A new class of irreducible pentanomials for polynomial-based multipliers in binary fields

Gustavo Banegas; Ricardo Custódio; Daniel Panario

doi:10.1007/s13389-018-0197-6

A new class of irreducible pentanomials for polynomial-based multipliers in binary fields

Gustavo Banegas
, Ricardo Custódio
, Daniel Panario

Technical University of Eindhoven
Universidade Federal de Santa Catarina
Carleton University

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

5 Citations (Scopus)

Abstract

We introduce a new class of irreducible pentanomials over F₂ of the form f(x) = x² ^b ⁺ ^c+ x^b ⁺ ^c+ x^b+ x^c+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F₂[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.

Original language	English
Pages (from-to)	359-373
Number of pages	15
Journal	Journal of Cryptographic Engineering
Volume	9
Issue number	4
DOIs	https://doi.org/10.1007/s13389-018-0197-6
Publication status	Published - 1 Nov 2019
Externally published	Yes

Keywords

Finite fields
Irreducible pentanomials
Modular reduction
Polynomial multiplication

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10.1007/s13389-018-0197-6

Cite this

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abstract = "We introduce a new class of irreducible pentanomials over F2 of the form f(x) = x2 b + c+ xb + c+ xb+ xc+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.",

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AU - Banegas, Gustavo

AU - Custódio, Ricardo

AU - Panario, Daniel

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Y1 - 2019/11/1

N2 - We introduce a new class of irreducible pentanomials over F2 of the form f(x) = x2 b + c+ xb + c+ xb+ xc+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.

AB - We introduce a new class of irreducible pentanomials over F2 of the form f(x) = x2 b + c+ xb + c+ xb+ xc+ 1. Let m= 2 b+ c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F2[x] combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm.

KW - Finite fields

KW - Irreducible pentanomials

KW - Modular reduction

KW - Polynomial multiplication

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DO - 10.1007/s13389-018-0197-6

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AN - SCOPUS:85073577324

SN - 2190-8508

VL - 9

SP - 359

EP - 373

JO - Journal of Cryptographic Engineering

JF - Journal of Cryptographic Engineering

IS - 4

ER -

A new class of irreducible pentanomials for polynomial-based multipliers in binary fields

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Keywords

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