Mathematical problems and solutions of the Ninth International Olympiad in Cryptography NSUCRYPTO

TL;DR

This paper presents a collection of cryptography problems from NSUCRYPTO 2022, including solutions and open problems across various topics like ciphers, quantum computing, and cryptographic protocols, aimed at students and researchers.

Contribution

It introduces new cryptographic problems and discusses open challenges, fostering research and education in modern cryptography.

Findings

Solutions to several cryptographic problems provided

Identification of open problems for future research

Coverage of diverse cryptography topics and challenges

Abstract

Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The mail goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in the field. We present problems of NSUCRYPTO'22 and their solutions. There are 16 problems on the following topics: ciphers, cryptosystems, protocols, e-money and cryptocurrencies, hash functions, matrices, quantum computing, S-boxes, etc. They vary from easy mathematical tasks that could be solved by school students to open problems that deserve separate discussion and study. So, in this paper, we consider several open problems on three-pass protocols, public and private keys pairs, modifications of discrete logarithm problem, cryptographic permutations and quantum circuits.