Abstract

A new general mathematical problem, suitable for publickey 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 Di#e-Hellman key agreement are proposed for an isogeny cryptosystem. The paper describes theoretical background and a publickey encryption technique, followed by security analysis and consideration of cryptosystem parameters selection. A demonstrative example of encryption is included as well.

Citations