  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.
