We provide new hash functions into (hyper)elliptic curves over finite fields. These functions aims at instantiating in a secure manner cryptographic protocols where we need to map strings into points on algebraic curves, typically user identities into public keys in pairingbased IBE schemes. Contrasting with recent Icart’s encoding, we start from “easy to solve by radicals” polynomials in order...

In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We find infinite families of t...

In this paper, we look at long geometric progressions on diferent model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huf curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinate (or y-coordinate) are in geometric progression. We fnd infnite families of twist...