Computing Homomorphisms Between Two Finite Groups

Computing a homomorphism between two given groups of points of elliptic curves over a finite field is a problem that seems to be quantum-resistant. Nowadays by raising the quantum computers, the quantum- resistant property of the cryptosystems has became a very crucial feature in cryptography and motivates us to consider computing of homomorphisms between two arbitrary groups G and G0. Th is problem can be stated computationally: Let G and G0 be two arbitrary groups. Compute the homomorphism f : G 􀀀! G0 explicitly, if any. In this paper, we briefly review existing methods in solving the problem above for elliptic curves groups and then we generalize it for two given arbitrary groups G and G0.