KangarooTwelve
draft-viguier-kangarootwelve-00
The information below is for an old version of the document.
| Document | Type |
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|---|---|---|---|
| Author | Benoît Viguier | ||
| Last updated | 2017-06-14 | ||
| Replaced by | draft-irtf-cfrg-kangarootwelve, draft-irtf-cfrg-kangarootwelve | ||
| RFC stream | (None) | ||
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| Additional resources | |||
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draft-viguier-kangarootwelve-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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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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