Cryptology ePrint Archive: Report 2006/145


Alexander Rostovtsev and Anton Stolbunov

Abstract: A new general mathematical problem, suitable for public-key cryptosystems, is proposed: morphism computation in a category of Abelian groups. In connection with elliptic curves over finite fields, the problem becomes the following: compute an isogeny (an algebraic homomorphism) between the elliptic curves given. The problem seems to be hard for solving with a quantum computer. ElGamal public-key encryption and Diffie-Hellman key agreement are proposed for an isogeny cryptosystem. The paper describes theoretical background and a public-key encryption technique, followed by security analysis and consideration of cryptosystem parameters selection. A demonstrative example of encryption is included as well.

Category / Keywords: public-key cryptography / public-key cryptography, elliptic curve cryptosystem, cryptosystem on isogenies of elliptic curves, isogeny star, isogeny cycle, quantum computer

Date: received 13 Apr 2006, last revised 29 May 2006

Contact author: stolbunov at list ru

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Version: 20060529:183027 (All versions of this report)

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