Geodesic
Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography
Prikladnaâ diskretnaâ matematika, no. 2 (2018), pp. 34-58

Voir la notice de l'article provenant de la source Math-Net.Ru

The mathematical problems, presented at the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016, and their solutions are considered. They are related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, the secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history. The problem is the following: construct $F\colon\mathbb F_2^5\to\mathbb F_2^5$ with maximum possible component algebraic immunity $3$ or prove that it does not exist. Alexey Udovenko from University of Luxembourg has found such a function.
Keywords: cryptography, ciphers, Boolean functions, biometry, blockchain
Mots-clés : Olympiad, NSUCRYPTO. 
@article{PDM_2018_2_a3,
     author = {N. Tokareva and A. Gorodilova and S. Agievich and V. Idrisova and N. Kolomeec and A. Kutsenko and A. Oblaukhov and G. Shushuev},
     title = {Mathematical methods in solutions of the problems presented at the {Third} {International} {Students'} {Olympiad} in {Cryptography}},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {34--58},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PDM_2018_2_a3/}
}
TY  - JOUR
AU  - N. Tokareva
AU  - A. Gorodilova
AU  - S. Agievich
AU  - V. Idrisova
AU  - N. Kolomeec
AU  - A. Kutsenko
AU  - A. Oblaukhov
AU  - G. Shushuev
TI  - Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2018
SP  - 34
EP  - 58
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2018_2_a3/
LA  - en
ID  - PDM_2018_2_a3
ER  - 
%0 Journal Article
%A N. Tokareva
%A A. Gorodilova
%A S. Agievich
%A V. Idrisova
%A N. Kolomeec
%A A. Kutsenko
%A A. Oblaukhov
%A G. Shushuev
%T Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography
%J Prikladnaâ diskretnaâ matematika
%D 2018
%P 34-58
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2018_2_a3/
%G en
%F PDM_2018_2_a3
N. Tokareva; A. Gorodilova; S. Agievich; V. Idrisova; N. Kolomeec; A. Kutsenko; A. Oblaukhov; G. Shushuev. Mathematical methods in solutions of the problems presented at the Third International Students' Olympiad in Cryptography. Prikladnaâ diskretnaâ matematika, no. 2 (2018), pp. 34-58. http://geodesic.mathdoc.fr/item/PDM_2018_2_a3/