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Published in:
2010 | OriginalPaper | Chapter
Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves
Authors : Pierre-Alain Fouque, Mehdi Tibouchi
Published in: Progress in Cryptology – LATINCRYPT 2010
Publisher: Springer Berlin Heidelberg
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Let
E
be a non-supersingular elliptic curve over a finite field
$\mathbb{F}_{\!q}$
. At CRYPTO 2009, Icart introduced a deterministic function
$\mathbb{F}_{\!q}\to E(\mathbb{F}_{\!q})$
which can be computed efficiently, and allowed him and Coron to define well-behaved hash functions with values in
$E(\mathbb{F}_{\!q})$
. 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.