Enhanced Montgomery Multiplication

Shay Gueron

doi:10.1007/3-540-36400-5_5

Enhanced Montgomery Multiplication

Shay Gueron

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We define the Non Reduced Montgomery Multiplication of order s, of A and B, modulo N (odd integer) by NRMM^s(A,B,N) = (AB + N (-ABN^-1 (mod 23^s))) 2^-s. Given an upper bound on A and B, with respect to N, we show how to choose the variable s in a way that guarantees that NRMM^s(A,B,N) < 2N. A few applications are demonstrated, showing the advantage of using NRMM^s with an appropriately chosen s, over the classical Montgomery Multiplication.

Original language	English
Pages (from-to)	46-56
Number of pages	11
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2523
DOIs	https://doi.org/10.1007/3-540-36400-5_5
State	Published - 2003

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/3-540-36400-5_5

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title = "Enhanced Montgomery Multiplication",

abstract = "We define the Non Reduced Montgomery Multiplication of order s, of A and B, modulo N (odd integer) by NRMMs(A,B,N) = (AB + N (-ABN-1 (mod 23s))) 2-s. Given an upper bound on A and B, with respect to N, we show how to choose the variable s in a way that guarantees that NRMMs(A,B,N) < 2N. A few applications are demonstrated, showing the advantage of using NRMMs with an appropriately chosen s, over the classical Montgomery Multiplication.",

author = "Shay Gueron",

year = "2003",

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AB - We define the Non Reduced Montgomery Multiplication of order s, of A and B, modulo N (odd integer) by NRMMs(A,B,N) = (AB + N (-ABN-1 (mod 23s))) 2-s. Given an upper bound on A and B, with respect to N, we show how to choose the variable s in a way that guarantees that NRMMs(A,B,N) < 2N. A few applications are demonstrated, showing the advantage of using NRMMs with an appropriately chosen s, over the classical Montgomery Multiplication.

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ER -

Enhanced Montgomery Multiplication

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