Theory and applications for a double-base number system

In this paper we present a rigorous theoretical analysis of the main properties of a double base number system, using bases 2 and 3; in particular we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus for logarithmic-like arithmetic with considerable hardware reductions in look-up table size. Two potential areas of applications are discussed: applications in digital signal processing for computation of inner products and in cryptography for computation of modular exponentiations.

• Type: Conference
• Year: 1997
• Where: ARITH
• Authors: Vassil S. Dimitrov, Graham A. Jullien, William C. Miller
• Keywords: Applied Computing, ARITH 1997, Basic Arithmetic Operations, Considerable Hardware Reductions, Rigorous Theoretical Analysis