Indian Institute of Information Technology, Allahabad

Department of Information Technology

Course Syllabus

1. Name of the Course: Introduction to Cryptography

2. LTP structure of the course: 2-1-1

3. Objective of the course: The objective of this course is to impart knowledge of the basic principles and concepts of modern cryptography. The course will focus on cryptographic problems and their cryptographic solutions. It material will comprise of both theory and applications with an exposure to the techniques that are in practice. The definitions of security and certain construction that meet these definitions shall be taught.

4. Outcome of the course: A student will have an understanding of modern cryptography which shall be self- sufficient for any second course in the area of security. Moreover, a student will be able to undertake any work in this area in the industry or research without any other course work.

5. Course Plan:

Unit | Topics for Coverage | |

Component 1 | Unit 1 | 1. Introduction: What is modern cryptography, Historical ciphers and their cryptanalysis, The heuristic versus the rigorous approach; adversarial models and principles of defining security 2. Perfectly-Secret Encryption: Definitions, the one-time pad; proven limitations 3. Private-Key (Symmetric) Encryption: Computational security, Defining secure, encryption, Constructing secure encryption; pseudo randomness, Stronger security notions, Constructing CPA-secure encryption, Modes of operation; CBC vs. CTR, Security of CTR with n − k bit counter for messages to size 2k blocks with proof directly to the LR definition, CCA attacks. |

Unit 2 | 4. Message Authentication Codes: Message integrity, Definition of security, Constructions from pseudorandom functions, CBC-MAC, Authenticated encryption. 5. Collision-Resistant Hash Functions: Definitions, The Merkle-Damgard transform, HMAC, Birthday attacks, The Random oracle model, Password hashing, Constructions of Pseudorandom Permutations (Block Ciphers) in Practice, Substitution-permutation and Feistel networks, DES and attacks on reduced-round versions, double-DES and triple-DES, AES, Hash functions from block ciphers. | |

Component 2 | Unit 3 | Number Theory: Preliminaries and basic group theory, Primes, factoring and RSA, Cryptographic assumptions in cyclic groups, Collision resistant hash functions from discrete log, Public-Key (Asymmetric) Cryptography: Introduction and motivation, Diffie-Hellman key exchange |

Unit 4 | Public-Key (Asymmetric) Encryption: The model and definitions, Hybrid encryption and KEM/DEM, El Gamal, RSA: textbook encryption, attacks on textbook RSA, padded RSA; CCA-secure RSA KEM. Digital Signatures: Definition and applications, Hash and sign, RSA signatures: textbook RSA, hashed RSA, security with ROM, Certificates and public-key infrastructures. |

6. Text Book:

7. References:

- Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, second edition 2014, CRC Press.
- Cryptography: Theory and Practice by Douglas Stinson, Third edition, CRC Press.
- Handbook of Applied Cryptography by Alfred Menezes, Paul Oorschot and Scott Vanstone. Available Online.
- Foundations of Cryptography by Oded Goldreich. Available Online.
- Cryptography, an Introduction by Nigel Smart. Available Online