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

TL;DR

This paper presents problems and solutions from the Fifth International Students' Olympiad in cryptography, covering topics like cipher attacks, Boolean functions, quantum circuits, and open problems in combinatorial matrix theory.

Contribution

It provides a comprehensive collection of cryptography problems, solutions, and new results, including the complete solution to a problem on Sylvester matrices.

Findings

Solved the problem of finding an invertible Sylvester matrix with a Sylvester inverse.

Presented solutions to cryptographic attack problems and quantum circuit challenges.

Discussed open problems in combinatorial matrix theory.

Abstract

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.