Cryptology ePrint Archive: Report 2021/073

Application of Velusqrt algorithm to Huff's and general Huff's curves

Michał Wroński

Abstract: In 2020 Bernstein, De Feo, Leroux, and Smith presented a new odd-degree $\ell$-isogeny computation method called Velusqrt. This method has complexity $\tilde{O}(\sqrt{\ell})$, compared to the complexity of $\tilde{O}(\ell)$ of the classical Vélu method. In this paper application of the Velusqrt method to Huff's and general Huff's curves is presented. It is showed how to compute odd-degree isogeny on Huff's and general Huff's curves using Velusqrt algorithm and $x$-line arithmetic for different compression functions.

Category / Keywords: applications / general Huff's curves and Huff's curves and compression on elliptic curves and isogeny-based cryptography and Velusqrt method

Date: received 21 Jan 2021

Contact author: michal wronski at wat edu pl

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Version: 20210122:203208 (All versions of this report)

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