Encoding Points on Hyperelliptic Curves over
Finite Fields in Deterministic Polynomial Time.
In M. Joye, A. Miyaji, and A. Otsuka, editors,
Pairing-Based Cryptography - Pairing 2010, volume 6487 of Lecture Notes
in Computer Science, pages 278-297. Springer, December 2010..
We provide new hash functions into (hyper)elliptic curves
over finite fields. These functions aim 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 pairing-based IBE schemes.
Contrasting with recent Icart's encoding, we start from
“easy to solve by radicals” polynomials in order to obtain
models of curves which in turn can be deterministically
“algebraically parameterized”. As a result of this
strategy, we obtain a low degree encoding map for Hessian
elliptic curves, and for the first time, hashing functions
for genus 2 curves. More generally, we present for any
genus (more narrowed) families of hyperelliptic curves with
this property. The image of these encodings is large enough
to be “weak” encodings in the sense of Brier et al. As
such they can be easily turned into admissible cryptographic
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