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.

翻译：每年，国际密码学奥林匹克竞赛“无休大学密码学”（NSUCRYPTO）都会为大学生、中学生以及密码学与计算机科学领域的专业人士提供数学问题。NSUCRYPTO的主要目标是吸引学生和青年研究人员关注现代密码学，并提高对该领域开放问题的认识。本文介绍了NSUCRYPTO'22的问题及其解答。共包含16个问题，涉及以下主题：密码、密码系统、协议、电子货币与加密货币、哈希函数、矩阵、量子计算、S盒等。这些问题从中学生可解决的简单数学任务，到值得单独讨论和研究的开放问题，难度各异。因此，本文探讨了若干关于三通协议、公私钥对、离散对数问题的变体、密码置换及量子电路的开放问题。