Orienting supersingular isogeny graphs

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Mathematical Cryptology Pub Date : 2020-01-01 DOI:10.1515/jmc-2019-0034

Leonardo Colò, D. Kohel

引用次数: 38

Abstract

Abstract We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs. As an application we introduce an oriented supersingular isogeny Diffie-Hellman protocol (OSIDH), analogous to the supersingular isogeny Diffie-Hellman (SIDH) protocol and generalizing the commutative supersingular isogeny Diffie-Hellman (CSIDH) protocol.

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超奇异同构图的定向

摘要引入了𝓞-oriented超奇异椭圆曲线的一类，并推导了相关的有向和无向的超奇异等构图的性质。作为一种应用，我们引入了一种面向超奇异同工Diffie-Hellman协议(OSIDH)，它类似于超奇异同工Diffie-Hellman协议(SIDH)，推广了可交换超奇异同工Diffie-Hellman协议(CSIDH)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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