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.

Additional Metadata
Keywords Cryptography, Finite field, Number theory, Polynomial, Squaring
Persistent URL dx.doi.org/10.1016/j.ipl.2017.12.002
Journal Information Processing Letters
Citation
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