Instructors: Dr. Avijit Dutta and Dr. Nilanjan Datta

Teaching Assistant: Mr. Bibhas Chandra Das

##### 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, Shannon Cipher, Perfect Security, Computational Ciphers and Semantic Security.
• Encryption: Stream Ciphers, Pseudo random generators, LFSR based stream ciphers, RC4 and its Cryptanalysis; Block ciphers: Design principle, AES and its design rationale, light-weight block cipher design; Security Notions, Modes of operation: ECB, CBC, OFB, Counter mode.
• Cryptanalysis: Goal and power of an adversary; 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 Integrity: 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, Light-weight AE design.
• 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:

 D. Boneh, V. Shoup: A Graduate Course in Applied Cryptography. [Online Link].

 J. Katz and Y. Lindell: Introduction to Modern Cryptography, Chapman & Hall/CRC, 2007. [Online Link]

 D. R. Stinson, M. B. Paterson: Cryptography Theory and Practice, 4th ed., Chapman & Hall/CRC, 2018. [Online Link]

 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]

 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. [Boardwork]

• Lecture 2: Classical Ciphers and their Cryptanalysis. [Boardwork] [Slide]

• Lecture 3: Perfect Secrecy [Boardwork]

• Lecture 4: Computation Security, Indistingishability under eavesdroppers, Semantic Security [Boardwork]

• Lecture 5: Pseudo-random generators (PRG), Stream Ciphers, Security for Multiple Encryptions, Chosen Plaintext Attacks (CPA) and CPA Security  [Boardwork]

• Lecture 6: Left-or-Right IND-CPA and Real-or-Random IND-CPA, Pseudo-random Functions (PRF), Constructing IND-CPA Secure encryptions from PRF [Boardwork]

• Lecture 7: PRP, SPRP, Modes of Operations: OCB, CBC, OFB, CTR Modes of Encryptions [Boardwork]

• Lecture 8: Tutorial [Problem Sheet] [Boardwork]

• Lecture 9: CCA, CCA Insecurity of some Popular encryption schemes, Message Authentication Code, EUF-CMA, SUF-CMA, Universal Forgery, Secure MAC Construction: PRF (fixed-length), CBC-MAC and it’s variant (variable-length) [Boardwork]

• Lecture 10: Authenticated Encryption, Motivation, Security Definition, AE Construction using Generic Composition, (In)-Security of EaM, EtM and MtE, Importance of Independence of keys in generic composition [Boardwork]

Public Key Cryptography

• Lecture 1: Introduction to Basic Number Theory: I [Boardwork]

• Lecture 2: Introduction to Basic Number Theory: II [Boardwork]

• Lecture 3: Number Theoretic Algorithms: I [Boardwork]

• Lecture 4: Number Theoretic Algorithms: II [Boardwork]

• Lecture 5: Primality Testing Algorithm, Introduction to Public Key Encryption [Boardwork]

• Lecture 6: Indistinguishable (multiple) encryption  in the presence of an eavesdropper [Boardwork]

• Lecture 7: Hybrid Encryption [Boardwork]

• Lecture 8: Chinese Remainder Theorem, Factoring Problem, RSA Problem [Boardwork]

• Lecture 9: RSA Algorithm, Insecurity of textbook RSA [Boardwork]

• Lecture 10: Discrete Logarithm Problem, Diffie-Hellman Problem, CDH, DDH, El-Gamal Encryption [Boardwork]

##### Assignments and/or Practice Problems:

• Problems on Classical Ciphers and Perfect Secrecy [Practice Problems]

• Programming Assignments on Number Theoretic Algorithms [Assignment 1] (Deadline: Sep 22, 2022)

• Assignment on Symmetric Key Encryption [Assignment II] (Deadline: Sep 24, 2022)