Full‐custom hardware implementation of point multiplication on binary Edwards curves for application‐specific integrated circuit elliptic curve cryptosystem applications

Abstract

This study presents an efficient and high‐speed very large‐scale integration implementation of point multiplication on binary Edwards curves over binary finite field GF(2m) with Gaussian normal basis representation. The proposed implementation is a low‐cost structure constructed by one digit‐serial multiplier. In the proposed scheduling of point multiplication, the field multiplier is busy during point addition and point doubling computations. In the field multiplier structure, by using the logical effort technique the delay is optimally decreased and the drive ability of the circuit in the point multiplication architecture is increased. Also, to reduce area and number of transistors of the point multiplication circuit, all components are selected based on low‐cost structures. The design is implemented in 0.18 μm CMOS technology over binary finite field GF(2233). The results confirm the validity of the proposed structure and its high performance in terms of delay and area cost.

Keywords

• full-custom hardware implementation
• point multiplication scheduling
• binary Edwards curves
• application-specific integrated circuit elliptic curve cryptosystem applications
• high-speed very large-scale integration implementation
• binary finite field GF(2m)