Dear Keccak Team and all,
We extended our previous techniques to pre-image challenges on
Keccak[r=1440, c=160, 4 rounds from 0 to 3]. We found the solutions by
first partially linearizing 3.5 rounds of Keccak-f permutation, and then
solving a linear system of probabilistic equations between a two-block
message and pre-image. One of the solutions is listed below.
A pre-image of 7d aa d8 07 f8 50 6c 9c 02 76 is:
"\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\xf5\x55\x32\xc2\x82\xed\x9e\xb\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x0\x7e\xe8\xb\xb2\x15\x21\x99\x1c\x6a\xd3\xfa\xc5\x51\xb2\x4d\x9c\x51\x72\x35\xc9\xde\x60\x90\x2c\xaa\x0\xde\x2e\x8\x8f\x7a\x86\xda\x6\xa5\x77\x81\xf4\xaf\x2e\xee\x40\x7a\x55\xe6\xfc\xee\x79\x8\x2c\xc5\x9b\x4\x77\x46\x58\xaa\x3d\xc2\x20\xd8\x76\x32\x6e\xb0\xb0\x87\x11\x1a\x18\xd3\xd2\x4c\xb\x92\x73\xa\xf0\xe6\x7c\x43\x55\xe8\x76\x32\x8f\x2d\xe8\x8c\xb6\x7c\x13\x79\x7a\xf7\x3c\xaa\x33\x4d\x9f\x47\x25\xd3\xb0\xdc\x5c\xf7\xe3\x7b\x81\x22\x63\xfa\xee\x47\x38\xc3\x1f\x2d\x1b\x7\x3e\x0\x90\x70\x73\x15\x38\xf1\x35\xca\x20\xce\x39\xae\xf3\x3e\x46\x7e\x31\x33\xf3\x9c\xfe\xce\x95\xc4\xe2\x2\x6a\xb4\x9c\x3d\xab\x70\x57\x1d\xe6\xfa\x4d\x6b\x7f\xa5\x48\xe7\x18\x52\xea\xbe\x8\xc5\xc1\x7e\xc4\xda\x5c\xb\x2\x6d\xc1"
message length = 2878
We are grateful to Ling Song for her help in the programming of an early
version of this work.
Best Regards,
Meicheng Liu (State Key Laboratory of Information Security,
Institute of Information Engineering,
Chinese Academy of Sciences, China)
Jian Guo (Nanyang Technological University, Singapore)
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