Geodesic
Post-quantum electronic digital signature scheme based on the enhanced form of the hidden discrete logarithm problem
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 2, pp. 212-220

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A digital signature scheme based on the computational difficulty of the hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. The modified quaternion algebra and its properties are considered as the algebraic carrier of the introduced post-quantum digital signature scheme. Formulas describing the set of local units associated with a given non-invertible vector of a modified quaternion algebra are derived. \newpage A new form of the hidden discrete logarithm problem has been formulated and a digital signature scheme has been developed on its base.
Keywords: post-quantum cryptography, cryptographic primitive, electronic signature, finite algebra, non-commutative associative algebra. 
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     author = {N. A. Moldovyan and I. K. Abrosimov},
     title = {Post-quantum electronic digital signature scheme based on the enhanced form of the hidden discrete logarithm problem},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2019_15_2_a4/}
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N. A. Moldovyan; I. K. Abrosimov. Post-quantum electronic digital signature scheme based on the enhanced form of the hidden discrete logarithm problem. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 2, pp. 212-220. http://geodesic.mathdoc.fr/item/VSPUI_2019_15_2_a4/