Cryptography

Course Objective: This course serves as an introduction to modern cryptography, emphasizing its classical goals: data privacy, authenticity, and integrity. It covers the fundamentals of both symmetric-key and public-key cryptography. Additionally, the course introduces advanced cryptography concepts, including commitment schemes, secret sharing, oblivious transfer, zero-knowledge proofs, and multi-party computation. We will implement practically everything we learn.
Privacy, secrecy, and security are central to our emerging “information society”, and cryptography is a key technology for achieving them; it is also a fascinating field of study in its own right. Cryptography lies at the center of this course: on the one end, we’ll look at problems of computer and information security, and then understand and implement cryptographic tools to solve them. We’ll also touch on some social issues surrounding the use of cryptography. At the other end, we’ll explore the mathematical structures from which cryptographic primitives are built, and learn how to use some of these techniques in real-world scenarios.

Pre-requisite: Discrete Mathematics, Probability and Statistics, Introduction to Computer Science

Coverage:
– Symmetric key cryptography: Symmetric Key Encryption, Pseudorandom number generators (PRG), Pseudorandom functions (PRF), Stream ciphers, Block ciphers, Modes of Operations, Security definitions for Encryption, Message integrity, Message authentication codes, Hash Functions.
– Public key cryptography: Diffie-Hellman Key Exchange, Discrete Logarithm Problem. Public key encryption, Security definitions, Factoring Problem, ElGamal Encryption, RSA Encryption. Digital Signatures, RSA Signature, DSA Signature. Introduction to Elliptic Curve, ECDSA Signature.
– Cryptography Applications: Public key infrastructure (PKI), Brief Introduction to TLS.
– Advanced Cryptography Concepts: Commitment Schemes, Secret Sharing, Oblivious Transfer, Zero knowledge Proofs, Multiparty Computation.

References: For the most part, we do not use a textbook. However, we do provide detailed lecture notes/slides, and, for some definitions and proofs, we refer to Goldwasser and Bellare’s notes (https://cseweb.ucsd.edu/~mihir/papers/gb.pdf)