A student and a graduate student from the Mechanics and Mathematics Faculty of NSU presented their research at the international seminar on discrete mathematics

Postgraduate student and undergraduate student Mechanics and Mathematics Faculty of Novosibirsk State University (MMF NSU) participated in the 15th International Seminar “Discrete Mathematics and Its Applications” named after academician Oleg Borisovich Lupanov. The scientific event was held at the Mechanics and Mathematics Faculty of Lomonosov Moscow State University.

The seminar is held once every three years and brings together specialists engaged in fundamental and applied problems of discrete mathematics and mathematical cybernetics. The organizers of the XV seminar were Lomonosov Moscow State University and the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, supported by the Moscow Center for Fundamental and Applied Mathematics.

This year, more than 100 specialists from Russia, Armenia, Jordan, China, and Uzbekistan participated in the seminar. Among the participants were researchers from Moscow, Yerevan, Tashkent, Shenzhen, Krasnoyarsk, Rostov-on-Don, Saratov, and Ulyanovsk.

NSU research — in the spotlight of the seminar

Novosibirsk State University was represented at the event by two researchers affiliated with the Mathematical Center in Akademgorodok:

• Alexander Baharev — second-year graduate student at the Mathematics and Mechanics Faculty of NSU, an employee of the Mathematical Center in Akademgorodok;
• Darya Severukhina — a third-year undergraduate student at the Faculty of Mechanics and Mathematics, NSU, an employee of the Mathematical Center in Akademgorodok.

Both participants are engaged in research in the field of post-quantum cryptography—a branch related to the development of cryptographic systems capable of resisting attacks using quantum computers.

Alexander Baharev spoke at plenary report “Post-quantum Cryptography”, dedicated to modern approaches to information security in the context of the development of quantum computing.

According to the graduate student, the opportunity to speak at the seminar arose thanks to a proposal from the organizers, who contacted the cryptography laboratory where he conducts his research.

— The conference organizers contacted the cryptography laboratory where I study, requesting a presentation on a new and promising field — post-quantum cryptography. The head of the laboratory suggested that I participate since post-quantum cryptography — cryptosystems resistant to attacks using a quantum computer — is the subject of my research., — told Alexander Bakharev.

In his speech, the researcher examined the reasons for the vulnerability of classical public-key cryptosystems to attacks using quantum computers, discussed the principles of post-quantum cryptography, and the main approaches to building resilient cryptosystems.

Special attention was given to the mathematical problems underlying post-quantum algorithms, as well as methods for their analysis. At the end of the report, Alexander Bakharev presented the research directions of his colleagues in the laboratory.

Lattice theory-based algorithms

Darya Severukhina presented the results of her work at the section “Coding Theory and Mathematical Issues of Information Security Theory.” Her report was titled “Algorithm for verifying whether perfect lattices belong to the same class”.

The study was conducted as part of a specialization in cryptography at the Department of Theoretical Cybernetics of the Faculty of Mechanics and Mathematics at NSU and is related to lattice theory problems used in the development of modern cryptographic algorithms.

Darya learned about the seminar from her academic advisor. She was interested in the wide range of scientific fields presented, the opportunity to get acquainted with the research of leading specialists, and to receive feedback on her own work.

— The seminar is traditionally held once every three years at MSU, featuring presentations by renowned scientists in the field of discrete mathematics and its applications. The topics vary widely—from the theory of functional systems to graph theory. It was this multidisciplinarity and the opportunity to hear about science firsthand, present one’s own results, and receive feedback from experts in the field that interested me., — told Darya Severukhina.

At the core of her research lies the lattice isomorphism problem—a mathematical problem that is significant for several cryptographic systems. The researcher studied it using the algebraic structure of ideal lattices.

Explaining the main idea of the work, Darya notes that a lattice can be represented as a set of points in space, arranged according to a certain structure. For example, the corners of the squares on graph paper form the simplest example of a lattice.

— The properties of such an object allow formulating problems that are difficult to solve even on a very powerful computer. Modern encryption algorithms are based on them—they are already used in information systems for data protection, — explained the student.

Within the research, Darya developed a polynomial algorithm that, for a certain class of perfect lattices, allows quickly determining whether two lattices can be isomorphic.

From fundamental mathematics to modern technologies

Post-quantum cryptography today is one of the promising directions in the development of information security. The spread of quantum computing in the future may pose a threat to a number of cryptographic algorithms currently in use. Therefore, the study of the mathematical foundations of new methods of information protection is of great importance for the development of digital technologies.

The participation of representatives of the IMF NSU in the international seminar named after Academician O. B. Lupanov provided an opportunity to present the research results of the university scientific school, discuss current tasks with colleagues from different countries, and get acquainted with modern directions in the development of discrete mathematics and mathematical cybernetics.