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

Gustavo Banegas (Corresponding author), Ricardo Custódio, Daniel Panario

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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Abstract

We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 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 F 2[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 languageEnglish
Pages (from-to)359–373
Number of pages15
JournalJournal of Cryptographic Engineering
Volume9
Issue number4
Early online date9 Nov 2018
DOIs
Publication statusPublished - 1 Nov 2019

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Polynomials
Time delay
Costs

Keywords

  • Finite fields
  • Irreducible pentanomials
  • Modular reduction
  • Polynomial multiplication

Cite this

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abstract = "We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 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 F 2[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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A new class of irreducible pentanomials for polynomial-based multipliers in binary fields. / Banegas, Gustavo (Corresponding author); Custódio, Ricardo; Panario, Daniel.

In: Journal of Cryptographic Engineering, Vol. 9, No. 4, 01.11.2019, p. 359–373.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Banegas, Gustavo

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N2 - We introduce a new class of irreducible pentanomials over F 2 of the form f(x) = x 2 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 F 2[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 F 2 of the form f(x) = x 2 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 F 2[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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KW - Irreducible pentanomials

KW - Modular reduction

KW - Polynomial multiplication

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