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.

By admin