Fast Elliptic Curve Algorithm Combining Frobenius Map and Table Reference to Adapt to Higher Characteristic

A new elliptic curve scalar multiplication algorithm is proposed. The algorithm offers about twice the troughput of some conventional OEF-base algorithms because it combines the Frobenius map with the table reference method based on base-φ expansion. Furthermore, since this algorithm suits conventional computational units such as 16, 32 and 64 bits, its base field Fpm is expected to enhance elliptic curve operation efficiency more than Fq (q is a prime) or F2n.

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