Information Security

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Information Security

• Teaching, training, research

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Topics in cryptology

• History of cryptology
• Basic ciphers and their properties
• Symmetric cryptography
• Public-key cryptography
• Encryption standards

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Topics in cryptographic protocols

• Key exchange
• Authentication
• Signature
• Secret sharing
• Zero-Knowledge Proofs

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Topics in number theory

• Complexity of algorithms
• Algorithms of factorization
• Testing of the primality
• Generation of large prime numbers
• Discrete logarithm in finite fields

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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

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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

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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?

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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 xy?

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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?

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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?

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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

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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

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the end

• Thank you for attention!