A multiplication algorithm with square-free Gauss period normal basis

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 multiplications in extension field. It is efficient for most cases; however, a few cases were not. In order to reduce the few inefficient cases without loss of the convenience of CVMA, this paper extends the idea to square-free GNB with improving CVMA.