an:07311617
Zbl 07311617
Tokareva, N.; Gorodilova, A.; Agievich, S.; Idrisova, V.; Kolomeec, N.; Kutsenko, A.; Oblaukhov, A.; Shushuev, G.
Mathematical methods in solutions of the problems presented at the third international students' olympiad in cryptography
EN
Prikl. Diskretn. Mat. 2018, No. 40, 34-58 (2018).
00458850
2018
j
94A60 97D50
cryptography; ciphers; Boolean functions; biometry; blockchain; olympiad; NSUCRYPTO
Summary: 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.