Efficient hyperelliptic curve cryptosystems using theta divisors

It has recently been reported that the performance of hyperelliptic curve cryptosystems (HECC) is competitive to that of elliptic curve cryptosystems (ECC). Concerning the security of HECC, the theta divisors play an important role. The scalar multiplication using a random base point is vulnerable to an exceptional procedure attack, which is a kind of side-channel attacks, using theta divisors. In the case of cryptographic protocols of the scalar multiplication using fixed base point, however, the exceptional procedure attack is not applicable. First, we present novel efficient scalar multiplication using theta divisors, which is the positive application of theta divisors on HECC. Second, we develop a window-based method using theta divisors that is secure against side-channel attacks. It is not obvious how to construct a base point D such that all pre-computed points are theta divisors. We present an explicit algorithm for generating such divisors.