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Several methods for finding a basis conversion matrix between two different bases in an extension field have been proposed. Among them, the one based on Gauss period normal basis (GNB) is on average the most efficient. However, since it needs to construct a certain tower field , some inefficient cases in which the towering degree becomes large have been(More)
Pollard's rho method is well-known as an efficient method for solving discrete logarithm problem (DLP). This paper adopts the DLP on the so-denoted G<sub>3</sub> over Barreto-Naehrig curve, together with XTR group. Then, this paper shows this idea with the proposed algorithm, and the experimental computation time of solving the DLP is reduced by about 15%.
Many public-key cryptographers have recently focused on cryptographic schemes based on pairing, which is a bilinear map from two elliptic curve groups to a group in an extension field. In order to provide efficient pairings, several kinds of pairing-friendly curves have been proposed. Since most of the pairing-friendly curves are defined over a certain(More)
Recent cryptographic applications such as elliptic curve cryptography and pairing-based cryptography often need arithmetic operations, especially vector multiplications in a certain extension field of large order. Thus, the authors have proposed cyclic vector multiplication algorithm (CVMA) with prime Gauss period normal basis (GNB) for accelerating(More)