The Fifth International Students' Olympiad in Cryptography -- NSUCRYPTO: problems and their solutions

Problems and their solutions of the Fifth International Students' Olympiad in cryptography NSUCRYPTO'2018 are presented. We consider problems related to attacks on ciphers and hash functions, Boolean functions, quantum circuits, Enigma, etc. We discuss several open problems on orthogonal arrays, Sylvester matrices and disjunct matrices. The problem of existing an invertible Sylvester matrix whose inverse is again a Sylvester matrix was completely solved during the Olympiad.