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A public key cryptosystem based on data complexity under quantum environment

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  • Special Focus on Security of Cyberspace
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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.

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Authors and Affiliations

  1. Computer School, Wuhan University, Wuhan, 430072, China

    WanQing Wu, HuanGuo Zhang, HouZhen Wang, ShaoWu Mao, JianWei Jia & JinHui Liu

  2. State Key Laboratory of Cryptology, Beijing, 100878, China

    HouZhen Wang

Authors
  1. WanQing Wu
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  2. HuanGuo Zhang
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  3. HouZhen Wang
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  4. ShaoWu Mao
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  5. JianWei Jia
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  6. JinHui Liu
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Correspondence to HouZhen Wang.

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Wu, W., Zhang, H., Wang, H. et al. A public key cryptosystem based on data complexity under quantum environment. Sci. China Inf. Sci. 58, 1–11 (2015). https://doi.org/10.1007/s11432-015-5408-5

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  • DOI: https://doi.org/10.1007/s11432-015-5408-5

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