ABSTRACT
The Diffie-Hellman key exchange protocol (DH) and the Rivest-Shamir-Adleman cryptosystem (RSA) are among the very first public key cryptosystems. As of today, elliptic curve groups are known to yield more efficient public key cryptosystems, as compared to the use of multiplicative groups, for the same classical security level. In both cases, though, group operations dominate the run time of these systems. This chapter presents some cryptographic applications of VS-VB, VS-FB, and FS-VB scalar multiplication. Time and memory complexity of a generic scalar multiplication algorithm can potentially be improved if algebraic properties of the underlying group are exploited. The survey aims to give a general overview of a large class of scalar multiplication algorithms. The chapter provides mathematical insight into the algorithms with some correctness arguments and complexity analysis. It also provides pseudocodes and examples for concrete understanding and convenient implementation of the algorithms.
