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Fast algorithm for modular reduction

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2 Author(s)
Kop, Q.K. ; Dept. of Electr. & Comput. Eng., Oregon State Univ., Corvallis, OR, USA ; Hung, C.Y.

The paper presents an algorithm for computing the residue R=X mod M. The algorithm is based on a sign estimation technique that estimates the sign of a number represented by a carry-sum pair produced by a carry save adder. Given the (n+k)-bit X and the n-bit M, the modular reduction algorithm computes the n-bit residue R in O(k+log n) time, and is particularly useful when the operand size is large. We also present a variant of the algorithm that performs modular multiplication by interleaving the shift-and-add and the modular reduction steps. The modular multiplication algorithm can be used to obtain efficient VLSI implementations of exponentiation cryptosystems

Published in:

Computers and Digital Techniques, IEE Proceedings -  (Volume:145 ,  Issue: 4 )

Date of Publication:

Jul 1998

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