The Seventh International Olympiad in Cryptography: Problems and solutions

IF 0.4 Q4 MATHEMATICS Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya Pub Date : 2021-06-02 DOI:10.33048/semi.2021.18.063

A. Gorodilova, N. Tokareva, S. Agievich, C. Carlet, V. Idrisova, K. Kalgin, D. Kolegov, A. Kutsenko, N. Mouha, M. Pudovkina, A. Udovenko

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引用次数: 2

Abstract

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. In 2020, it was held for the seventh time. Prizes and diplomas were awarded to 84 participants in the first round and 49 teams in the second round from 32 countries. In this paper, problems and their solutions of NSUCRYPTO'2020 are presented. We consider problems related to attacks on ciphers and hash functions, protocols, permutations, primality tests, etc. We discuss several open problems on JPEG encoding, Miller -- Rabin primality test, special bases in the vector space, AES-GCM. The problem of a modified Miller -- Rabin primality test was solved during the Olympiad. The problem for finding special bases was partially solved.

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第七届国际密码学奥林匹克竞赛：问题与对策

国际密码学奥林匹克运动会NSUCRYPTO是一个独特的奥林匹克运动会，为来自任何国家的专业人士、中小学生和大学生提供科学数学问题。其目的是让年轻的研究人员参与解决现代密码学中好奇而棘手的科学问题。2020年，它举行了第七次。来自32个国家的84名第一轮参赛者和49支第二轮参赛队伍获得了奖品和文凭。本文介绍了NSUCRYPTO’2020存在的问题及其解决方案。我们考虑了与攻击密码和散列函数、协议、排列、素性测试等有关的问题。我们讨论了JPEG编码、Miller-Rabin素性测试、向量空间中的特殊基、AES-GCM等方面的几个开放问题。在奥林匹克运动会期间，一个改良的米勒-拉宾素性测试的问题得到了解决。找到特殊基地的问题得到了部分解决。

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