The WHIRLPOOL Hash Function 

M51 - The Whirlpool Galaxy
M51 (Whirlpool) Galaxy in Canes Venatici. Image courtesy of William McLaughlin.

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Table 1: Differences between RIJNDAEL and W

  RIJNDAEL W
Block size (bits) 128, 160, 192, 224, or 256 always 512
Number of rounds 10, 11, 12, 13, or 14 always 10
Key schedule dedicated a priori algorithm the round function itself
GF(28) reduction polynomial x8 + x4 + x3 + x + 1 (0x11B) x8 + x4 + x3 + x2 + 1 (0x11D)
Origin of the S-box mapping uu-1 over GF(28),
plus affine transform
recursive structure (see below)
Origin of the round constants polynomials xi over GF(28) successive entries of the S-box
Diffusion layer left-multiplication by the
4×4 circulant MDS matrix
cir(2, 3, 1, 1)
right-multiplication by the
8×8 circulant MDS matrix
cir(1, 1, 4, 1, 8, 5, 2, 9)

The recursive structure of the "tweaked" S-box:
The Whirlpool S-box

The E mini-box:
     u      0 1 2 3 4 5 6 7 8 9 A B C D E F
E(u) 1 B 9 C D 6 F 3 E 8 7 4 A 2 5 0

The E -1 mini-box:
     u      0 1 2 3 4 5 6 7 8 9 A B C D E F
E -1(u) F 0 D 7 B E 5 A 9 2 C 1 3 4 8 6

The R mini-box:
     u      0 1 2 3 4 5 6 7 8 9 A B C D E F
R(u) 7 C B D E 4 9 F 6 3 8 A 2 5 1 0
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Last update2008.11.25
Copyright © 2001, 2008 by Paulo S. L. M. Barreto.  All rights reserved.