Abstract: To the question of the mathematical problems of RSA public-key cryptosystem and elliptic curve cryptosystem can't be against quantum computer,a mathematical problem,suitable for constructing public-key cryptosystem,is proposed: computing an isogeny between the given elliptic curves.The computational complexity for solving this problem is exponential.The problem is hard for solving with a quantum computer.A public-key cryptosystem scheme named ECIIES is proposed for an isogeny crypto system.ECIIES which based on the basic Elgamal scheme,can be against chosen ciphertext attacks by using a MAC function about intermediate variables and ciphertext.At last,the scheme ECIIES is proved to be IND-CCA2 security in the random oracle model.