In this article we propose three optimizations of indifferentiable hashing onto (prime order subgroups of) ordinary elliptic curves over finite fields $mathbb{F}_{!q}$. One of them is dedicated to elliptic curves $E$ provided that $q equiv 11 (mathrm{mod} 12)$. The other two optimizations take place respectively for the subgroups $mathbb{G}_1$, $mathbb{G}_2$ of some pairing-friendly curves. The performance gain comes from the smaller number of required exponentiations in $mathbb{F}_{!q}$ for hashing to $E(mathbb{F}_{!q})$, $mathbb{G}_2$ (resp. from the absence of necessity to hash directly onto $mathbb{G}_1$). In particular, our results affect the pairing-friendly curve BLS12-381 (the most popular in practice at the moment) and the (unique) French curve FRP256v1 as well as almost all Russian standardized curves and a few ones from the draft NIST SP 800-186.

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