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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)
Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field must be efficiently carried out. The authors show efficient arithmetic operations of extension field for Xate pairing especially with Freeman(More)
This paper first introduces cyclic vector multiplication algorithm (CVMA) that is a multiplication algorithm in extension field. Then, it is also introduced that CVMA is useful under the tight restrictions of pairing-based cryptographies. Then, this paper points out a problem about the calculation cost of CVMA. For this problem, this paper proposes an(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)
Pairing–based cryptosystems are well implemented with Ate–type pairing over Barreto–Naehrig (BN) curve. Then, for instance, their securities depend on the difficulty of Discrete Logarithm Problem (DLP) on the so–denoted G 3 over BN curve. This paper, in order to faster solve the DLP, first proposes to utilize Gauss period Normal Basis (GNB) for Pollard's(More)