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Fast parallel DNA-based algorithms for molecular computation: discrete logarithm

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Abstract

Diffie and Hellman (IEEE Trans. Inf. Theory 22(6):644–654, 1976) wrote the paper in which the concept of a trapdoor one-way function was first proposed. The Diffie–Hellman public-key cryptosystem is an algorithm that converts input data to an unrecognizable encryption, and converts the unrecognizable data back into its original decryption form. The security of the Diffie–Hellman public-key cryptosystem is based on the difficulty of solving the problem of discrete logarithms. In this paper, we demonstrate that basic biological operations can be applied to solve the problem of discrete logarithms. In order to achieve this, we propose DNA-based algorithms that formally verify our designed molecular solutions for solving the problem of discrete logarithms. Furthermore, this work indicates that public-key cryptosystems based on the difficulty of solving the problem of discrete logarithms are perhaps insecure.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Kaohsiung University of Applied Sciences, No. 415, Chien Kung Road, Kaohsiung City, 807-78, Taiwan, Republic of China

    Weng-Long Chang & Kawuu Weicheng Lin

  2. Department of Computer Science, National PingTung University of Education, No. 4-18 Ming Shen Road, Pingtung, 900, Taiwan, Republic of China

    Shu-Chien Huang

  3. Computer Center and Institute of Electrical Engineering, National Taipei University, 151, University Rd., San Shia, 237, Taipei County, Taiwan, Republic of China

    Michael (Shan-Hui) Ho

Authors
  1. Weng-Long Chang
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  2. Shu-Chien Huang
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  3. Kawuu Weicheng Lin
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  4. Michael (Shan-Hui) Ho
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Correspondence to Weng-Long Chang.

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Chang, WL., Huang, SC., Lin, K.W. et al. Fast parallel DNA-based algorithms for molecular computation: discrete logarithm. J Supercomput 56, 129–163 (2011). https://doi.org/10.1007/s11227-009-0347-9

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  • DOI: https://doi.org/10.1007/s11227-009-0347-9

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