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

fYear

1997

fDate

6-9 Jul 1997

Firstpage

44

Lastpage

51

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic, 1997. Proceedings., 13th IEEE Symposium on

Conference_Location

Asilomar, CA

ISSN

1063-6889

Print_ISBN

0-8186-7846-1

Type

conf

DOI

10.1109/ARITH.1997.614878

Filename

614878