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Information Security

Information Security. Teaching, training, research. Topics in cryptology. History of cryptology Basic ciphers and their properties Symmetric cryptography Public-key cryptography Encryption standards . Topics in cryptographic protocols. Key exchange Authentication Signature

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Information Security

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  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=(f1,…,fn) – 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=(f1,,,fn)- 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 systems • The journal «Intelligent systems» • Web site www.cryptography.ru

  13. theend • Thank you for attention!

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