KangarooTwelve
draftirtfcfrgkangarootwelve02
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Authors  Benoît Viguier , David Wong , Gilles Van Assche , Quynh Dang , Joan Daemen  
Last updated  20200312 (Latest revision 20200124)  
Replaces  draftviguierkangarootwelve  
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draftirtfcfrgkangarootwelve02
Crypto Forum B. Viguier InternetDraft Radboud University Intended status: Informational D. Wong, Ed. Expires: September 13, 2020 Facebook G. Van Assche, Ed. STMicroelectronics Q. Dang, Ed. NIST J. Daemen, Ed. Radboud University March 12, 2020 KangarooTwelve draftirtfcfrgkangarootwelve02 Abstract This document defines the KangarooTwelve eXtendable Output Function (XOF), a hash function with output of arbitrary 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 roundreduced 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 InternetDraft is submitted in full conformance with the provisions of BCP 78 and BCP 79. InternetDrafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as InternetDrafts. The list of current Internet Drafts is at https://datatracker.ietf.org/drafts/current/. InternetDrafts 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 InternetDrafts as reference material or to cite them other than as "work in progress." This InternetDraft will expire on September 13, 2020. Viguier, et al. Expires September 13, 2020 [Page 1] InternetDraft KangarooTwelve March 2020 Copyright Notice Copyright (c) 2020 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/licenseinfo) 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 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 . . . . . . . . . . . . . . . . . . . . 5 2.2. Tree hashing over F . . . . . . . . . . . . . . . . . . . 6 2.3. length_encode( x ) . . . . . . . . . . . . . . . . . . . 9 3. Test vectors . . . . . . . . . . . . . . . . . . . . . . . . 9 4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 11 5. Security Considerations . . . . . . . . . . . . . . . . . . . 11 6. References . . . . . . . . . . . . . . . . . . . . . . . . . 12 6.1. Normative References . . . . . . . . . . . . . . . . . . 12 6.2. Informative References . . . . . . . . . . . . . . . . . 13 Appendix A. Pseudocode . . . . . . . . . . . . . . . . . . . . . 14 A.1. Keccakp[1600,n_r=12] . . . . . . . . . . . . . . . . . . 14 A.2. KangarooTwelve . . . . . . . . . . . . . . . . . . . . . 15 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 16 1. Introduction This document defines the KangarooTwelve eXtendable Output Function (XOF) [K12], i.e. a generalization of a hash function that can return an output of arbitrary length. KangarooTwelve is based on a Keccakp permutation specified in [FIPS202] and has a higher speed than SHAKE and SHA3. The SHA3 functions process data in a serial manner and are unable to optimally exploit parallelism available in modern CPU architectures. Similar to ParallelHash [SP800185], KangarooTwelve splits the input message in fragments to exploit available parallelism. It then applies an inner hash function F on each of them separately before applying F again on the concatenation of the digests. It makes use Viguier, et al. Expires September 13, 2020 [Page 2] InternetDraft KangarooTwelve March 2020 of Sakura coding for ensuring soundness of the tree hashing mode [SAKURA]. The inner hash function F is a sponge function and uses a roundreduced version of the permutation Keccakf used in SHA3, making it faster than ParallelHash. Its security builds up on the scrutiny that Keccak has received since its publication [KECCAK_CRYPTANALYSIS]. With respect to [FIPS202] and [SP800185] functions, KangarooTwelve features the following advantages: o Unlike SHA3224, SHA3256, SHA3384, SHA3512, KangarooTwelve has an extendable output. o Unlike any [FIPS202] defined function, similarly to functions defined in [SP800185], KangarooTwelve allows the use of a customization string. o Unlike any [FIPS202] and [SP800185] functions but ParallelHash, KangarooTwelve splits the input message in fragments to exploit available parallelism. o Unlike ParallelHash, KangarooTwelve does not have overhead when processing short messages. o The Keccakf permutation in KangarooTwelve has half the number of rounds of the one used in SHA3, making it faster than any function defined in [FIPS202] and [SP800185]. 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 bytestring. Viguier, et al. Expires September 13, 2020 [Page 3] InternetDraft KangarooTwelve March 2020 ab 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. 2. Specifications KangarooTwelve is an eXtendable Output Function (XOF). It takes as input two bytestrings (M, C) and a positive integer L where M bytestring, is the Message and C bytestring, is an OPTIONAL Customization string and L positive integer, the number of output bytes requested. 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. Viguier, et al. Expires September 13, 2020 [Page 4] InternetDraft KangarooTwelve March 2020 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 Keccakf[1600] used in SHAKE and SHA3 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 bytestring, 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 168byte blocks. 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 allzero. 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 bytelong input where the last byte is in the `01``7F` range. This is the case in KangarooTwelve. A pseudocode version is available as follows: Viguier, et al. Expires September 13, 2020 [Page 5] InternetDraft KangarooTwelve March 2020 F(input, outputByteLen): offset = 0 state = `00`^200 # === 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`^(200LastBlockLength) 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 C to a single input string S in a reversible way. length_encode( C ) gives the length in bytes of C as a bytestring. length_encode( x ) may be abbreviated as l_e( x ). See Section 2.3. S = M  C  length_encode( C ) Then, split S into n chunks of 8192 bytes. S = S_0  ..  