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

摘要

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-#PHI# expansion. Further-more, since this algorithm suits conventional computational units such as 16, 32 and 64 bits, its base field F_p~m is expected to enhance elliptic curve operation efficiency more than F_q (q is a prime) or F_2~n.