# E0 235: Cryptography (Fall 2021)

• Instructors: Chaya Ganesh and Arpita Patra   Course credits: 3:1   Lecture time: T,Th 3:30-5 pm   Venue: Microsoft Teams.

• TAs: Girisha B Shankar (girishabs AT iisc DOT ac DOT in), Moumita Dutta (moumitadutta AT iisc DOT ac DOT in)

• Office Hours: By appointment. Contact Girisha/Moumita or the instructor to make an appointment.

• Objective:
This course offers a graduate introduction to cryptography, the science of securing data and computation against various adversarial behaviors. At the end of the course, you should be able to:
1. Formally define security properties and reason about them mathematically.
2. Understand cryptographic constructions at work: what makes them secure.

• Intended Audience: All students with curiosity about cryptography are welcome. Mathematical maturity is expected.

• Syllabus:
• 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, Lamportâ€™s scheme, RSA signatures.
• Protocols: Identification protocols, proving properties in zero knowledge, non-interactive proof systems and applications.

• References:
• Introduction to Modern Cryptography, Jonathan Katz and Yehuda Lindell. [Link]
• A Graduate Course in Applied Cryptography, Dan Boneh and Victor Shoup. [Link]
• Foundations of Cryptography, Oded Goldreich. [Link]

• Prerequisites: Mathematical maturity, Familiarity/ease with reading and writing proofs, Algorithmic concepts, Elementary number theory, Elementary discrete mathematics.

• Course Policy:

• Homeworks - 40%
• In-class Quizzes - 24%
• Final exam - 36%

• Collaboration:
You are encouraged to discuss homework problems with your peers. However, you must write up your own solutions, and list the names of your collaborators in each homework you turn in.