Title :
Theory and applications for a double-base number system
Author :
Dimitrov, V.S. ; Jullien, G.A. ; Miller, W.C.
Author_Institution :
VLSI Res. Group, Windsor Univ., Ont., Canada
Abstract :
Presents 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
Keywords :
arithmetic; cryptography; digital arithmetic; geometry; number theory; signal processing; table lookup; basic arithmetic operations; cryptography; digital signal processing; double-base number system; geometric interpretation; hardware reductions; index calculus; inner product computation; logarithmic-like arithmetic; lookup table size; modular exponentiation computation; sparse representation; Calculus; Computational complexity; Computer applications; Digital arithmetic; Digital signal processing; Finite impulse response filter; Hardware; Signal processing algorithms; Table lookup; Very large scale integration;
Conference_Titel :
Computer Arithmetic, 1997. Proceedings., 13th IEEE Symposium on
Conference_Location :
Asilomar, CA
Print_ISBN :
0-8186-7846-1
DOI :
10.1109/ARITH.1997.614878
