• To gain knowledge about the mathematics of the cryptographic algorithms.
  • To get an insight into the working of different existing cryptographic algorithms.
  • To learn how to use cryptographic algorithms in security.



  • Design and implement a new unbreakable cryptosystem
  • Blend the existing cryptographic algorithms with the existing communication protocols
  • Analyze and application of cryptography for secure eCommerce and other secret transactions


Unit – I

Origins of Cryptography- Issues - Codes and ciphers - Preliminary ideas of factoring and testing - gcd and its complexity.


Unit – II

Symmetric Key Cryptosystems- Block ciphers - Substitution ciphers - DES and Feistel ciphers and the problem of breaking them - The field Z/pZ - Euler's φ function.


Unit – III

Stream Ciphers- Linear feedback shift registers and associated results - Geffe generator - Diffe-Hellman key exchange - Bit commitment using symmetric key.


Unit – IV

Public-key Cryptosystems- Discrete logarithm - RSA and Miller-Rabin - Authentication - Digital signatures - Merkle-Hellman Knapsack public key cipher.


Unit – V

Factoring and other topics- Pollard ρ-heuristic - Pollard p-1 algorithm - Quadratic sieve algorithm - Zero-knowledge proof idea - Recent developments.



  • A. J. Menezes, P. Van Oorschot , and S. Vanstone, "Handbook of Applied Cryptography", CRC Press



  • William Stallings, "Cryptography and Network Security", Pearson Education, 3rd Edition, Reprint 2003