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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
David W. Matula , Southern Methodist University
Alex Fit-Florea , Southern Methodist University
Mitchell Aaron Thornton , Southern Methodist University
<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>

M. A. Thornton, A. Fit-Florea and D. W. Matula, "Table Lookup Structures for Multiplicative Inverses Modulo 2^k," Computer Arithmetic, IEEE Symposium on(ARITH), Cape Cod, Massachusetts, USA, 2005, pp. 156-163.
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