Storage free basis conversion over composite finite fields of odd characteristics

2013-09-19
Sial, M Riaz
Akyıldız, Ersan
We study the Finite Fields of type Fq, q = p2pn from the efficient implementation point of view. We found that we can represent these fields with irreducible polynomials in the form f(x) = xp − x − a. By using this representation we have found a way of constructing normal basis for the field, together with transmission matrix between normal basis and algebraic basis (Polynomial Basis) of Fq and vice versa. The key point is that this matrix and its inverse can be computed very efficiently without any memory requirement.
Citation Formats
M. R. Sial and E. Akyıldız, “Storage free basis conversion over composite finite fields of odd characteristics,” presented at the International Information Security and Cryptology Conference, ( 20 - 21 Eylül 2013), Ankara, Türkiye, 2013, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88172.