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
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Copyright Notice
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publication of this document. Please review these documents
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carefully, as they describe your rights and restrictions with respect
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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
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