A public key cryptosystem based on data complexity under quantum environment

Abstract

Since the Shor algorithm showed that a quantum algorithm can efficiently calculate discrete log-arithms and factorize integers, it has been used to break the RSA, EIGamal, and ECC classical public key cryptosystems. This is therefore a significant issue in the context of ensuring communication security over in-secure channels. In this paper, we prove that there are no polynomial-size quantum circuits that can compute all Boolean functions (of which there are 22 n cases) in the standard quantum oracle model. Based on this, we propose the notion of data complexity under a quantum environment and suggest that it can be used as a condition for post-quantum computation. It is generally believed that NP-complete problems cannot be solved in polynomial time even with quantum computers. Therefore, a public key cryptosystem and signature scheme based on the difficulty of NP-complete problems and the notion of data complexity are presented here. Finally, we analyze the security of the proposed encryption and signature schemes.