Storage free basis conversion over composite finite fields of odd characteristics

Date

2013-09-19

Author

Sial, M Riaz
Akyıldız, Ersan

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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.

Subject Keywords

Finite fields, Composite field, Basis conversion, Polynomial basis, Normal basis, Vandermonde matrix, Reciprocal polynomial

URI

https://hdl.handle.net/11511/88172

Conference Name

International Information Security and Cryptology Conference, ( 20 - 21 Eylül 2013)

Collections

Graduate School of Applied Mathematics, Conference / Seminar

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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.