Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
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 cu...
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| Main Author: | |
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| Format: | article |
| Language: | EN |
| Published: |
IEEE
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/f6fdbacc8da341fba95e183ad8656db5 |
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| Summary: | 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. |
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