Irina Pankratova | Searcharxiv

arXiv2020

On the Sixth International Olympiad in Cryptography NSUCRYPTO

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 of modern cryptography. From the very beginning, the concept of the Olympiad was not to focus on solving olympic tasks but on including unsolved research problems at the intersection of mathematics and cryptography. The Olympiad history starts in 2014. In 2019, it was held for the sixth time. In this paper, problems and their solutions of the Sixth International Olympiad in cryptography NSUCRYPTO'2019 are presented. We consider problems related to attacks on ciphers and hash functions, protocols, Boolean functions, Dickson polynomials, prime numbers, rotor machines, etc. We discuss several open problems on mathematical countermeasures to side-channel attacks, APN involutions, S-boxes, etc. The problem of finding a collision for the hash function Curl27 was partially solved during the Olympiad.

cs.CR↗

arXiv2015

Spectral asymptotics for a singularly perturbed fourth order locally periodic self-adjoint elliptic operator

We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic equation with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The presence of large parameters in the lower order terms and the dependence of the coefficients on the slow variable give rise to the effect of localization of the eigenfunctions. We show that the $j$th eigenfunction can be approximated by a rescaled function that is constructed in terms of the $j$th eigenfunction of fourth or second order order effective operators with constant coefficients, depending on the large parameters.

math.AP↗