Tetsuya Tamura

A Hardware-Oriented Algorithm for Computing in Jacobians and Its Implementation for Hyperelliptic Curve Cryptosystems

In this paper, we present algorithms, suitable for hardware implementation, for computation in the Jacobian of a hyperelliptic curve defined over GF(2 n ). We take curves of genus 3 and 6, designed by using 0.27-um CMOS gate array technology, and estimate the number of multiplication operations and the size and speed of hardware based on the proposed algorithm. It is shown that hardware for genus 6 curves computes an addition (resp. doubling) operation in 100 (resp. 29) clock cycles and can work at clock frequencies of up to 83 MHz We also compare a hyperelliptic curve cryptosystem with RSA and elliptic curve cryptosystems from the viewpoint of hardware implementation.