  NSUCRYPTO is the unique cryptographic 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. From the very beginning, the
concept of the Olympiad was not to focus on solving olympic tasks but on
including unsolved research problems at the intersection of mathematics and
cryptography. The Olympiad history starts in 2014. In 2019, it was held for the
sixth time. In this paper, problems and their solutions of the Sixth
International Olympiad in cryptography NSUCRYPTO'2019 are presented. We
consider problems related to attacks on ciphers and hash functions, protocols,
Boolean functions, Dickson polynomials, prime numbers, rotor machines, etc. We
discuss several open problems on mathematical countermeasures to side-channel
attacks, APN involutions, S-boxes, etc. The problem of finding a collision for
the hash function Curl27 was partially solved during the Olympiad.
