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Mathematical problems and their solutions of the Fourth International Students' Olympiad in cryptography NSUCRYPTO'2017 are presented. We consider problems related to attacks on ciphers and hash functions, cryptographic Boolean functions,…

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.…

NSUCRYPTO is the unique cryptographic Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific…

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,…

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving…

Non-Stop University CRYPTO is the International Olympiad in Cryptography that was held for the eight time in 2021. Hundreds of university and school students, professionals from 33 countries worked on mathematical problems in cryptography…

We present the problems and solutions to the 63rd Annual International Mathematical Olympiad.

The description of the image of cubic function $f(x) = x^3+x$ over finite field $F_{2^n}$ was stated as a problem in the NSUCrypto olympiad in 2017. This problem was marked by organizers as <<unsolved>>. In this work we propose the full…

We present the problems and solutions to the 61st Annual International Mathematical Olympiad

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…

The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated,…

We ask whether two or more images of arithmetic may inhabit the same space via different encodings. The answers have significance for a class of processor design that does all its computation in an encrypted form, without ever performing…

The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, is called 'the grasshopper problem'. To this problem Kos developed theory from unique viewpoints by reference of Noga Alon's combinatorial…

The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number…

The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We…

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate…

OpenAI and DeepMind's AIs recently got gold at the IMO math olympiad and ICPC programming competition. We show frontier AI is similarly good at hacking by letting GPT-5 compete in elite CTF cybersecurity competitions. In one of this year's…

We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…

An astonishingly diverse biomolecular circuitry orchestrates the functioning machinery underlying every living cell. These biomolecules and their circuits have been engineered not only for various industrial applications but also to perform…

Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…