GF(2 n) Montgomery multiplication using Polynomial Residue Arithmetic

Dimitrios Schinianakis; Alexander Skavantzos; Thanos Stouraitis

doi:10.1109/ISCAS.2012.6271958

GF(2 ⁿ) Montgomery multiplication using Polynomial Residue Arithmetic

Dimitrios Schinianakis, Alexander Skavantzos, Thanos Stouraitis

Electrical Engineering

Research output: Contribution to conference › Paper › peer-review

4 Scopus citations

Abstract

A methodology for incorporating Polynomial Residue Arithmetic (PRA) in the Montgomery multiplication algorithm for polynomials in GF(2 ⁿ) is presented in this paper. The mathematical conditions that need to be satisfied, in order for this incorporation to be valid are examined and performance results are given in terms of the field characteristic n, the number of moduli elements L, and the moduli word-length w. The proposed architecture is highly parallelizable and flexible, as it supports Polynomial-to-PRA and PRA-to-Polynomial conversions, Chinese Remainder Theorem (CRT) for polynomials, Montgomery multiplication, and Montgomery exponentiation in the same hardware.

Original language	British English
Pages	3033-3036
Number of pages	4
DOIs	https://doi.org/10.1109/ISCAS.2012.6271958
State	Published - 2012
Event	2012 IEEE International Symposium on Circuits and Systems, ISCAS 2012 - Seoul, Korea, Republic of Duration: 20 May 2012 → 23 May 2012

Conference

Conference	2012 IEEE International Symposium on Circuits and Systems, ISCAS 2012
Country/Territory	Korea, Republic of
City	Seoul
Period	20/05/12 → 23/05/12

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10.1109/ISCAS.2012.6271958

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abstract = "A methodology for incorporating Polynomial Residue Arithmetic (PRA) in the Montgomery multiplication algorithm for polynomials in GF(2 n) is presented in this paper. The mathematical conditions that need to be satisfied, in order for this incorporation to be valid are examined and performance results are given in terms of the field characteristic n, the number of moduli elements L, and the moduli word-length w. The proposed architecture is highly parallelizable and flexible, as it supports Polynomial-to-PRA and PRA-to-Polynomial conversions, Chinese Remainder Theorem (CRT) for polynomials, Montgomery multiplication, and Montgomery exponentiation in the same hardware.",

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doi = "10.1109/ISCAS.2012.6271958",

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note = "2012 IEEE International Symposium on Circuits and Systems, ISCAS 2012 ; Conference date: 20-05-2012 Through 23-05-2012",

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AU - Schinianakis, Dimitrios

AU - Skavantzos, Alexander

AU - Stouraitis, Thanos

PY - 2012

Y1 - 2012

N2 - A methodology for incorporating Polynomial Residue Arithmetic (PRA) in the Montgomery multiplication algorithm for polynomials in GF(2 n) is presented in this paper. The mathematical conditions that need to be satisfied, in order for this incorporation to be valid are examined and performance results are given in terms of the field characteristic n, the number of moduli elements L, and the moduli word-length w. The proposed architecture is highly parallelizable and flexible, as it supports Polynomial-to-PRA and PRA-to-Polynomial conversions, Chinese Remainder Theorem (CRT) for polynomials, Montgomery multiplication, and Montgomery exponentiation in the same hardware.

AB - A methodology for incorporating Polynomial Residue Arithmetic (PRA) in the Montgomery multiplication algorithm for polynomials in GF(2 n) is presented in this paper. The mathematical conditions that need to be satisfied, in order for this incorporation to be valid are examined and performance results are given in terms of the field characteristic n, the number of moduli elements L, and the moduli word-length w. The proposed architecture is highly parallelizable and flexible, as it supports Polynomial-to-PRA and PRA-to-Polynomial conversions, Chinese Remainder Theorem (CRT) for polynomials, Montgomery multiplication, and Montgomery exponentiation in the same hardware.

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T2 - 2012 IEEE International Symposium on Circuits and Systems, ISCAS 2012

Y2 - 20 May 2012 through 23 May 2012

ER -

GF(2 ⁿ) Montgomery multiplication using Polynomial Residue Arithmetic

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