Miyaji Laboratory

Elliptic curve based cryptosystem is an efficient public key cryptosystem. It relies on the difficulty of elliptic curve discrete logarithmic problem(ECDLP). Elliptic curve cryptosystem (ECC) with a key size of 170 bits provides the same level of security as RSA with a key size of 1024 bits. It is expected that ECC will become popular for many information security applications in the near future. The ECDSA signature etc. have been put to practical use by SSL/TSL for such reasons. The challenging part of ECC is to compute the scalar multiplication kP for k ∈ Z and an elliptic-curve point P. One of the speeding-up methods is to reduce the number of hamming weight (±1). The purpose of our study is to propose an efficient algorithm that is tolerant to the side channel attack. In addition, we plan to use `characteristic' in the scalar multiplication utilizing the benefit of existing algorithms those do not use memory. Moreover, improving the existing algorithm and the scalar multiplication using JSF are also considered besides new algorithm construction.