Geodesic
Post-quantum cryptosystems: open problems and solutions. Lattice-based cryptosystems
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 4, pp. 46-90

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The paper provides an overview of the main approaches to the construction of post-quantum cryptographic systems that are currently used. The area of lattice-based cryptography is analyzed in detail. We give the description and characteristics of some known lattice-based cryptosystems whose security is based on the complexity of the shortest vector problem, learning with errors problem, and their variations. The main approaches to solving the problems from lattice theory, on which attacks on the corresponding cryptosystems are based, are analyzed. In particular, some known theoretical estimates of time and memory complexity of lattice basis reduction and lattice sieving algorithms are presented. Tab. 6, illustr. 1, biblogr. 93.
Keywords: post-quantum cryptography, quantum computer, integer lattice. 
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     title = {Post-quantum cryptosystems: open problems and solutions. {Lattice-based} cryptosystems},
     journal = {Diskretnyj analiz i issledovanie operacij},
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E. S. Malygina; A. V. Kutsenko; S. A. Novoselov; N. S. Kolesnikov; A. O. Bakharev; I. S. Khilchuk; A. S. Shaporenko; N. N. Tokareva. Post-quantum cryptosystems: open problems and solutions. Lattice-based cryptosystems. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 4, pp. 46-90. http://geodesic.mathdoc.fr/item/DA_2023_30_4_a3/