Instructor: Arpita Patra (Email: arpita AT iisc DOT ac DOT in)

Timings: 03:30 pm - 05:00 pm on Monday and Wednesday.

Venue: CSA 112

Study Materials

[KL] “Introduction to Modern Cryptography” by Jonathan Katz and Yehuda Lindell, second edition 2014, CRC Press.
[Gol] “Foundations of Cryptography” by Oded Goldreich.
[BS] “A Graduate Course in Applied Cryptography” by Dan Boneh and Victor Shoup. [Link]
[Sti] “Cryptography: Theory and Practice” by Douglas R. Stinson, third edition 2003, CRC.
[MOV] “Handbook of Applied Cryptography” by Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, first edition 1997, CRC Press.

Course Description

One way Functions (Permutations), Hard-core Predicates, Pseudo-random Generators, (Strong) Pseudo-random Functions (Permutations).
Secret Key Encryptions (SKE): Various security notions such as Perfect Security, Semantic Security, Indistinguishability based Security, CPA Security, CCA Security, Constructions, Block Cipher Mode of Operations.
Message Authentication Codes (MAC): Various Security notions such as CMA Security, (weak/strong) CMVA security, Domain Extension, CBC-MAC.
Advanced Encryption Schemes: Authenticated Encryptions.
Introduction to Secure Computation (Yao’s 2PC protocol and Circuit Garbling).
Number Theory: Preliminaries, Modular arithmetic, elementary group theory, CRT, hardness assumptions.
Trapdoor permutations: definitions, construction based on factoring, CR Hash functions based on number-theoretic assumptions.
Public-key encryption: Implications of Semantic Security, Textbook RSA, Padded RSA, ElGamal, CCA secure public key encryption.
Digital signatures: definitions, hash-and-sign paradigm, Lamport’s scheme, RSA signatures.
Protocols: Identification protocols, proving properties in zero knowledge, non-interactive proof systems and applications.

Grading

Announcements

Improper academic behaviour: Copying during exams, copying of homework assignments, term papers or manuscripts, verbatim or paraphrased. Allowing or facilitating copying, or writing a report or exam for someone else. Using unauthorized material and collaborating when not authorized. [Details]
Action: In the case of a violation of the academic integrity, the student’s ID will be reported to the Office of Career Counselling and Placement (OCCaP).

Lecture 1 : Introduction, Classical Crypto vs. Modern Crypto, Three Pillars of Modern crypto (definition + assumption + proof), Classical ciphers and pitfalls. Inroad towards Modern Crypto.
References : [Slides], Chapter 1 of KL and BS
Date : 05-08-2026

Lecture 2 : Perfect Security for SKE: Definition, Construction (Vernam Cipher), Proof; Drawbacks of OTP.
References : [Slides], Chapter 2 of KL and BS
Date : 10-08-2026

Lecture 3 : More definitions of Perfect Security and their equivalence with Shannon's perfect security definition. Shannon's Theorem. Perfect Indistinguishability-- game-based definition. Proof of limitations on key space/length and key reusability.
References : [Slides], Chapter 2 of KL and BS
Date : 12-08-2026

Lecture 4 : Perfect Security for Secret Sharing: Definition. Threshold Secret Sharing: Constructions (Additive Secret Sharing, Ito-Saito-Nishizeki Secret Sharing), Analysis.
References : [Slides], Chapter 13 of Sti, Chapter 13 of KL and Chapter 22 of BS
Date : 17-08-2025

Lecture 5 : Basics concept of Abstract Algebra. Polynomials over Field. Lagrange Interpolation. Shamir Secret Sharing. Perfectly-Secure Message Transmission (PSMT). BGW MPC Protocol for Linear Functions.
References : [Slides], Chapter 13 of Sti, Chapter 13 of KL and Chapter 22 of BS
Date : 19-08-2025