Paper 2021/085

Complete Analysis of Implementing Isogeny-based Cryptography using Huff Form of Elliptic Curves

Suhri Kim


In this paper, we present the analysis of Huff curves for implementing isogeny-based cryptography. In this regard, we first investigate the computational cost of the building blocks when compression functions are used for Huff curves. We also apply the square-root V\'elu formula on Huff curves and present a new formula for recovering the coefficient of the curve, from a given point on a Huff curve. From our implementation, the performance of Huff-SIDH and Montgomery-SIDH is almost the same, and the performance of Huff-CSIDH is 6\% faster than Montgomery-CSIDH. We further optimized Huff-CSIDH by exploiting Edwards curves for computing the coefficient of the image curve and present the Huff-Edwards hybrid model. As a result, the performance of Huff-Edwards CSIDH is almost the same as Montgomery-Edwards CSIDH. The result of our work shows that Huff curves can be quite practical for implementing isogeny-based cryptography but has some limitations.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
IsogenyPost-quantum cryptographyMontgomery curvesHuff curvesSIDHCSIDH
Contact author(s)
suhrikim @ gmail com
2021-10-05: last of 2 revisions
2021-01-27: received
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      author = {Suhri Kim},
      title = {Complete Analysis of Implementing Isogeny-based Cryptography using Huff Form of Elliptic Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2021/085},
      year = {2021},
      note = {\url{}},
      url = {}
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