In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and provides smaller signatures than the existing schemes based on the integer factorization and integer discrete logarithm problems.

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key cryptosystems.

Hyperelliptic curves have been used to de ne discrete logarithm problems as cryptographic one-way functions. However, no e cient algorithm for construction of secure hyperelliptic curves is known until now. In this paper, e cient algorithms are presented to construct secure discrete logarithm problems on hyperelliptic curves whose Jacobian varieties are either simple or isogenous to a product o...

This paper reports on the computation of a discrete logarithm in finite field F 2 ...

In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and provides smaller signatures than the existing schemes based on the integer factorization and integer discrete logarithm problems.

A Σ-protocol for proving equality of the discrete logarithm of two pairs of numbers is presented and used in an electronic voting scheme originally proposed in [CGS97]. Further, the notion of zero knowledge is introduced and a modified (1-bit challenge) version of Schnorr’s identification scheme is shown to be zero knowledge. 1 Proving Discrete Logarithm Equality

1. Introduction In this paper we generalize the parallelized lambda method for computing invariants in real qua-dratic function elds. A basic such invariant is the regulator, which plays an important role in cryptosystems based on real quadratic function elds. For example, in the key-exchange protocol by Scheidler, Stein and Williams SSW96], the regulator provides a measure for the key space; m...

Using FPGAs to compute the discrete logarithms of elliptic curves is a well-known method. However, until to date only CPU clusters succeeded in computing new elliptic curve discrete logarithm records. This work presents a high-speed FPGA implementation that was used to compute the discrete logarithm of a 113-bit Koblitz curve. The core of the design is a fully unrolled, highly pipelined, self-s...