On calculating multiplicative inverses modulo 2m

Ortal Arazi; Hairong Qi

doi:10.1109/TC.2008.54

On calculating multiplicative inverses modulo 2^m

Ortal Arazi
, Hairong Qi

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

12 Scopus citations

Abstract

This paper presents a procedure for calculating multiplicative inverses modulo 2^m, based on a novel mathematical approach. The procedure is suitable for software implementation on a general-purpose processor. When counting the total number of word-level processor multiplications, the computational effort involved in calculating a multiplicative inverse is 2/3 that of a single multiplication of m-bit values, in addition to a few word-level multiplications. For standard processor word sizes, the number of these additional multiplications does not exceed 12. This introduces a clear advantage of the proposed method when compared to other known methods presented in the literature.

Original language	English
Pages (from-to)	1435-1438
Number of pages	4
Journal	IEEE Transactions on Computers
Volume	57
Issue number	10
DOIs	https://doi.org/10.1109/TC.2008.54
State	Published - 15 Sep 2008
Externally published	Yes

Keywords

Modular arithmetic
Modular multiplication
Modular multiplicative inverse

ASJC Scopus subject areas

Software
Theoretical Computer Science
Hardware and Architecture
Computational Theory and Mathematics

Access to Document

10.1109/TC.2008.54

Cite this

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AB - This paper presents a procedure for calculating multiplicative inverses modulo 2m, based on a novel mathematical approach. The procedure is suitable for software implementation on a general-purpose processor. When counting the total number of word-level processor multiplications, the computational effort involved in calculating a multiplicative inverse is 2/3 that of a single multiplication of m-bit values, in addition to a few word-level multiplications. For standard processor word sizes, the number of these additional multiplications does not exceed 12. This introduces a clear advantage of the proposed method when compared to other known methods presented in the literature.

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