Architectures for exponentiation over GD(2/sup n/) adopted for smartcard application

Two exponentiation circuits are proposed. Using the fact that squaring is a linear operation over GF(2/sup n/), a time-space tradeoff in smartcard-based circuitry is presented. It is shown how multiplication is performed by a single shift, based on replacing the public key alpha /sup a/ in GF(2/sup n/) by its minimal polynomial. Other considerations, related to structure regularity and the possible use of dynamic shift registers, are also treated.<
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