Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves

Let E be a non-supersingular elliptic curve over a finite field Fq. At CRYPTO 2009, Icart introduced a deterministic function Fq → E(Fq) which can be computed efficiently, and allowed him and Coron to define well-behaved hash functions with values in E(Fq). Some properties of this function rely on a conjecture which was left as an open problem in Icart’s paper. We prove this conjecture below as well as analogues for other hash functions.

• Type: Journal
• Year: 2010
• Where: LATINCRYPT
• Authors: Pierre-Alain Fouque, Mehdi Tibouchi
• Keywords: Cryptology, Deterministic Function Fq, Hash Functions, LATINCRYPT 2010, finite field Fq