Abstract
Irreducible Polynomials over GF(p) and the multiplicative inverses under it are important in cryptography. Presently the method of deriving irreducible polynomials of a particular prime modulus is very primitive and time consuming. In this paper, in order to find all irreducible polynomials, be it monic or non-monic, of all prime moduli p with all its order m, a fast deterministic computer algorithm based on an algebraic method producing a (m×m) matrix is proposed. The maximum number of terms in each column of the matrix is 2 where j is the column index. General Terms Algorithms, Irreducible polynomial.
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