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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Autor principal:	Suhri Kim
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Post-quantum cryptography isogeny-based cryptography Huff curves Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/f6fdbacc8da341fba95e183ad8656db5
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id	oai:doaj.org-article:f6fdbacc8da341fba95e183ad8656db5
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spelling	oai:doaj.org-article:f6fdbacc8da341fba95e183ad8656db52021-11-25T00:00:59ZComplete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves2169-353610.1109/ACCESS.2021.3128515https://doaj.org/article/f6fdbacc8da341fba95e183ad8656db52021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9615246/https://doaj.org/toc/2169-3536In 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.Suhri KimIEEEarticlePost-quantum cryptographyisogeny-based cryptographyHuff curvesElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 154500-154512 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Post-quantum cryptography isogeny-based cryptography Huff curves Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Post-quantum cryptography isogeny-based cryptography Huff curves Electrical engineering. Electronics. Nuclear engineering TK1-9971 Suhri Kim Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
description	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.
format	article
author	Suhri Kim
author_facet	Suhri Kim
author_sort	Suhri Kim
title	Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
title_short	Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
title_full	Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
title_fullStr	Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
title_full_unstemmed	Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves
title_sort	complete analysis of implementing isogeny-based cryptography using huff form of elliptic curves
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/f6fdbacc8da341fba95e183ad8656db5
work_keys_str_mv	AT suhrikim completeanalysisofimplementingisogenybasedcryptographyusinghuffformofellipticcurves
_version_	1718414731201478656

Complete Analysis of Implementing Isogeny-Based Cryptography Using Huff Form of Elliptic Curves

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