The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

We present a variation of the index calculus attack by Gaudry which can be used to solve the
discrete logarithm problem in the Jacobian of hyperelliptic curves. The new algorithm has a …

This dissertation has two chapters. In the first chapter we talk about the discrete logarithm
problem, more specifically we concentrate on the Diffie-Hellman key exchange protocol. We …

Semirings as an algebraic structure have been known since 1934, but remained unapplied
for mathematical purposes for a long time. It has only been in the past decade that they have …

In this paper, we show how the Weil descent attack of Gaudry, Hess and Smart can be
adapted to work for some hyperelliptic curves defined over fields of odd characteristic. This …

We review the construction of a generalization of the Weil pairing, which is non-degenerate
and bilinear, and use it to construct a reduction from the discrete logarithm problem on …

In this paper, we show how the method introduced by Gaudry, Hess and Smart can be
extended to a family of algebraic curves using Artin-Schreier extensions. This family also …

We discuss a special class of permutation polynomials over finite fields focusing on some
recent work on their factorization. In particular we obtain permutation polynomials with …

We present polynomial time algorithms for certain generalizations of the hidden number
problem which has played an important role in gaining understanding of the security of …

We study the number Nq (n, m1, m2) of polynomials of degree n over a finite field F q with all
irreducible factors of degree bigger than m2 and less than or equal to m1. Applying the …