The present invention relates to information security and discloses a method of establishing public key cryptographic protocols against the quantum computational attack. The method includes the following steps: definition of an infinite non-abelian group G; choosing two private keys in G by two entities; a second entity computing y, and sending y to a first entity; the first entity computing x and z, and sending (x, z) to the second entity; the second entity computing w and v, and sending (w, v) to the first entity; the first entity computing u, and sending u to the second entity; and the first entity computing KA, and the second entity computing KB, thereby reaching a shared key K=KA=KB. The security guarantee of a public key cryptographic algorithm created by the present invention relies on unsolvability of a problem, and has an advantage of free of the quantum computational attack.