Abstract
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.
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Acknowledgements
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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Moldovyan, D.N., Moldovyan, A.A., Phieu, H.N., Nguyen, M.H. (2019). Post-quantum Commutative Encryption Algorithm. In: Vinh, P., Rakib, A. (eds) Context-Aware Systems and Applications, and Nature of Computation and Communication. ICCASA ICTCC 2019 2019. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 298. Springer, Cham. https://doi.org/10.1007/978-3-030-34365-1_16
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DOI: https://doi.org/10.1007/978-3-030-34365-1_16
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