We study the problem of finding efficiently computable non-degenerate multilinear maps from G1 to G2, where G1 and G2 are groups of the same prime order, and where computing discrete logarithms in G1 is hard. We present several applications to cryptography, explore directions for building such maps, and give some reasons to believe that finding examples with n > 2

In 1977, Adleman, Manders and Miller had briefly described how to extend their square root extraction method to the general rth root extraction over finite fields, but not shown enough details. Actually, there is a dramatic difference between the square root extraction and the general rth root extraction because one has to solve discrete logarithms for rth root extraction. In this paper, we cla...

Exact values and bounds on the k-error linear complexity of p-periodic sequences which are constant on the cyclotomic classes are determined. This family of sequences includes sequences of discrete logarithms, Legendre sequences and Hall’s sextic residue sequence.

In this paper, we describe a new algorithm for discrete logarithms in small characteristic. It works especially well when the characteristic is fixed. Indeed, in this case, we obtain a total complexity of L(1/4 + o(1)).

We present an algorithm for the computation of the discrete logarithm in logarithmic `-Class Groups. This is applied to the calculation to the `-rank of the wild kernel WK2 of a number field F and in the determination of generators of the `-part of WK2(F ).

In 2004, Zhang and Xiao proposed a multisignature scheme based on ElGamal discrete logarithm algorithm which allows a signer group to sign a signature and a verifier group to verify the validity of the signed signature. In this paper, we will show that any verifier in the verifier group can break their scheme by replacing the valid signed message with another forged one which will also be authe...

This paper presents a method for generating prime moduli with a special form which can simplify the modular reduction process and reduce the storage requirement. Such moduli will be particularly useful for implementing discrete log cryptosystems under the environment with limited computing and storage resources.

1. INTRODUCTION. The development of the famous Hardy inequality (in both its discrete and continuous forms) during the period 1906–1928 has its own history or, as we have called it, prehistory. Contributions of mathematicians other than G. are important here. In this article we describe some of those contributions. We also include and comment upon several facts and early proofs that are not ava...

We describe in this article how we have been able to extend the record for computations of discrete logarithms in characteristic 2 from the previous record over F2503 to a newer mark of F2607 , using Coppersmith’s algorithm. This has been made possible by several practical improvements to the algorithm. Although the computations have been carried out on fairly standard hardware, our opinion is ...