Cornell University

Fall 2011

Instructor: Rafael Pass

Time:
TR 1:25-2:40

Place: Thurston 220

Course Web page: http://www.cs.cornell.edu/courses/cs6830/2011fa/

Office
Hours: by appointment.

TA: Eleanor
Birrell

The
modern study of cryptography investigates techniques for facilitating
interactions between distrustful entities. In our connected society, such
techniques have become indispensable---enabling, for instance, automated teller
machines, secure wireless networks, internet banking, satellite
radio/television and more.

In this
course we introduce some of the fundamental concepts of this study. Emphasis
will be placed on the foundations of cryptography and in particular on precise
definitions and proof techniques.

Topics
include: one-way functions, encryption, signatures, pseudo-random number
generation, zero-knowledge and basic protocols.

Note:
This will be a theory course. You will be expected to read and write formal
definitions and mathematical proofs. This is not a course in security: you will
not learn how to secure your system. Cryptography is only one (important) part
of security. We will not study cryptographic acronyms or all cryptographic
protocols in use today. Rather we focus on some of the fundamental design
paradigms and on notions that will allow you to critically evaluate
cryptographic protocols.

General ease with algorithms and elementary probability theory, maturity with mathematical proofs (to be able to read and write mathematical proofs)

We
are using the course management system, **CMS**.
Please login to http://cms.csuglab.cornell.edu/
and check whether you are registered. There will be a list of courses you are
registered for, and CS 6830 should be one of them. If not, please send
your full name and Cornell netid to the TA so he can register you. You
can check your grades and submit homework in CMS.

There
will be roughly 5 homeworks (and potentially a final project). The grade will
be based on homework assignments, scribe and class participation (and the final
project).

You are free to collaborate with other students on the homework, but you must turn in your own individually written solution and you must specify the names of your collaborators. Additionally, you may make use of published material, provided that you acknowledge all sources used. Note that it is a violation of this policy to submit a problem solution that you are unable to explain orally to me. Typed problem sets are strongly preferred.

Homework 1 is due on Sep 6.

You will need the following notation and preliminaries.

Lecture
notes covering a large fraction of the course can be found here.

There
is no required textbook for the course. However, most of the topics we will
cover can be found in the following excellent reference.

- Oded Goldreich. Foundations of Cryptography. This is a very comprehensive treatment of the theoretical foundations of cryptography. Volume I contains most of the material we will cover in class. Other topics such as encryption, signatures and secure computation are in Volume II.

**Introduction:**- Introduction
and Overview.
- Information
Theoretic Security.

*Shannon’s Definition of security. One-time Pads. Limitations of the Information Theoretic Approach.*

** **

**Computational Hardness and One-wayness:**- One-way
Functions and Computationally bounded adversaries.

*Randomized Efficient Algorithms. One-way functions (OWF).*

Collections of OWFs. *Number Theory and Candidate One-way functions/permutations and trapdoor permutations.**Weak and Strong OWFs. Hardness Amplification.*

** **

**Indistinguishability, Randomness and Pseudorandomness:**- Computational
Indistinguishability and Pseudorandom Generators (PRG) and Functions
(PRF).

*Definitions of Computational Indistinguishability and Pseudorandomness.*

*Hard-core bits. Constructions of
a PRGs and PRFs.*

- Hard-core
bits from any one-way function.

*The Goldreich-Levin Theorem.*

*Hard-core functions. The XOR
Lemma.*

- Imperfect
Randomness, and Hardness v.s. Randomness.

*Impossibility of deterministic extraction.*

Universal Hashfunctions and seeded extractors.

PRG and Derandomization of BPP. - Private-Key
Encryption.

*Definitions and Constructions* - Public-Key
Encryption.

*Definitions and Constructions.*

**Zero-Knowledge:**- Semantical
Security:

*Zero knowledge-based definitions
of encryption. Equivalence with indistinguishability-based definitions.*

- Zero-Knowledge
Proofs:

*Definitions and construction of ZK proofs for Graph-Isomorphism and Graph 3-coloring.* - Witness
Indistinguishability

*Constant-round
ZK.
*

**Applications:****Authentication:**- Digital
Signatures.

*Definitions and Constructions* - Hash
functions.
- Message
Authentication Codes.
- Zero
Knowledge-based Authentication
**.**

1.
**Computing on Secret Inputs:**

- Secret
Sharing.
- Secure
Computation.

*Oblivious Transfer.*

General secure computation. - Fully Homomorphic Encryption.

2.
**Composability:**

*1.
*Composability
of Encryption schemes.

*Chosen
challenge-text, Chosen plain-text, Chosen cipher-text 1 and 2 (CCA1, CCA2).
Malleability. *

2.
Composability
of Zero-Knowledge proofs.

3.

Please
note that scribe notes are only rough notes of the lectures. Scribers please
follow this template. If you need help with LaTeX,
here is a small tutorial file and its source. Don’t forget to hand in your LaTeX
source as well along with your scribe!

- Lecture 1: Introduction (Aug 25)
- Lecture 2: Perfect Secrecy (Aug 30, Sidharth Telang)
- Lecture 3: One-Way Functions (Sep 1, Costandino Dufort Moriates)
- Lecture 4: Hardness Amplification Theorem (Sep 6, Sujay Jayakar)
- Lecture 5: Levin's OWF and Multiplication (Sep 8, Shyam Lenna)
- Lecture 6: OWFs and Hard-Core Bits (Sep 13, David Goff)
- Lecture 7: Hard-Core Bits from any OWF (Sep 15, Remus Radu)
- Lecture 8: Computational Indistinguishability (Sep 22, Nick Alessi)
- Lecture 9: Indistinguishability and Pseudorandomness (Sep 27, Anthony Chang)
- Lecture 10: Pseudorandom Generators (Sep 29, Karn Seth)
- Lecture 11: Probabilistic Random Functions (Oct 4, Shentong Wang)
- Lecture 12: Missing (Oct 6, ???)
- Lecture 13: Multi-Message Security (Oct 18, Shyam Lenna)
- Lecture 14: Public Key Encryption (Oct 20, Nick Alessi)
- Lecture 15: PKE and Zero Knowledge (Oct 27, Sujay Jayakar)
- Lecture 16: Zero Knowledge Proofs - Part 1 (Nov 1, Lior Seeman)
- Lecture 17: Zero Knowledge Proofs - Part 2 (Nov 3, Remus Radu)
- Lecture 18: Zero Knowledge Proofs - Part 3 (Nov 8, Karn Seth)
- Lecture 19: Zero Knowledge Proofs - Part 4 (Nov 10, Shentong Wang)
- Lecture 20: Authentication (Nov 15, Sidharth Telang)
- Lecture 21: Authentication - Part 2 (Nov 17, Shentong Wang)
- Lecture 22: Secure Computation (Nov 22, Sujay Jayakar)

- CS 513: System Security. This course discusses security and survivability for computers and communications networks. The course will include discussions of policy issues (e.g. the national debates on cryptography policy) as well as the discussions of the technical alternatives for implementing the properties that comprise "trustworthiness" in a computing system. Mechanisms for authorization and authentication as well as cryptographic protocols will be covered.
- CS 6810: Theory of Computation This course gives an advanced treatment of theory of computation, computational-complexity theory, and other topics in computing theory.
- CS 4830: Introduction Cryptography. This course is an undergraduate introductory course to cryptography.
- CS 7832: Crypto breakfast. This course is a cryptography reading group focusing on advanced topics.