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Issue No. 04 - April (2003 vol. 52)
ISSN: 0018-9340
pp: 428-439
<p><b>Abstract</b>—In cryptographic applications, the use of normal bases to represent elements of the finite field <tmath>{\rm GF}( 2^{m})</tmath> 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 <tmath>{\rm GF}( 2^{m})</tmath>. 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.</p>
Finite fields, multiplication, normal bases, composite fields, optimal bases.

A. Reyhani-Masoleh and M. A. Hasan, "Efficient Multiplication Beyond Optimal Normal Bases," in IEEE Transactions on Computers, vol. 52, no. , pp. 428-439, 2003.
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