S_(n1) S_0 = .. = S_(n2) = 8192 bytes S_(n1) <= 8192 bytes From S_1 .. S_(n1), compute the 32byte Chaining Values CV_1 .. CV_(n1). In order to be optimally efficient, this computation SHOULD exploit the parallelism available on the platform such as SIMD instructions. Viguier, et al. Expires September 13, 2020 [Page 6] InternetDraft KangarooTwelve March 2020 CV_i = F( S_i`0B`, 32 ) Compute the final node: FinalNode. o If S <= 8192 bytes, FinalNode = S o Otherwise compute FinalNode as follows: FinalNode = S_0  `03 00 00 00 00 00 00 00` FinalNode = FinalNode  CV_1 .. FinalNode = FinalNode  CV_(n1) FinalNode = FinalNode  length_encode(n1) 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 ++ The following figure illustrates the computation flow of KangarooTwelve for S > 8192 bytes: Viguier, et al. Expires September 13, 2020 [Page 7] InternetDraft KangarooTwelve March 2020 ++  S_0  ++  ++  `03``00`^7  ++  ++ F(..`0B`,32) ++  S_1 > CV_1  ++ ++  ++ F(..`0B`,32) ++  S_2 > CV_2  ++ ++  ... ...  ++ F(..`0B`,32) ++  S_(n1) > CV_(n1)  ++ ++  ++  l_e( n1 )  ++  ++ F(..`06`, L)  `FF FF` > output ++ We provide a pseudocode version in Appendix A.2. 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`  +++ Viguier, et al. Expires September 13, 2020 [Page 8] InternetDraft KangarooTwelve March 2020 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_(n1)  ..  x_0  n where x = sum from i=0..n1 of 256**i * x_i and where n is the smallest nonnegative integer such that x < 256**n. n is also the length of x_(n1)  ..  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 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` Viguier, et al. Expires September 13, 2020 [Page 9] InternetDraft KangarooTwelve March 2020 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` Viguier, et al. Expires September 13, 2020 [Page 10] InternetDraft KangarooTwelve March 2020 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 relies on the cryptanalysis of Keccak and provides with the same security strength as SHAKE128, i.e., 128 bits of security against all attacks To be more precise, KangarooTwelve is made of two layers: o The inner function F. This layer relies on cryptanalysis. KangarooTwelve's F function is exactly Keccak[r=1344, c=256] (as Viguier, et al. Expires September 13, 2020 [Page 11] InternetDraft KangarooTwelve March 2020 in SHAKE128) reduced to 12 rounds. Any reducedround cryptanalysis on Keccak is also a reducedround cryptanalysis of KangarooTwelve's F (provided the number of rounds attacked is not higher than 12). o The tree hashing over F. This layer is a mode on top of F 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 128bit security strength, the output L must be chosen long enough so that there are no generic attacks that violate 128bit security. So for 128bit (second) preimage security the output should be at least 128 bits, for 128bit of security against multi target preimage attacks with T targets the output should be at least 128+log_2(T) bits and for 128bit collision security the output should be at least 256 bits. Furthermore, when the output length is at least 256 bits, KangarooTwelve achieves NIST's postquantum security level 2 [NISTPQ]. 6. References 6.1. Normative References [FIPS202] National Institute of Standards and Technology, "FIPS PUB 202  SHA3 Standard: PermutationBased Hash and ExtendableOutput 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.rfceditor.org/info/rfc2119>. [SP800185] National Institute of Standards and Technology, "NIST Special Publication 800185 SHA3 Derived Functions: cSHAKE, KMAC, TupleHash and ParallelHash", WWW https://doi.org/10.6028/NIST.SP.800185, December 2016. Viguier, et al. Expires September 13, 2020 [Page 12] InternetDraft KangarooTwelve March 2020 6.2. Informative References [K12] Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., and R. Van Keer, "KangarooTwelve: fast hashing based on Keccakp", WWW http://eprint.iacr.org/2016/770.pdf, August 2016. [KECCAK_CRYPTANALYSIS] Keccak Team, "Summary of Thirdparty cryptanalysis of Keccak", WWW https://www.keccak.team/third_party.html, 2017. [NISTPQ] National Institute of Standards and Technology, "Submission Requirements and Evaluation Criteria for the PostQuantum Cryptography Standardization Process", WWW https://csrc.nist.gov/CSRC/media/Projects/PostQuantum Cryptography/documents/callforproposalsfinaldec 2016.pdf, December 2016. [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. [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. Viguier, et al. Expires September 13, 2020 [Page 13] InternetDraft KangarooTwelve March 2020 Appendix A. Pseudocode The subsections 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. Keccakp[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)) Viguier, et al. Expires September 13, 2020 [Page 14] InternetDraft KangarooTwelve March 2020 # 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' 64bit word toward the bits with higher indexes by 'y' positions. The 8bytes bytestring x is interpreted as a 64bit word in littleendian 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 Viguier, et al. Expires September 13, 2020 [Page 15] InternetDraft KangarooTwelve March 2020 Authors' Addresses Benoit Viguier Radboud University Toernooiveld 212 Nijmegen The Netherlands EMail: b.viguier@cs.ru.nl David Wong (editor) Facebook EMail: davidwong.crypto@gmail.com Gilles Van Assche (editor) STMicroelectronics EMail: gilles.vanassche@st.com Quynh Dang (editor) National Institute of Standards and Technology EMail: quynh.dang@nist.gov Joan Daemen (editor) Radboud University EMail: joan@cs.ru.nl Viguier, et al. Expires September 13, 2020 [Page 16]