Software Elliptic Curve Cryptography

In this thesis, we study the software implementation of the NIST-recommended elliptic curves over prime fields. Our implementation goals are to achieve a fast, small, and portable cryptographic library, which supports elliptic curve digital signature generation and verification. The implementation results are presented on a Pentium I1 448.81 MHz. We also consider the sliding window algorithm (SWA) and combine it with integer representations to generate point multiplication methods. We present a modified Katti representation to improve the SWA speed. We also present a simple signed binary representation (SSBR). A generalized sliding window algorithm is proposed which can be combined with the SSBR to obtain fast and efficient methods for both single and multiple point multiplication. These methods can use available memory efficiently, and so are ideal for memory-constrained devices.