Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis

Authors:
Huapeng Wu
Affiliations:
-
Venue:
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Year:
1999

Citing 11
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Abstract

Bit-parallel finite field multiplication in F2m using polynomial basis can be realized in two steps: polynomial multiplication and reduction modulo the irreducible polynomial. In this article, we prove that the modular polynomial reduction can be done with (r - 1)(m - 1) bit additions, where r is the Hamming weight of the irreducible polynomial. We also show that a bit-parallel squaring operation using polynomial basis costs not more than [m+k-1/2] bit operations if an irreducible trinomial of form xm+xk+1 over F2 is used. Consequently, it is argued that to solve multiplicative inverse in F2m using polynomial basis can be as good as using normal basis.