E. S. Malygina, A. V. Kutsenko, S. A. Novoselov, N. S. Kolesnikov, A. O. Bakharev, I. S. Khilchuk, A. S. Shaporenko, N. N. Tokareva
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Post-Quantum Cryptosystems: Open Problems and Solutions. Lattice-Based Cryptosystems
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 characterization of some known
lattice-based cryptosystems whose resilience 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.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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