Efficient Multiplication Beyond Optimal Normal Bases

Authors:
Arash Reyhani-Masoleh;M. Anwar Hasan
Affiliations:
-;-
Venue:
IEEE Transactions on Computers
Year:
2003

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Abstract

In cryptographic applications, the use of normal bases to represent elements of the finite field {\rm GF}( 2^{m}) is quite advantageous, especially for hardware implementation. In this article, we consider an important field operation, namely, multiplication which is used in many cryptographic functions. We present a class of algorithms for normal basis multiplication in {\rm GF}( 2^{m}). Our proposed multiplication algorithm for composite finite fields requires a significantly lower number of bit level operations and, hence, can reduce the space complexity of cryptographic systems.