We present an efficient bit-parallel algorithm for squaring in GF(2m) using polynomial basis. This algorithm achieves competitive efficiency while being aimed at any choice of low-weight irreducible polynomial. For a large class of irreducible polynomials it is more efficient than the previously best general squarer. In contrast, other efficient squarers often require a change of basis or are suitable for only a small number of irreducible polynomials. Additionally, we present a simple algorithm for modular reduction with equivalent cost to the state of the art for general irreducible polynomials. This fast reduction is used in our squaring method.

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Keywords Cryptography, Finite field, Number theory, Polynomial, Squaring
Persistent URL dx.doi.org/10.1016/j.ipl.2017.12.002
Journal Information Processing Letters
Niehues, L.B. (L. Boppre), Custódio, R. (R.), & Panario, D. (2018). Fast modular reduction and squaring in GF(2m). Information Processing Letters, 132, 33–38. doi:10.1016/j.ipl.2017.12.002