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PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES
Authors: Alexander Rostovtsev, Anton StolbunovAbstract:
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.
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