Theory and applications for a double-base number system

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	Similar Articles Articles by V.S. Dimitrov Articles by G.A. Jullien Articles by W.C. Miller

13th IEEE Symposium on Computer Arithmetic (ARITH-13 '97)

Asilomar, CA

March 06-March 09

ISBN: 0-8186-7846-1

	ASCII Text	x
	V.S. Dimitrov, G.A. Jullien, W.C. Miller, "Theory and applications for a double-base number system," Computer Arithmetic, IEEE Symposium on, pp. 44, 13th IEEE Symposium on Computer Arithmetic (ARITH-13 '97), 1997.

	BibTex	x
	@article{ 10.1109/ARITH.1997.614878, author = {V.S. Dimitrov and G.A. Jullien and W.C. Miller}, title = {Theory and applications for a double-base number system}, journal ={Computer Arithmetic, IEEE Symposium on}, volume = {0}, year = {1997}, issn = {1063-6889}, pages = {44}, doi = {http://doi.ieeecomputersociety.org/10.1109/ARITH.1997.614878}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Computer Arithmetic, IEEE Symposium on TI - Theory and applications for a double-base number system SN - 1063-6889 SP EP A1 - V.S. Dimitrov, A1 - G.A. Jullien, A1 - W.C. Miller, PY - 1997 KW - number theory KW - double-base number system KW - sparse representation KW - geometric interpretation KW - basic arithmetic operations KW - index calculus KW - logarithmic-like arithmetic KW - hardware reductions KW - lookup table size KW - digital signal processing KW - inner product computation KW - cryptography KW - modular exponentiation computation VL - 0 JA - Computer Arithmetic, IEEE Symposium on ER -

V.S. Dimitrov, VLSI Res. Group, Windsor Univ., Canada

G.A. Jullien, VLSI Res. Group, Windsor Univ., Canada

W.C. Miller, VLSI Res. Group, Windsor Univ., Canada

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.1997.614878

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.

Index Terms:

number theory, double-base number system, sparse representation, geometric interpretation, basic arithmetic operations, index calculus, logarithmic-like arithmetic, hardware reductions, lookup table size, digital signal processing, inner product computation, cryptography, modular exponentiation computation

Citation:

V.S. Dimitrov, G.A. Jullien, W.C. Miller, "Theory and applications for a double-base number system," arith, pp.44, 13th IEEE Symposium on Computer Arithmetic (ARITH-13 '97), 1997

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