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.
翻译:国际密码学奥林匹克运动会(NSCULYPTO)是一个独特的奥林匹克运动会,它包含任何国家的专业人员、中小学和大学生的科学数学问题,其目的是让年轻研究人员参与解决现代密码学的奇特和棘手的科学问题。2020年,它举行了第七次。第一轮有84人参加,第二轮有来自32个国家的49个球队获得奖项和文凭。在本论文中,提出了NSCULYPTO'2020的问题及其解决办法。我们考虑了与攻击密码和散列功能、协议、调整、初等测试等有关的问题。我们讨论了JPEG编码、Miller-Rabin初等测试、矢量空间的特殊基地AES-GCM等几个公开的问题。修改米勒-拉宾初等试验的问题在奥林匹克期间得到解决。寻找特殊基地的问题部分得到解决。