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

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May 2010, 4(2): 215-235. doi: 10.3934/amc.2010.4.215

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

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

Received June 2009 Revised March 2010 Published May 2010

Abstract
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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.

Keywords: group action, Public-key cryptography, finite field., isogeny, elliptic curve, ideal class group.

Mathematics Subject Classification: 94A60, 14G5.

Citation: Anton Stolbunov. Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Advances in Mathematics of Communications, 2010, 4 (2) : 215-235. doi: 10.3934/amc.2010.4.215

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