Post-quantum Commutative Encryption Algorithm

  • Dmitriy N. Moldovyan
  • Alexandr A. Moldovyan
  • Han Ngoc Phieu
  • Minh Hieu NguyenEmail author
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 298)


It is considered an extended notion of the commutativity of the encryption. Using the computational difficulty of the hidden discrete logarithm problem, a new method and post-quantum probabilistic algorithm for commutative encryption are proposed. The finite non-commutative associative algebra containing a large set of the global left-sided unites is used as the algebraic carrier of the proposed method and probabilistic commutative cipher. The latter is secure to the known-plaintext attack and, therefore, efficient to implement on its base a post-quantum no-key encryption protocol. Main properties of the algebraic carrier, which are used in the commutative encryption method, are described.


Post-quantum cryptography Commutative probabilistic encryption No-key protocol Hidden logarithm problem Finite non-commutative algebra Associative algebra 



The reported study was partially funded by Russian Foundation for Basic Research (project #18-57-54002-Viet_a) and by VietNam Academy of Science and Technology (project # QTRU01.08/18-19).


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Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  • Dmitriy N. Moldovyan
    • 1
  • Alexandr A. Moldovyan
    • 1
  • Han Ngoc Phieu
    • 2
  • Minh Hieu Nguyen
    • 2
    Email author
  1. 1.Laboratory of Cybersecurity and Post-quantum CryptosystemsSt. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences (SPIIRAS)St. PetersburgRussia
  2. 2.Faculty of Electronics and TelecommunicationsAcademy of Cryptography TechniquesHanoiVietnam

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