Course Name: 

Number Theory and Cryptography (IT462) (2018 Curriculum)


B.Tech (IT)


Programme Specific Electives (PSE)

Credits (L-T-P): 

(3-0-2) 4


Introduction to Number Theory: Prime Numbers, Fermat’ s Little Theorem and Euler’s Theorem, Testing for Primality, Chinese Remainder Theorem, Discrete Logarithms. Euclidean Algorithm, Extended Euclidean Algorithm, Euler’ s Phi Function. Finite Fields: Groups, Rings, and Fields, Modular Arithmetic, Euclidean Algorithm, Finite Fields of The Form GF(p), Polynomial Arithmetic, Finite Fields Of the Form GF(2n); Introduction to Cryptography: Symmetric Cryptography, Substitution Cipher, Shift Cipher (or Caesar Cipher), Affine Cipher, Hill cipher. Stream Ciphers: Stream Ciphers vs. Block Ciphers, Encryption and Decryption with Stream Ciphers, Random Numbers and an Unbreakable Stream Cipher, Random Number Generators, One-Time Pad, Towards Practical Stream Ciphers, Shift Register-Based Stream Ciphers, Linear Feedback Shift Registers (LFSR), Known-Plaintext Attack Against Single LFSRs. The Data Encryption Standard (DES) and Alternatives: Confusion and Diffusion, Double DES (2DES)
and Triple DES (3DES). Advanced Encryption Standard (AES). Block Ciphers: Modes of Operation, Electronic Codebook Mode (ECB), Cipher Block Chaining Mode (CBC), Output Feedback Mode (OFB), Cipher Feedback Mode (CFB), Counter Mode (CTR), Galois Counter Mode (GCM). Introduction to Public-Key Cryptography: Practical Aspects of Public-Key Cryptography, RSA Cryptosystem, Elliptic Curve Cryptosystems. Digital Signatures: RSA Signature Scheme, Elgamal Digital Signature Scheme, Digital Signature Algorithm (DSA), Elliptic Curve Digital Signature Algorithm (ECDSA).


“Cryptography and Network Security: Principles and Practices”, 4th Edition, W. Stallings, Prentice Hall, 2005.
“Cryptography and Network Security”, 6th Edition, William Stallings, Pearson, 2013.
“Understanding Cryptography A Textbook for Students and Practitioners”, Christ of Paar, Jan Pelzl, Springer.
“Cryptography, Theory and Practice”, 3rd Edition, Douglas R. Stinson, CRC Press, 2006.
“Network Security Private Communication in a Public World”, C. Kaufman et al., Prentice Hall, 2002.
“Applied Cryptography”, 2nd Edition, Bruce Schneier, Wiley, 1996.
“Handbook of Applied Cryptography”, A. Menezes, P. Van Oorschot, S. Vanstone, CRC Press, Fifth Printing, 2001.
“Elementary Number Theory with Applications”, Thomas Koshy, 2nd Edition, Academic Press, 2007.
"A Computational Intro. to Number Theory and Algebra", Victor Shoup, 2nd Ed., Cambridge Univ. Press, 2005.


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National Institute of Technology Karnataka,
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