Cryptology ePrint Archive: Report 2018/554

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

Gustavo Banegas and Ricardo Custodio and Daniel Panario

Abstract: We introduce a new class of irreducible pentanomials over ${\mathbb F}_{2^m}$ of the form $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ 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 $\mathbb{F}_2[x]$ 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.

Category / Keywords: irreducible pentanomials and polynomial multiplication and modular reduction and finite fields

Original Publication (in the same form): Journal of Cryptographic Engineering

Date: received 29 May 2018, last revised 10 Nov 2018

Contact author: gustavo at crytpme in

Available format(s): PDF | BibTeX Citation

Version: 20181110:142830 (All versions of this report)

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