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Evolutionary cryptography theory based generating method for a secure Koblitz elliptic curve and its improvement by a hidden Markov models

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Abstract

Considering potential attacks from cloud-computing and quantum-computing, it is becoming necessary to provide higher security elliptic curves. The hidden Markov models are introduced for designing the trace-vector computation algorithm to accelerate the search for elliptic curve (EC) base-points. We present a new algorithm for secure Koblitz EC generation based on evolutionary cryptography theory. The algorithm is tested by selecting a secure Koblitz EC over the field F(22000), with experiments showing that both the base field and base point of the secure curve generated exceed the parameter range for Koblitz curves recommended by NIST. The base fields generated go beyond 1900 bits, which is higher than the 571 bits recommended by NIST. We also find new secure curves in the range F(2163)—F(2571) recommended by NIST. We perform a detailed security analysis of those secure curves, showing that those we propose satisfy the same security criteria as NIST.

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Authors and Affiliations

  1. Key Lab of Specialty Fiber Optics and Optical Access Network, Ministry of Education, Shanghai University, Shanghai, 200072, China

    Chao Wang

  2. Computer School of Wuhan University, Wuhan, 430072, China

    HuanGuo Zhang

  3. Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education, Wuhan, 430072, China

    HuanGuo Zhang

  4. Huawei Technologies CO. LTD., Shanghai, 201206, China

    LiLi Liu

Authors
  1. Chao Wang
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  2. HuanGuo Zhang
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  3. LiLi Liu
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Correspondence to Chao Wang.

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Wang, C., Zhang, H. & Liu, L. Evolutionary cryptography theory based generating method for a secure Koblitz elliptic curve and its improvement by a hidden Markov models. Sci. China Inf. Sci. 55, 911–920 (2012). https://doi.org/10.1007/s11432-012-4552-4

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  • DOI: https://doi.org/10.1007/s11432-012-4552-4

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