Fast Exponentiation in Extension Field with Frobenius Mappings

This paper proposes an exponentiation method with Frobenius mappings. Our method is closely related to so-called interleaving exponentiation. Different from the interleaving exponentiation methods, our method can carry out several exponentiations using same base at the same time. The efficiency to use Frobenius mappings for an exponentiation in extension field is well introduced by Avanzi and Mihailescu. This exponentiation method is based on so-called simultaneous exponentiation and uses many Frobenius mappings. Their method more decreased the number of multiplications; however, the number of Frobenius mappings inversely increased. Compared to their method , the number of multiplications needed for the proposed method becomes about 20% larger; however, that of Frobenius mappings becomes small enough.