We give a comparison of the performance of the recently proposed torus-based public key cryptosystem CEILIDH, and XTR. Underpinning both systems is the mathematics of the two dimen...
We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems ...
Abstract. We present efficient compression algorithms for subgroups of multiplicative groups of finite fields, we use our compression algorithms to construct efficient public key c...
Abstract. Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm pr...
This paper aims at introducing generalized Jacobians as a new candidate for discrete logarithm (DL) based cryptography. The motivation for this work came from the observation that ...