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Course Detail

Course Name Cryptography and Applications
Course Code 21SN604
Program M. Tech. in Cyber Security Systems & Networks
Semester 1
Credits 4


  • 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


  1. William Stallings “Cryptography and Network Security” Fifth Edition, Prentice Hall, 2011
  2. Alfred J Menzes, Paul C Van Oorshot and Scott A. Vanstone “Handbook of Applied

    Cryptography”, CBC Press, 1996

  3. Stein William. “Elementary number theory. Primes, congruence’s, and secrets.” A

    computational approach

  4. Neal Koblitz “A course in Number Theory and Cryptography” Springer-Verlag 1994
  5. ChristofPaar, “Understanding Cryptography”, Springer-Verlag-2010

Course Objectives

  • CO1: Understanding the mathematics behind cryptography and how to use the theorems for research purposes (PO1, PSO4)
  • CO2: Learn Symmetric key cryptography and the advantages and disadvantages, how to build stream ciphers and detect the weaknesses and attacks (PO1, PO2, PSO4, PSO3)
  • CO3: Implementation of DES, AES Algorithm and the corresponding attacks existing on them (PO1, PO3, PSO1 PSO3, PSO4)
  • CO4: Public key Cryptography advantages as well as various existing algorithms are explored, their proofs and how to currently attack them if implemented incorrectly. (PO1, PO2, PO3, PSO1, PSO3, PSO4)
  • CO5: Understand basic points of Elliptic Curves and calculate point addition and doubling (PO1, PSO2)
  • CO6: Understand the difference between Digital Signatures and MACs, as well as the different algorithms existing plus their corresponding weaknesses (PO1, PO2, PO3, PSO3) CO7: Learn about Hash functions properties, how to construct strong hash function and history of hash functions, as well as constructing SHA-1 (PO1, PO2, PO3, PSO2, PSO4)

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