- Unit 1: Concepts of Number Theory: Number Theory, GCD, Euclidean algorithm, Extended Euclidean algorithm, prime numbers, congruence, how to solve congruence equations, Chinese remainder theorem, residue classes and complete residue systems, Euler Fermat theorem, primitive roots.
- Unit 2: Symmetric Key Cryptographic Systems: Caesar and affine ciphers, mono-alphabetic substitutions, transposition, homophonic, Vigenere and Beaufort ciphers, one-time pad, product/iterated/block ciphers, DES and AES. Heavy discussion is given to the security of these ciphers, not only are they studied in an algorithm sense but their attacks and defences are also discussed, modes of operation: CBC, ECB.
- Unit 3: Cryptanalysis of symmetric keys- Attack Models, Linear, Differential and various others such as meet-in-the-middle attack .PKCS- Concepts of PKCS, Diffie Hellman key-exchange protocol, RSA, Rabin and EL Gamal cryptosystems.
- Unit 4: Stream Ciphers and Digital Signatures- synchronous, self-synchronizing attack ciphers, linear feedback shift registers, Digital Signatures-RSA, multiple RSA and ElGamal signatures, digital signature standard.
- Unit 5: Hash Functions and MACs- Hash functions: the Merkle-Damgard construction, Message Authentication Codes, security of Hash functions, security weakness of MD4, MD5, SHA1,SHA2, construction of SHA3.
- Unit 6: Basic elliptic curve cryptography: definition, mathematical formulation of them, elliptic curve cryptography and pairings, elliptic digital signature algorithm, advantages, implementation of elliptic curve cryptography, point addition, point doubling, elliptic diffie hellman key exchange.
- Unit 7: Key exchange protocols, Kerberos, Certificates, Man-in-the-middle-attack, Public key infrastructures
