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Efficient Multiplication Beyond Optimal Normal Bases
April 2003 (vol. 52 no. 4)
pp. 428-439

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.

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Index Terms:
Finite fields, multiplication, normal bases, composite fields, optimal bases.
Arash Reyhani-Masoleh, M. Anwar Hasan, "Efficient Multiplication Beyond Optimal Normal Bases," IEEE Transactions on Computers, vol. 52, no. 4, pp. 428-439, April 2003, doi:10.1109/TC.2003.1190584
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