Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time

TL;DR

This paper introduces families of hyperelliptic curves over finite fields that can be encoded efficiently and deterministically, improving the practicality of cryptographic schemes based on such curves.

Contribution

It provides the first known deterministic polynomial-time encoding methods for certain hyperelliptic curves over finite fields.

Findings

Efficient deterministic encoding functions for specific hyperelliptic curves.

Polynomial-time algorithms for encoding points on these curves.

Potential applications in cryptography and secure communications.

Abstract

We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function.