Security and privacy breaches are constantly on the news. Often these breaches are due to vulnerabilities in the design and implementations of software components. In this class we will study some of the formal tools that have been developed to formally support the correctness of software with respect to security and privacy requirements. We will focus on a few security and privacy properties such as: information flow control and noninterference, provable security, and differential privacy.
The course consists of a series of lectures on different formalisms that have been developed to reason about security and privacy properties. The basic formalism we will use is the one provided by relational program logics. We will first study a deterministic logic which is useful for reasoning about information flows and noninterference. Then, we will study a probabilistic extension of this logic which supports reasoning about cryptographic security and differential privacy. We will see how different natural proofs from cryptography and differential privacy can be expressed using this formalism. We will also experiment practically with these topics on different examples by using the EasyCrypt tool, which you can find here.
The course has a significant component based on analysis of algorithms, and formal techniques. So, the following are required classes: CAS CS 237 or equivalent; CAS CS 320 or equivalent; CAS CS 330 or equivalent; or consent of instructor. Additionally, some rudimentary understanding of probability and statistics is expected.
The course has two main requirements:
The grading will be based on assignments, participation in class, and project.
The final grade will be composed as:
Projects can take different forms depending on the interest of each student but all the projects must have a research component. Some examples of what would constitute a good project are:
Date  Topic  Notes 

Tu 1/21  No Class 

Tr 1/23  Introduction to the topic + basic logic recap 
Slides Notes: Section 1.1.1 
Tu 1/28  Basics of the while language (syntax and semantics) + Basic Hoare Logic 

Tr 1/30  Basic Hoare Logic and properties 

Tu 2/4  Information flow and Noninterference 

Tr 2/6  Relational Hoare Logic 

Tu 2/11  Relational Hoare Logic 

Tr 2/13  Differential privacy  basic 

Tu 2/18  No Class  President's Day substitute Monday 

Tr 2/20  Probabilistic extension of the While language 

Tu 2/25  Approximate Probabilistic Relational Hoare Logic 

Tr 2/27  Examples of differentially private proofs using composition 

Tu 3/3  Formal Proofs for Cryptography 

Tr 3/5  Examples of cryptography formal proofs 

Tu 3/10  No Class  spring break 

Tr 3/12  No Class  spring break 

Tu 3/17  Differential Privacy  more advanced topics 

Tr 3/19  Approximate Probabilistic Coupling 

Tu 3/24  Examples of differentially private proofs using Coupling 

Tr 3/26  Examples of differentially private proofs using Coupling 

Tu 3/31  Advanced techniques for formal cryptography proofs 

Tr 4/02  More advanced examples of formal cryptography proofs 

Tu 4/07  More advanced examples of formal cryptography proofs 

Tr 4/09  More advanced examples of formal cryptography proofs 

Tu 4/14  Reasoning about accuracy of differentially private programs 

Tr 4/16  Reasoning about accuracy of differentially private programs 

Tu 4/21  Students' presentation 

Tr 4/23  Students' presentation 

Tu 04/28  Students' presentation 

Tr 04/30  Students' presentation 
