A Fast Elliptic Curve Cryptosystem LSI Embedding Word-Based Montgomery Multiplier

Elliptic curve cryptosystems are expected to be a next standard of public-key cryptosystems. A security level of elliptic curve cryptosystems depends on a difficulty of a discrete logarithm problem on elliptic curves. The security level of a elliptic curve cryptosystem which has a public-key of 160-bit is equivalent to that of a RSA system which has a public-key of 1024-bit. We propose an elliptic curve cryptosystem LSI architecture embedding word-based Montgomery multipliers. A Montgomery multiplication is an efficient method for a finite field multiplication. We can design a scalable architecture for an elliptic curve cryptosystem by selecting structure of word-based Montgomery multipliers. Experimental results demonstrate effectiveness and efficiency of the proposed architecture. In the hardware evaluation using 0.18 μm CMOS library, the highspeed design using 126 Kgates with 20 × 8-bit multipliers achieved operation times of 3.6 ms for a 160-bit point multiplication. key words: elliptic curve cryptosystem, Montgmery multiplier, public-key cryptosystem, LSI design