后量子密码系统：开放问题与解决方案。基于网格的密码系统

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2024-02-16 DOI:10.1134/S1990478923040087

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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引用次数: 0

摘要

摘要本文概述了目前使用的构建后量子密码系统的主要方法。本文详细分析了基于网格的密码学领域。我们对一些已知的基于晶格的密码系统进行了描述和表征，这些系统的复原力基于最短向量问题、带误学习问题及其变体的复杂性。我们分析了解决格理论问题的主要方法，这些方法是攻击相应密码系统的基础。特别是，介绍了一些已知的网格基础还原和网格筛分算法的时间和内存复杂度的理论估计值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Post-Quantum Cryptosystems: Open Problems and Solutions. Lattice-Based Cryptosystems

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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.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

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.