The Seventh International Olympiad in Cryptography: Problems and solutions

The International Olympiad in Cryptography NSUCRYPTO is the unique olympiad containing scientic mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientic problems of modern cryptography. In 2020, it was held for the seventh time. Prizes and diplomas were awarded to 84 participants in the rst 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 modied Miller Rabin primality test was solved during the Olympiad. The problem for nding special bases was partially solved. qorodilovD eFeFD okrevD xFxFD egievihD FFD grletD gFD sdrisovD FeFD ulginD uFFD uolegovD hFxFD uutsenkoD eFFD wouhD xFD udovkinD wFeFD dovenkoD eFxFD he eventh snterntionl ylympid in gryptogrphyX prolems nd solutionsF PHPI qorodilov eFeFD okrev xFxFD egievih FFD grlet gFD sdrisov FeFD ulgin uFFD uolegov hFxFD uutsenko eFFD wouh xFD udovkin wFeFD dovenko eFxF