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
