Computer Science

Introduction to CryptographyCSCIGA 3210001 
Fall 2015 
For hints and further reading, use the Hintomatic.
Lectures

Mondays 11:00am12:50pm WWH 517 
Instructor 
Oded Regev 
Office hours

Mondays 9:45am10:45am, 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. Last year's course 
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. 
Date  Class Topic 
Sep 14  Introduction, Perfect Secrecy. Number theory. Lectures 1+2 of Peikert, Lecture 1 of Dodis, Section 1.3 of PassShelat. 
Sep 21  (Proof of Shannon's Theorem) Finishing number theory. Oneway functions (and collections thereof). Weak oneway functions. 
Sep 28  Examples of oneway functions. A bit on going from weak to strong OWFs. Weak OWFs to strong OWFs. Informal discussion of indistinguishability and pseudorandom generators. 
Oct 5  Collections of oneway functions. More examples of OWFs. Application of OWFs to password storage. 
Oct 13  Indistinguishability. Pseudorandom generators. Expanding PRGs. 
Oct 19  BlumMicali PRG. Hardcore bits. GoldreichLevin; Pseudorandom functions: motivation and definition 
Oct 26  Constructing Pseudorandom functions 
Nov 2  Pseudorandom permutations and LubyRackoff; symmetric key encryption, definitions of security and constructions 
Nov 9  Finishing symmetric key encryption; public key encryption 
Nov 11  Trapdoor oneway permutations; DiffieHellman protocol and ElGamal cryptosystem. Authentication (model only) 
Nov 23  Semantic security of PKE. Authentication security definition and info theoretic construction. 
Nov 30  Computational construction of MAC using PRF. Expanding input of MACs using CRHF or almost universal hash functions. 
Dec 7  Authenticated encryption. Digital Signatures. Zero Knowledge 
Dec 9  Latticebased cryptography (bonus class) 
Dec 14  Final exam 