1. Information Security Teaching, training, research

2. Topics in cryptology History of cryptology Basic ciphers and their properties Symmetric cryptography Public-key cryptography Encryption standards

3. Topics in cryptographic protocols Key exchange Authentication Signature Secret sharing Zero-Knowledge Proofs

4. Topics in number theory Complexity of algorithms Algorithms of factorization Testing of the primality Generation of large prime numbers Discrete logarithm in finite fields

5. Topics in information security Notion of information security Russian State documents on information security Threats of information security Means of information security Confidentialness, integrity, accessibility of information and their ensuring

6. Problems for mathematical research Permutations and their characteristics Latin squares and their characteristics Automata and models of ciphers Automata and models of security Equations in permutations Boolean equations

7. Example 1 Let F=(f 1,…,f n ) – be Boolean functions of n variables. When F is a permutation? What cyclic structure can it have? What is the set of differences of F? When the set of differences of F is maximal?

8. Example 2 Let F=(f 1,,,f n )- be a set of Boolean functions of 2n variables. When F is a Latin square? How to describe the set of such functions? When Latin squares F’ and F’’ in Boolean representation are orthogonal? When this Latin square is isomorphic to the square x+y?

9. Example 3 Let A=(X,S,Y,f,g) be a finite automaton in Boolean parametrization. When A is a substitution automaton? How to invert the automaton A? How to find equivalent states of A? How to restore the input sequence by the output and the initial state?

10. Examples 4 Counters (period of states is maximal and equals the output period) Let A=(S,f,g) be automaton without inputs in Boolean parametrization. When A has maximal period of states? When the period of states of A is equal to the period of outputs? When A has equivalent states?

11. Forms of activity Lecture course «Combinatorial Methods in Discrete Mathematics» Lecture course «Complexity and Optimization of Algorithms» Lecture course «Algebraic Cryptology» Lecture course «Basics of Information Security.» Seminar Information Security and Cryptology

12. Documents Web site www.intsys.msu.ru of the chair of Mathematical theory of intelligent systemswww.intsys.msu.ru The journal «Intelligent systems» Web site www.cryptography.ruwww.cryptography.ru

13. the end Thank you for attention!