High-degree compression functions on alternative models of elliptic curves and their applications

@article{Wronski2021HighdegreeCF,
  title={High-degree compression functions on alternative models of elliptic curves and their applications},
  author={Michal Wro'nski and Tomasz Kijko and Robert Drylo},
  journal={Fundam. Informaticae},
  year={2021},
  volume={184},
  pages={107-139}
}
This paper presents method for obtaining high-degree compression functions using natural symmetries in a given model of an elliptic curve. Such symmetries may be found using symmetry of involution [–1] and symmetry of translation morphism τT = P + T, where T is the n-torsion point which naturally belongs to the E(𝕂) for a given elliptic curve model. We will study alternative models of elliptic curves with points of order 2 and 4, and specifically Huff’s curves and the Hessian family of… 
1 Citations

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

TLDR
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.

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