| 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
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.
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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].
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:
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
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
The Customization string serves as domain separation. It is typically a short string such as a name or an identifier (e.g. URI, ODI...)
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
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
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" | +---------+---------------+---------------+-------------------------+
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*.
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.
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
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"
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"
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"
None.
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].
| [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. |
| [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. |
The sub-sections of this appendix contain pseudo code definitions of KangarooTwelve.
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))
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.
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
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