Highly Regular Architectures for Finite Field Computation Using Redundant Basis

Authors:
Huapeng Wu;M. Anwarul Hasan;Ian F. Blake
Affiliations:
-;-;-
Venue:
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Year:
1999

Citing 12
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Abstract

In this article, an extremely simple and highly regular architecture for finite field multiplier using redundant basis is presented, where redundant basis is a new basis taking advantage of the elegant multiplicative structure of the set of primitive nth roots of unity over F2 that forms a basis of F2m over F2. The architecture has an important feature of implementation complexity trade-off which enables the multiplier to be implemented in a partial parallel fashion. The squaring operation using the redundant basis is simply a permutation of the coefficients. We also show that with redundant basis the inversion problem is equivalent to solving a set of linear equations with a circulant matrix. The basis appear to be suitable for hardware implementation of elliptic curve cryptosystems.