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Science China Information Sciences

, Volume 58, Issue 11, pp 1–11 | Cite as

A public key cryptosystem based on data complexity under quantum environment

  • WanQing Wu
  • HuanGuo Zhang
  • HouZhen Wang
  • ShaoWu Mao
  • JianWei Jia
  • JinHui Liu
Research Paper Special Focus on Security of Cyberspace
  • 122 Downloads

Abstract

Since the Shor algorithm showed that a quantum algorithm can efficiently calculate discrete logarithms 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 insecure channels. In this paper, we prove that there are no polynomial-size quantum circuits that can compute all Boolean functions (of which there are \({2^{{2^n}}}\) 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.

Keywords

public key cryptography information security NP-complete problem complexity theory quantum computation 
110102 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • WanQing Wu
    • 1
  • HuanGuo Zhang
    • 1
  • HouZhen Wang
    • 1
    • 2
  • ShaoWu Mao
    • 1
  • JianWei Jia
    • 1
  • JinHui Liu
    • 1
  1. 1.Computer SchoolWuhan UniversityWuhanChina
  2. 2.State Key Laboratory of CryptologyBeijingChina

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