In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to genera...
Nguyen and Shparlinski recently presented a polynomial-time algorithm that provably recovers the signer's secret DSA key when a few bits of the random nonces k (used at each s...
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
Abstract This contribution describes how an elliptic curve cryptosystem can be implemented on very low cost microprocessors with reasonable performance. We focus in this paper on t...
Abstract. This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over...
Daniel J. Bernstein, Peter Birkner, Marc Joye, Tan...