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The mathematical problems and their solutions of the Third InternationalStudents' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We considermathematical problems related to the construction of algebraic immune vectorialBoolean functions and big Fermat numbers, problems about secrete sharingschemes and pseudorandom binary sequences, biometric cryptosystems and theblockchain technology, etc. Two open problems in mathematical cryptography arealso discussed and a solution for one of them proposed by a participant duringthe Olympiad is described. It was the first time in the Olympiad history.

Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography