O(n)-depth circuit algorithm for modular exponentiation

Authors:
T. Hamano;N. Takagi;S. Yajima;F. P. Preparata
Affiliations:
-;-;-;-
Venue:
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Year:
1995

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Abstract

An O(n)-depth polynomial-size combinational circuit algorithm is proposed for n-bit modular exponentiation, i.e., for the computation of "x/sup y/ mod m" for arbitrary integers x, y and m. Represented as n-bit binary integers, within bounds 2/sup n-1//spl les/m2/sup n/ and 0/spl les/x,ym. The algorithm is a generalization of the square-and-multiply method. An obvious implementation of the square-and-multiply method yields a circuit of depth O(nlogn) and size O(n/sup 3/). In the proposed algorithm, the terms x/sup 2/ mod m's for all i's /spl epsiv.