Open AccessComplete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
Author(s) -
Suhri Kim
Publication year - 2021
Publication title -
ieee access
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.587
H-Index - 127
ISSN - 2169-3536
DOI - 10.1109/access.2021.3128515
Subject(s) - aerospace , bioengineering , communication, networking and broadcast technologies , components, circuits, devices and systems , computing and processing , engineered materials, dielectrics and plasmas , engineering profession , fields, waves and electromagnetics , general topics for engineers , geoscience , nuclear engineering , photonics and electrooptics , power, energy and industry applications , robotics and control systems , signal processing and analysis , transportation
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 present a new formula for recovering the coefficient of the curve, from a given point on a Huff curve, which is essential for implementing SIDH. We also apply the square-root Vélu formula on Huff curves and further optimize Huff-CSIDH by exploiting Edwards curves for computing the coefficient of the image curve and present the Huff-Edwards hybrid model. 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. 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.