We define a security notion for non-interactive key distribution protocols. We identify an apparently hard computational problem related to pairings, the Bilinear Diffieâ€“Hellman problem (BDH). Afterâ€¦ (More)

We study several known volume computation algorithms for convex d-polytopes by classifying them into two classes, triangulation methods and signed-decomposition methods. By incorporating theâ€¦ (More)

We present a fast algorithm for building ordinary elliptic curves over finite prime fields having arbitrary small MOV degree. The elliptic curves are obtained using complex multiplication by anyâ€¦ (More)

We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over nite elds. More precisely, the running time for instances withâ€¦ (More)

The discrete logarithm problem in Jacobians of curves of high genus g over finite fields Fq is known to be computable with subexponential complexity Lqg (1/2, O(1)). We present an algorithm for aâ€¦ (More)

We provide explicit formulae for realising the group law in Jacobians of superelliptic curves of genus 3 and C3,4 curves. It is shown that two distinct elements in the Jacobian of a C3,4 curve can beâ€¦ (More)

We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in X and Y are low with respect to their genera. The finite base fieldsâ€¦ (More)