A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Bit-Serial Systolic Divider and Multiplier for Finite Fields GF(2/sup m/)
IEEE Transactions on Computers - Special issue on computer arithmetic
Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes
Designs, Codes and Cryptography
On Computing Multiplicative Inverses in GF(2/sup m/)
IEEE Transactions on Computers
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Modulo arithmetic operations especially modulo multiplication have extensive applications in elliptic curve cryptanalysis, error control coding and linear recurring sequences. These operations have steadily grown in the word size in the past. Current designs and approaches may not be the most efficient for such high word sizes. Also usually, most approaches optimize for either area or speed, not both. In this paper, we examine certain properties and elucidate certain alternative strategies of and on the Itoh-Tsujii algorithm[1] that will make it suitable for this emerging scenario. These strategies take a holistic approach to the problem, and aims at optimizing both speed and area for a given word length. These claims are supported by mathematical analysis, simulation and synthesis of a prototype of the suggested strategy. We also examine various enhancements that cam be effected in the given architecture.