1
             offset   += blockSize

         FinalNode = FinalNode || length_encode( numBlock ) || `FF FF`

         return F(FinalNode || `06`, outputByteLen)
     end





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Author's Address

   Benoit Viguier
   Radboud University
   Toernooiveld 212
   Nijmegen
   The Netherlands

   EMail: b.viguier@cs.ru.nl










































Viguier                   Expires June 17, 2018                [Page 14]


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