IAI

Course Objective:

Cryptology is concerned with the conceptualization, definition, and construction of computing systems that address security concerns. The objective of this course is to provide a basic understanding of cryptographic concepts, mathematical tools used for cryptography and how to use these tools in solving cryptographic problems, building new cryptographic primitives, analyzing the security of cryptographic protocols, and understanding key management and key exchange issues at a basic level. The focus is given on the basic mathematical tools as well as some new advanced cryptographic tools and the advances in research using those tools.

 

Syllabus:

 

• Introduction: Classical Ciphers and Its Cryptanalysis, Principles of Modern Cryptography.
• Perfect Secrecy: Perfect Secrecy: Various Definitions and their equivalence, One Time Pad and Its Limitation, Shannon Cipher.
• Symmetric-Key Encryption: Computational Ciphers, Semantic Security, IND-CPA Security,  Pseudo random generators, Stream Ciphers, Pseudo random functions/permutations, Block ciphers, Modes of operation: ECB, CBC, OFB, Counter mode.
• Primitive Design and Its Cryptanalysis: LFSR based stream ciphers, RC4 and its Cryptanalysis; Block Cipher: Design principle, Example: AES and its design rationale, Basic Cryptanalysis Techniques: Differential and Linear Cryptanalysis; Some advanced cryptanalysis (integral, impossible differential) and its applications.
• Hash Function: Collision resistant (CR) hash functions, birthday attacks CR hash, The Merkle- Damgard paradigm, Joux’s multi-collsion attacks; Universal hash functions (UHF), constructing UHFs.
• Message Authentication: Message authentication codes (MACs); Designing MACs from CR hash, Case Study: HMAC, Sponge based MACs; Designing MACs from UHF, The Carter-Wegman MACs, Nonce based MACs.
• Authenticated Encryption (AE): Motivation, Security, Designing AE: Generic Paradigm, Integrated AE; Features of AE.
• Public Key Cryptosystems: Basics of Number theory, Number theoretic Algorithm, Primality testing algorithm, Integer Factorization Problem, Discrete Logarithm Problem, Diffie Hellman Key Exchange Protocol, RSA Encryption and Its variants, Elgamal Encryption Scheme, Digital Signatures, Commitment Scheme, Secret Sharing, Fiat-Shamir Identification Scheme.

 

References:

 

[1] J. Katz and Y. Lindell: Introduction to Modern Cryptography, Chapman & Hall/CRC, 2007. [Online Link]
[2] D. Boneh, V. Shoup: A Graduate Course in Applied Cryptography. [Online Link]
[3] M. Rosulek: The Joy of Cryptography. [Online Link]
[4] D. R. Stinson, M. B. Paterson: Cryptography Theory and Practice, 4th ed., Chapman & Hall/CRC, 2018. [Online Link]
[5] K. Sakiyama, Y. Li and Y. Sasaki: Security of Block Ciphers: From Algorithm Design to Hardware Implementation, Published by Wiley & Sons, Incorporated, John, 2016. ISBN 10: 1118660013. [Available in Library]
[6] V. Shoup: A Computational Introduction to Number Theory and Algebra, Cambridge University Press. [Online Link]

Board-works and Slides:

     Symmetric Key Cryptography

• Lecture 1: Introduction to Cryptology and Classical Ciphers. [Boardwork]
  
  
• Lecture 2: Motivation of Modern Cryptography and Introduction to Perfect Secrecy. [Boardwork] [Slide]
  
  
• Lecture 3: Perfect Secrecy [Boardwork]
  
  
• Upcoming Lecture: Computation Security, Indistingishability under eavesdroppers, Semantic Security
  
  
  
  Public Key Cryptography
  
  
• Lecture 1: Introduction to Basic Number Theory. [Boardwork]
  
  

 

Assignments and/or Practice Problems:

• Assignment on Classical Ciphers and Perfect Secrecy [Assignment 1]