Let G be finite group and K a number field or a p-adic field with ring of integers OK . In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K0(OK [G], K) as an abstract abelian group. We solve the discrete logarithm problem, both in K0(OK [G], K) and the locally free class group cl(OK [G]). All algorithms have been implemented in MAGMA for th...

In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem in degree 0 class groups of non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of Õ(q), where q is the cardinality of the ground field. Moreover, it is proven...

In 1984, Shamir proposed the concept of the Identity-Based (ID-Based) cryptosystem. Instead of generating and publishing a public key for each user, the ID-Based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large publickey file is not ...

Joint work wih Francois Morain. A connection between the discrete logarithm problem over Fq^h and the problem of decoding Reed-Solomon codes over Fq has been proposed and studied by Cheng, Wang at FOCS 2004, essentially in a theoretical manner to study the hardness of decoding a ReedSolomon codes when a large number of errors occurs. We propose to study this reduction in a reverse direction fro...

We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is based on a discrete logarithm problem on the quotient of certain modules defined through the N\'{e}ron-Severi groups. The discrete logarithm problem is reduci...

-------------------------------------------------------------------ABSTRACT-----------------------------------------------------Blind signature scheme provide the feature that a user is able to get a signature without giving the actual message to the signer. Many Blind signature schemes have been proposed in which security are based on intractability of factoring or DLP (Discrete Logarithm Prob...

We show how to apply the canonical path method to a non-reversible Markov chain with no holding probability: a random walk used in Pollard’s Rho algorithm for discrete logarithm. This is used to show that the Pollard Rho method for finding the discrete logarithm on a cyclic group G requires O( √ |G| (log |G|)3/2) steps until a collision occurs and discrete logarithm is possibly found, not far f...

This paper introduces a knapsack cryptosystem based on the problem of discrete logarithm. The proposed algorithm obtains the public knapsack values by finding the discrete logarithms of the secret knapsack ones. Also, it encrypts the message block by obtaining its binary bits and then computing the modular multiplication of the public knapsack values corresponding to the 1-bits of the binary fo...

There are many cryptographic protocols the security of which depends on the diiculty of solving the discrete logarithm problem (8], 9], 14], etc.). In 10] and 18] it was described how to apply the number eld sieve algorithm to the discrete logarithm problem in prime elds. This resulted in the asymptotically fastest known discrete log algorithm for nite elds of p elements. Very little is known a...

The discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems. Recently, real quadratic congruence function fields were used to construct a public key distribution system. The security of this public key system is based on the difficulty of a discrete logarithm problem in these fields. In this paper, we present a probabilistic algorith...