Principles of Cryptography

Credit: 3


  • 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.



Algebra: Group, cyclic group, cyclic subgroup, field, probability. Number Theory: Fermat's theorem , Cauchy 's theorem, Chinese remainder theorem, primality testing algorithm, Euclid's algorithm for integers, quadratic residues, Legendre symbol, Jacobi symbol etc..



Cryptography and cryptanalysis, Classical Cryptography, substitution cipher, different type of attack: CMA,CPA,CCA etc, Shannon perfect secrecy, OTP, Pseudo random bit generators, stream ciphers and RC4.



Block ciphers: Modes of operation, DES and its variants, AES, linear and differential cryptanalysis.



One-way function , trapdoor one-way function, Public key cryptography, RSA cryptosystem, Diffie-Hellman key exchange algorithm, Elgamal Cryptosystem.



Cryptographic hash functions, secure hash algorithm, Message authentication, digital signature, RSA digital signature, Elgamal digital signature.



  • Building a new unbreakable cryptosystem

  • Blending the existing cryptographic algorithms with the existing communication protocols

  • Analyzing and application of cryptography for secure eCommerce and other secret transactions



  1. Stinson. D. Cryptography: Theory and Practice, third edition, Chapman & Hall/CRC, 2010.


Reference Books:

  1. W. Stallings, Cryptography and Network Security Principles and practice, 5/e, Pearson Education Asia, 2012.

  2. Behrouz A. Forouzan and Debdeep Mukhopadhyay, Cryptography and Network Security, second edition, Tata McGraw Hill, 2011

  3. Thomas Koshy, Elementary Number Theory with applications, Elsevier India, 2005.