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Theory and applications for a double-base number system
Asilomar, CA March 06-March 09
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.1997.61487813th IEEE Symposium on Computer Arith ...
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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
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@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
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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