Computer Arithmetic, IEEE Symposium on (2005)

Cape Cod, Massachusetts, USA

June 27, 2005 to June 29, 2005

ISSN: 1063-6889

ISBN: 0-7695-2366-8

pp: 156-163

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2005.43

Mitchell Aaron Thornton , Southern Methodist University

Alex Fit-Florea , Southern Methodist University

David W. Matula , Southern Methodist University

ABSTRACT

<p>We introduce an inheritance property and related table lookup structures applicable to simplified evaluation of the modular operations "multiplicative inverse", "discrete log", and "exponential residue" in the particular modulus 2^k. Regarding applications, we describe an integer representation system of Benschop for transforming integer multiplications into additions which benefits from our table lookup function evaluation procedures.</p> <p>We focus herein on the multiplicative inverse modulo 2^k to exhibit simplifications in hardware implementations realized from the inheritance property. A table lookup structure given by a bit string that can be interpreted with reference to a binary tree is described and analyzed. Using observed symmetries, the lookup structure size is reduced allowing a novel direct lookup process for multiplicative inverses for all 16-bit odd integers to be obtained from a table of size less than two KBytes. The 16-bit multiplicative inverse operation is also applicable for providing a seed inverse for obtaining 32/64-bit multiplicative inverses by one/two iterations of a known quadratic refinement algorithm.</p>

INDEX TERMS

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CITATION

Mitchell Aaron Thornton,
Alex Fit-Florea,
David W. Matula,
"Table Lookup Structures for Multiplicative Inverses Modulo 2^k",

*Computer Arithmetic, IEEE Symposium on*, vol. 00, no. , pp. 156-163, 2005, doi:10.1109/ARITH.2005.43