4 Jean-Philippe Aumasson and Daniel J. Bernstein
2 Specification of SipHash
SipHash is a family of PRFs SipHash-c-d where the integer parameters c and d
are the number of compression rounds and the number of finalization rounds. A
compression round is identical to a finalization round and this round function is
called SipRound. Given a 128-bit key k and a (possibly empty) byte string m,
SipHash-c-d returns a 64-bit value SipHash-c-d(k, m) computed as follows:
1. Initialization: Four 64-bit words of internal state v
0
, v
1
, v
2
, v
3
are initialized
as
v
0
= k
0
⊕ 736f6d6570736575
v
1
= k
1
⊕ 646f72616e646f6d
v
2
= k
0
⊕ 6c7967656e657261
v
3
= k
1
⊕ 7465646279746573
where k
0
and k
1
are the little-endian 64-bit words encoding the key k.
2. Compression: SipHash-c-d processes the b-byte string m by parsing it as
w = d(b + 1)/8e > 0 64-bit little-endian words m
0
, . . . , m
w−1
where m
w−1
includes the last 0 through 7 bytes of m followed by null bytes and ending
with a byte encoding the positive integer b mod 256. For example, the one-
byte input string m = ab is parsed as m
0
= 01000000000000ab. The m
i
’s are
iteratively processed by doing
v
3
⊕ = m
i
and then c iterations of SipRound, followed by
v
0
⊕ = m
i
3. Finalization: After all the message words have been processed, SipHash-c-d
xors the constant ff to the state:
v
2
⊕ = ff
then does d iterations of SipRound, and returns the 64-bit value
v
0
⊕ v
1
⊕ v
2
⊕ v
3
.
Fig. 2.1 shows SipHash-2-4 hashing a 15-byte m.
The function SipRound transforms the internal state as follows (see also Fig.2.2):
v
0
+ = v
1
v
2
+ = v
3
v
1
≪= 13 v
3
≪= 16
v
1
⊕ = v
0
v
3
⊕ = v
2
v
0
≪= 32
v
2
+ = v
1
v
0
+ = v
3
v
1
≪= 17 v
3
≪= 21
v
1
⊕ = v
2
v
3
⊕ = v
0
v
2
≪= 32
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