Abstract
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.
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Fouque, PA., Tibouchi, M. (2010). Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves. In: Abdalla, M., Barreto, P.S.L.M. (eds) Progress in Cryptology – LATINCRYPT 2010. LATINCRYPT 2010. Lecture Notes in Computer Science, vol 6212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14712-8_5
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DOI: https://doi.org/10.1007/978-3-642-14712-8_5
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