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Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
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DOI：10.1109/ACCESS.2021.3128515.png)
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Abstract
En 中文
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 Velu 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.
Keywords:
Cryptography
Elliptic curves
Arithmetic
Costs
Computational efficiency
Quantum computing
Protocols
Post-quantum cryptography
isogeny-based cryptography
Huff curves
Journal
IF:
3.6
Papers:
9.7W
Citations:
29.4W
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