Syllabus

Introduction to cryptography: Notions of cryptographic secrecy Block ciphers Stream ciphers Public-key cryptography Iterated and cascade ciphers Cryptanalysis Implementation attacks Complexity theory Authentication and identification Ownership protection Covert communications
The integers: Basic number theory The Euclidean algorithm Prime fields Quadratic residues Quadratic reciprocity The Jacobi symbol Primality testing The Fermat algorithm The Solovay–Strassen algorithm The Miller–Rabin algorithm Factoring of integers The Pollard algorithm for factoring Square roots in a prime field. Cryptography based on the integer ring: Biprime cryptography Implementing biprime cryptography Protocol attacks on biprime cryptography Direct attacks on biprime encryption Factoring biprimes The quadratic sieve The number-field sieve The Rabin cryptosystem The rise and fall of knapsack cryptosystems. Cryptography based on the discrete logarithms: Diffie–Hellman key exchange Discrete logarithms The Elgamal cryptosystem Trapdoor one-way functions The Massey–Omura cryptosystem The Pohlig–Hellman algorithm The Shanks algorithm The Pollard algorithm for discrete logarithms The method of index calculus Complexity of the discrete-log problem. Information-theoretic methods in cryptography: Probability space Entropy Perfect secrecy The Shannon–McMillan theorem Unicity distance Entropy of natural language Entropy expansion Data compaction The wiretap channel. Block ciphers: Block substitution The Feistel network The Data Encryption Standard Using the Data Encryption Standard Double and triple DES encryption The Advanced Encryption Standard Differential cryptanalysis Linear cryptanalysis. Stream ciphers: State-dependent encryption Additive stream ciphers Linear shift-register sequences The linear-complexity attack Analysis of linear complexity Keystreams from nonlinear feedback Keystreams from nonlinear combining Keystreams from nonlinear functions The correlation attack Pseudorandom sequences Nonlinear sets of sequences Authentication and ownership protection Authentication: Identification Authentication signatures Hash functions The birthday attack Iterated hash constructions Formal hash functions Practical hash functions

To build capability in analyzing and solving problems related secure communication

To build capability to design algorithms for security in communication related applications

Students will have concepts on coding theory required for secure communication

Richard E Blahut, Cryptography and Secure communication, Cambridge press , 1st Edition 2014

Douglas R. Stinson, Cryptography: Theory and Proctice, Chapman and Hall , 3rd Edition 2005

R Bose, Information Theory Coding and Cryptography, McGraw-Hill , 2nd Edition 2017

Bruce Schneier, Applied Cryptography: Protocols, Algorithms and source codes, Wiley , 2nd Edition 2007