The Laboratory was established in 2001 to provide teaching and research in mathematical foundations of cryptography, cryptoanalysis, information and software security. It is closely related with the Chair of Mathematical Cybernetics and collaborates with the Scientific Research Computing Center (MSU), the Institute for Information Security Issues (MSU), and Association for Information Security.

Staff members:

• Anashin Vladimir, Senior Research Fellow, Dr.Sc.

Main Scientific directions

The Laboratory of Mathematical Problems of Computer Security is performing a thorough research on mathematical problems in cryptoanalysis, information security, and program verification. The most important achievements are the results in

• the analysis of asymmetric cryptosystems (we described the structural properties and established new upper bounds for the cardinality of key space for McEllice-Sidelnikov cryptosystem),
• the analysis of cryptographic hash-functions (by applying the differential cryptoanalysis technique we found the best known parameters for the hash-function MD4),
• the study of cryptographic properties of Boolean functions (we developed a novel techniques for the analysis of the affinity and balance properties of Boolean functions and for the construction of annihilators for Boolean functions),
• the development of new cryptoanalysis techniques (designing of attacks on filtering generators),
• the development of new algorithms for solving systems of non-linear Boolean equations,
• symbolic dynamics and p-adic analysis (we developed a new approach to designing stream cryptosystems by means of the p-adic analysis).

We also gave rise to a number of approaches to solving an equivalence checking problem and equivalent transformation problem for computer programs, developed an algebraic theory of program schemata, and developed novel techniques for program verification.