Abstract.It is shown constructively that a strongly extensional function of bounded variation on an interval is regulated, in a sequential sense that is classically equivalent to the usual one.

ABSTRACT. This is a study of the MOR cryptosystem using the special linear group over finite fields. The automorphism group of the special linear group is analyzed for this purpose. At our current state of knowledge, I show that this MOR cryptosystem has better security than the ElGamal cryptosystem over finite fields.

In this paper we study a key exchange protocol similar to the DiffieHellman key exchange protocol, using abelian subgroups of the automorphism group of a non-abelian nilpotent group. We also generalize group no. 92 of the Hall-Senior table [16] to an arbitrary prime p and show that, for those groups, the group of central automorphisms is commutative. We use these for the key exchange we are studying.

In this paper, we describe a new Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The algorithm depends on a property of the the group of rational points of an elliptic curve and is thus not a generic algorithm. The algorithm that we describe has some similarities with the most powerful indexcalculus algorithm for the discrete logarithm problem over a finite field.

In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equivalent to the El-Gamal cryptosystem over finite fields.