Abstract
There are introduced three methods for defining finite 6-dimensional associative algebras over the ground finite field GF(p), every one of which contains a set of the global right-sided units. Formulas describing the set of the global units are presented for every of the considered three algebras that contain \(p^s\) global units, where \(s=2,3,4.\) The algebras are used as carriers of the hidden discrete logarithm problem that is used as the base cryptographic primitive of the post-quantum digital signature algorithms.
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Acknowledgement
The reported study was partially funded by the Russian Foundation for Basic Research (project #18-07-00932-a); The Ministry of Science and Technology (MOST) under grant KC.01.22/16-20/.
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Moldovyan, N.A., Moldovyan, D.N., Moldovyan, A.A., Nguyen, H.M., Trinh, L.H.T. (2020). Post-quantum Digital-Signature Algorithms on Finite 6-Dimensional Non-commutative Algebras. In: Dang, T.K., Küng, J., Takizawa, M., Chung, T.M. (eds) Future Data and Security Engineering. FDSE 2020. Lecture Notes in Computer Science(), vol 12466. Springer, Cham. https://doi.org/10.1007/978-3-030-63924-2_19
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