Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography
This work documents incremental results from a cryptography competition, primarily relevant to students and researchers in mathematical cryptography.
The paper presents mathematical problems and solutions from the Third International Students' Olympiad in Cryptography, covering topics like algebraic immune Boolean functions and blockchain, and includes a solution to an open problem by a participant, a first in the event's history.
The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history.