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 n th roots of unity over F 2 that forms a basis of F 2m over F 2. 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.
This work was done when he worked for his Ph.D degree with the Dept of ECE, University of Waterloo.
Currently, he is with the Motorola Lab on a sabbatical leave from the University of Waterloo.
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© 1999 Springer-Verlag Berlin Heidelberg
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Wu, H., Hasan, M.A., Blake, I.F. (1999). Highly Regular Architectures for Finite Field Computation Using Redundant Basis. In: Koç, Ç.K., Paar, C. (eds) Cryptographic Hardware and Embedded Systems. CHES 1999. Lecture Notes in Computer Science, vol 1717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48059-5_23
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