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  Introduction to EasyCrypt + Basics of the while language (syntax and semantics) + Basic Hoare Logic 
Slides EasyCrypt Manual: Chapter 1 Installing EasyCrypt Emacs Text Editor EasyCrypt example: logicexampfill.ec logicexamp.ec 
Tr 1/30  Basic Hoare Logic and properties 
Slides 
Tu 2/4  Hoare Logic  part 1 
Slides 
Tr 2/6  Hoare Logic  part 2 
Slides 
Tu 2/11  Hoare Logic and Information flow 
Slides 
Tr 2/13  Noninterference and Relational Hoare Logic 
Slides 
Tu 2/18  No Class  President's Day substitute Monday 

Tr 2/20  Noninterference and Relational Hoare Logic 
Slides 
Tu 2/25  Probabilistic While Language 
Slides 
Tr 2/27  Probabilistic Relational Reasoning 
Slides 
Tu 3/3  Formal Proofs for Cryptography 
Slides 
Tr 3/5  Formal Proofs for Cryptography 
Slides 
Tu 3/10  No Class  spring break 

Tr 3/12  No Class  spring break 

Tu 3/17  Probabilistic Relational Hoare Logic 
Slides 
Tr 3/19  Probabilistic Relational Hoare Logic 
Slides 
Tu 3/24  Approximate Probabilistic Hoare Logic 
Slides 
Tr 3/26  Approximate Probabilistic Hoare Logic 
Slides 
Tu 3/31  Approximate Probabilistic Hoare Logic 
Slides 
Tr 4/02  Differential privacy 
Slides 
Tu 4/07  Differential Privacy 
Slides 
Tr 4/09  Examples of differentially private proofs 
Slides 
Tu 4/14  Formal Proofs for Cryptography (Cont.) 
Slides 
Tr 4/16  Formal Proofs for Cryptography (Cont.) 
Slides 
Tu 4/21  Formal Proofs for Cryptography (Cont.) 
Slides 
Tr 4/23  Examples of differentially private proofs using Coupling 
Slides 
Tu 04/28  Students' presentations 

Tr 04/30  Students' presentations 

Date  Topic  Notes 

Week 1  EasyCrypt's Ambient Logic 
Slides 
Week 2  EasyCrypt's Hoare Logic 
Slides 
Week 3  EasyCrypt's Hoare Logic 
Questions and answers relating to Assignment 1 
Week 4  Noninterference and EasyCrypt's Relational Hoare Logic 
EasyCrypt Manual: Section 3.4 
Week 5  Noninterference and EasyCrypt's Relational Hoare Logic 
Questions and answers relating to Assignment 2 
Week 6  EasyCrypt's pRHL (probabilistic Relational Hoare
Logic) 
EasyCrypt Manual: Section 3.4 
Week 7  Working with Procedure Calls and Adversaries 
EasyCrypt Manual: Sections 2.4 and 3.4 
Week 8  Pseudorandom Generators (PRGs) 
EasyCrypt Manual: Sections 2.4 and 3.4 
Week 9  More probabilistic Hoare Logic (pHL) 
EasyCrypt Manual: Section 3.4 
Week 10  Differential Privacy 

Week 11  Differentially Private Sums 

Assignment  Topic  Files 

Assignment 0  EasyCrypt's Ambient Logic 

Assignment 1  EasyCrypt's Hoare Logic 

Assignment 2  Noninterference and EasyCrypt's Relational Hoare Logic 

Assignment 3  Probabilistic Noninterference and EasyCrypt's pRHL 
