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Hardware Implementation of Finite Fields of Characteristic Three

D. Page, N. P. Smart, Hardware Implementation of Finite Fields of Characteristic Three. Cryptographic Hardware and Embedded Systems (CHES). B. S. Kaliski Jr., C. K. Koc, C. Paar, (eds.). ISSN 0302-9743, pp. 529–539. February 2003. No electronic version available.

Abstract

In this paper we examine a number of ways of implementing characteristic three arithmetic in hardware. While this type of arithmetic is not traditionally used in cryptographic systems, recent advances in Tate and Weil pairing based cryptosystems show that it is potentially valuable. We examine a hardware oriented representation of the field elements, comparing the resulting algorithms for field addition and multiplication operations, and show that characteristic three arithmetic need not significantly under-perform comparable characteristic two alternatives.

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