Principles of Cryptography
Credit: 3
Objective
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To gain knowledge about the mathematics of the cryptographic algorithms.
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To get an insight into the working of different existing cryptographic algorithms.
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To learn how to use cryptographic algorithms in security.
Unit-I
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..
Unit-II
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.
Unit-III
Block ciphers: Modes of operation, DES and its variants, AES, linear and differential cryptanalysis.
Unit-IV
One-way function , trapdoor one-way function, Public key cryptography, RSA cryptosystem, Diffie-Hellman key exchange algorithm, Elgamal Cryptosystem.
Unit-V
Cryptographic hash functions, secure hash algorithm, Message authentication, digital signature, RSA digital signature, Elgamal digital signature.
Outcome
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Building a new unbreakable cryptosystem
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Blending the existing cryptographic algorithms with the existing communication protocols
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Analyzing and application of cryptography for secure eCommerce and other secret transactions
Textbook:
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Stinson. D. Cryptography: Theory and Practice, third edition, Chapman & Hall/CRC, 2010.
Reference Books:
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W. Stallings, Cryptography and Network Security Principles and practice, 5/e, Pearson Education Asia, 2012.
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Behrouz A. Forouzan and Debdeep Mukhopadhyay, Cryptography and Network Security, second edition, Tata McGraw Hill, 2011
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Thomas Koshy, Elementary Number Theory with applications, Elsevier India, 2005.