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 Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://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 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 Viguier Expires December 16, 2017 [Page 1]

Internet-Draft KangarooTwelve June 2017 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]. Viguier Expires December 16, 2017 [Page 2]

Internet-Draft KangarooTwelve June 2017 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` Viguier Expires December 16, 2017 [Page 3]

Internet-Draft KangarooTwelve June 2017 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 Viguier Expires December 16, 2017 [Page 4]

Internet-Draft KangarooTwelve June 2017 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: Viguier Expires December 16, 2017 [Page 5]

Internet-Draft KangarooTwelve June 2017 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. Viguier Expires December 16, 2017 [Page 6]

Internet-Draft KangarooTwelve June 2017 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" Viguier Expires December 16, 2017 [Page 7]

Internet-Draft KangarooTwelve June 2017 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" Viguier Expires December 16, 2017 [Page 8]

Internet-Draft KangarooTwelve June 2017 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 Viguier Expires December 16, 2017 [Page 9]

Internet-Draft KangarooTwelve June 2017 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. Viguier Expires December 16, 2017 [Page 10]

Internet-Draft KangarooTwelve June 2017 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)) Viguier Expires December 16, 2017 [Page 11]

Internet-Draft KangarooTwelve June 2017 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 Viguier Expires December 16, 2017 [Page 12]

Internet-Draft KangarooTwelve June 2017 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 Viguier Expires December 16, 2017 [Page 13]