Undergraduate course (for third and fourth year students)

Lectures: Andrej Dujella         Exercises: Marcel Maretic


Classical cryptography. Basic notions. Caesar, Vigenère, Playfair and Hill ciphers. Rotor machines. Statistical methods in cryptoanalysis.

Modern block ciphers. Data Encryption Standard (DES). Cryptanalysis of DES. Advanced Encryption Standard (AES).

Public key cryptography. Idea of public key cryptography. Key exchange, digital signature. RSA cryptosystem. Other public-key cryptosystems.

Primality tests and factoring. Pseudoprimes. Soloway-Strassen and Miller-Rabin primality tests. Factor bases. Continued fraction factoring method. Quadratic sieve method.

Lecture notes (in Croatian)

Basic references

  1. A. Dujella, M. Maretic: Kriptografija, Element, Zagreb, 2007.

  2. D. R. Stinson: Cryptography. Theory and Practice, CRC Press, Boca Raton, 1996 (first edition), 2002 (second edition), 2005 (third edition).

  3. N. Koblitz: A Course in Number Theory and Cryptography, Springer-Verlag, New York, 1994.

Additional references

  1. F. L. Bauer: Decrypted Secrets. Methods and Maxims of Cryptology, Springer-Verlag, Berlin, 2000.

  2. E. Biham, A. Shamir: Differential Cryptanalysis of the Data Encryption Standard, Springer-Verlag, New York, 1993.

  3. J. Buchmann: Introduction to Cryptography, Springer-Verlag, New York, 2000.

  4. J. Daemen, V. Rijmen: The Design of Rijndael. AES - The Advanced Encryption Standard, Springer-Verlag, Berlin, 2002.

  5. D. Kahn: The Codebreakers. The Story of Secret Writing, Scribner, New York, 1996.

  6. E. Kranakis: Primality and Cryptography, Teubner, Stuttgart; John Wiley, Chichester, 1987.

  7. A. J. Menezes, P. C. Oorschot, S. A. Vanstone: Handbook of Applied Cryptography, CRC Press, Boca Raton, 1996.

  8. R. A. Mollin: An Introduction to Cryptography, Chapman & Hall/CRC Press, Boca Raton, 2001.

  9. R. A. Mollin: RSA and Public-Key Cryptography, Chapman & Hall/CRC Press, Boca Raton, 2002.

  10. A. Petho: Algebraische Algorithmen, Vieweg, Braunschweig, 1999.

  11. K. H. Rosen: Elementary Number Theory and Its Applications, Addison-Wesley, Reading, 1993.

  12. A. Salomaa: Public-Key Cryptography, Springer-Verlag, Berlin, 1996.

  13. B. Schneier: Applied Cryptography, John Wiley, New York, 1995.

  14. G. J. Simmons (Ed.): Contemporary Cryptology, The Science of Information Integrity, IEEE Press, Piscataway, 1992.

  15. S. Singh: The Code Book, Fourth Estate, London, 1999.

  16. N. Smart: Cryptography. An Introduction, McGraw-Hill, New York, 2002.

  17. W. Stallings: Cryptography and Network Security. Principles and Practice, Prentice Hall, Upper Sadle River, 2005.

  18. W. Trappe, L. C. Washington: Introduction to Cryptography with Coding Theory, Prentice Hall, Upper Sadle River, 2002.

  19. M. Welschenbach: Cryptography in C and C++, Apress, Berkeley, 2001.

Student seminar - Elliptic curves and their applications in cryptography (2002/2003)

Introduction to Number Theory - Undergraduate course

Number Theory in Cryptography - Graduate course (2003/2004)

Examples of homework exercises:

1999/2000: zad1 zad2 zad3 zad4 zad5 zad6

2000/2001: zad1 zad2 zad3 zad4 zad5

2001/2002: zad1 zad2 zad3 zad4 zad5 zad6

2002/2003: zad1 zad2 zad3 zad4 zad5

2003/2004: zad1 zad2 zad3 zad4 zad5

2004/2005: zad1 zad2 zad3 zad4 zad5

2005/2006: zad1 zad2 zad3 zad4

2006/2007: zad1 zad2 zad3 zad4 zad5

Andrej Dujella home page