Efficient method for multiplication over galois fields

Cryptography – Particular algorithmic function encoding

Reexamination Certificate

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C708S001000, C708S002000, C708S003000, C708S200000, C380S029000, C713S150000, C713S164000, C713S189000

Reexamination Certificate

active

07003106

ABSTRACT:
The improved AES processing method provides an efficient alternative to both Mips intensive multiplication and to conventional table lookup, used to multiply terms over a Galois field (GF). The improved method takes advantage of the fact that in the GF, any non zero element X can be represented by a power of a primitive element P. The improved method thereby results in a 2 by 256 table. The log base P of the terms being multiplied are looked up and summed, and the anti-log of the sum is looked up in the same table.

REFERENCES:
patent: 6263470 (2001-07-01), Hung et al.
patent: 6510228 (2003-01-01), Rose
Nicolas T. Curtois, “Is AES a Secure Cipher”, http://www.cryptosystem.net/aes/, last visit: Jun. 8, 2005.
Mike Scott, “Rijndael Block Cipher—rijndael.c”, Apr. 21, 1999.
“Federal Information Processsing Standards Publication 197”, Nov. 26, 2001.
Federal Information Processing Standards Advanced Encryption Standard.
Pierre-Antoine Benatar, General Cryptographic Knowledge, 2001.
Chris Woods, Building Secure Frame Relay Virtual Private Networks, 2001.

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