MSc in Mathematics


Information Security (Module Information theory)


Istvan Szabo, leading research fellow, Dept. of Probability Theory and Statistics, Institute of Mathematics




4th semester


Cryptographic Methods in Information Security:

  • Data Security in Information Systems (Confidentiality, Integrity, Authenticity);
  • Mathematical Background: Information Theory (Shannon Model, Entropy, Unicity Distance), Complexity Theory, Number Theory, Finite Fields;
  • Short History of Cryptography: Experiences, Risks;
  • Hierarchy in Cryptography: Primitives, Schemes, Protocols, Applications;
  • Random- and Pseudorandom Bits Generators
  • Stream Ciphers: Linear Feedback Shift Registers, Stream Ciphers based on LFSRs, Linear Complexity, Stream Ciphers in practice /GSM-A5, Bluetooth-E0, WLAN-RC4/, The NIST Statistical Test Suite;
  • Block Ciphers: Primitives /DES, 3DES, IDEA, AES/, Linear and Differential Cryptanalysis;
  • Public-Key Encryption: Primitives /KnapSack, RSA, ElGamal public-key encryption, Elliptic curve cryptography,…/, Digital Signatures, Types of attacks on PKS /integer factorisation problem, Quadratic/Number field sieve factoring, wrong parameters,…/;
  • Hash Functions and Data Integrity: Requirements, Standards and Attacks /birthday, pseudo-collisions,… attacks/
  • Cryptographic Protocols: Modes of operations, Key management protocols, Secret sharing, Internet protocols /SSL/TLS, IPSEC, SSH,…/
  • Cryptography in Information Systems /Applications/: Digital Signatures systems /algorithms, keys, ETSI CWA requirements, Certification Authority, SSCD Protection Profile, X-509v3 Certificate,…/, Mobile communications /GSM/, PGP, SET,…, Quantum Cryptography /quantum computation, quantum key exchange, quantum teleportation/;

Evaluation Standard in Information Systems (FIPS PUB 140-2:2002: Security Requirements for Cryptographic Modules, ISO/IEC 15408: Common Criteria for Information Technology Security Evaluation /PPs, STs, EALs, SFs,…/; ISO/IEC 17799: Information technology - Security techniques - Code of practice for information security management; Hungarian Information Evaluation Scheme).


Suggested readings:


form of tuition


mode of assessment

oral exam