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Issue No.04 - April (2003 vol.52)
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.
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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