Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves

Anton Stolbunov

doi:10.3934/amc.2010.4.215

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2010, Volume 4, Issue 2: 215-235. Doi: 10.3934/amc.2010.4.215

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Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves

Anton Stolbunov^1,

1.
Department of Telematics, Norwegian University of Science and Technology, O.S. Bragstads plass 2a, N-7491 Trondheim

Received: May 31, 2009

Revised: February 28, 2010

Published: April 2010

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Abstract

We propose a public-key encryption scheme and key agreement protocols based on a group action on a set. We construct an implementation of these schemes for the action of the class group $\mathcal{CL}(\mathcal{O}_K)$ of an imaginary quadratic field $K$ on the set $\mathcal{ELL}$_p,n$(\mathcal{O}_K)$ of isomorphism classes of elliptic curves over $\mathbb{F}_p$ with $n$ points and the endomorphism ring $\mathcal{O}_K$. This introduces a novel way of using elliptic curves for constructing asymmetric cryptography.

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Mathematics Subject Classification: 94A60, 14G50.

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