Computer Science
Courant Institute

Introduction to Cryptography

CSCI-GA 3210-001

Fall 2013

Homework assignments

Work is graded based on correctness, clarity, and conciseness. All solutions must be typeset in Latex, following the templates provided, and submitted both in print and electronically (send both TeX and PDF). Only submit work that you believe is correct; if you cannot solve a problem completely, you will get significantly more credit if you clearly identify the gaps in your solution. We recommend starting any longer solution with an informal yet accurate proof summary that describes the core idea. Collaboration and consultation with external material is allowed, but must be declared for each question. The final exam will be based on homework questions.

For hints and further reading, use the Hint-o-matic.

Some Information

Lectures

Mondays 5:00pm-7:00pm, WWH 201
Instructor

Oded Regev
Office hours

Mondays 3pm-4pm, WWH 303
Reading

Introduction to Cryptography, by Jonathan Katz and Yehuda Lindell. A good introductory book.
Foundations of Cryptography, Vol. 1 and 2 by Oded Goldreich. A comprehensive book for those who want to understand the material in greater depth.
Lecture notes by Yevgeniy Dodis, which we'll follow closely
Lecture notes by Chris Peikert
Lecture notes by Rafael Pass and Abhi Shelat.
Requirements
 Active participation in class, homework assignments, final exam
Prerequisites
 Students are expected to be comfortable reading and writing mathematical proofs, be at ease with algorithmic concepts, and have elementary knowledge of discrete math, number theory, and basic probability. No programming will be required for the course.

Schedule

Date Class Topic
Sep 9 Introduction, Perfect Secrecy. Number theory. Lectures 1+2 of Peikert, Lecture 1 of Dodis, Section 1.3 of Pass-Shelat.
Sep 16 (Proof of Shannon's Theorem) Finishing number theory. One-way functions (and collections thereof). Weak one-way functions. Examples of one-way functions.
Sep 23 Proof of weak-to-strong one-way functions. Collections of one-way functions. Informal discussion of indistinguishability and pseudorandom generators.
Sep 30 More examples of OWFs. Application of OWFs to password storage. Indistinguishability. Pseudorandom generators. Expanding PRGs.
Oct 7 Blum-Micali PRG. Hard-core bits. Goldreich-Levin.
Oct 21 Finishing Goldreich-Levin; Pseudorandom functions
Oct 28 Constructing Pseudorandom functions; pseudorandom permutations
Nov 4 Finishing pseudorandom permutations and Luby-Rackoff; symmetric key encryption, definitions of security and constructions
Nov 11 Finishing symmetric key encryption; public key encryption
Nov 18 Trapdoor one-way permutations; Diffie-Hellman protocol and ElGamal cryptosystem. Authentication (model only)
Nov 25 Semantic security of PKE. Authentication security definition and info theoretic construction.
Dec 2 Computational construction of MAC using PRF. Expanding input of MACs. Digital Signatures.
Dec 9 Zero Knowledge
Dec 11 Lattice-based cryptography
Dec 16 Final exam