# CS 7880 - Special Topics in Cryptography, Fall 2020

### Course Description

The course will cover various advanced topics in cryptography, at the forefront of current research. One of the main themes will be *secure computation over encrypted data*, but we will explore other topics as well.
**Logistic:** Tuesdays 12- 1:40, Thursdays 2:50 - 4:30 pm

Online over Zoom.

**Prerequisites:** We will assume basic knowledge of crypto at the level of an undergrad crypto course. For example, we assume students have familiarity with one way functions, symmetric and public key encryption, reduction-based proofs of security. If you are unfamiliar with some of these topics, it may still be possible to take the course with some additional self-learning to catch up.

### Grading

Each registered student needs to prepare one lecture for the course.

Discuss with the instructor to come up with a topic and the paper(s) to cover for the lecture.
### Preliminary List of Topics

- Fully Homomorphic Encryption (FHE): Learning with Errors, Regev encryption, Gentry-Sahai-Waters cryptosystem.
- Fully Homomorphic Signatures, Attribute-Based Encryption, Multi-Key FHE
- Homomorphic Secret Sharing
- Garbled Circuits, Functional Encryption, Laconic Function Evaluation
- Obfuscation: Definitions, Negative Results, Applications, Connection to Functional Encryption, Compute-and-Compare Obfuscation, Recent iO Constructions.
- Oblivious RAM: constructions and lower bounds, Garbled RAM, Doubly Efficient PIR
- Verifiable Computations, Succinct Non-interactive arguments (SNARGs), Non-interactive zero knowledge (NIZKs)

### Lectures

** Class/Date ** | **Topic Covered** | **Resources** | **Video, Notes** |

9/15/20 | Learning with Errors (LWE), Regev Encryption | MIT Course Notes | video |

9/17/20 | Fully Homomorphic Encryption from Ground Up | Eurocrypt19 Talk | video, notes |

9/22/20 | Gentry-Sahai-Waters (GSW) FHE | MIT Couse Notes, Simons Video | video, notes |

9/24/20 | Bootstrapping, Fully Homomorphic Signatures | paper 1, paper 2 | video1,video2, notes, slides |

### Suggested Projects

### Resources

The following textbook is useful as a reference:
Simons Workshop

Introduction to Modern Cryptography by Katz and Lindell.

Other useful resources include:

Graduate Crypto Book by Dan Boneh and Victor Shoup.

Lecture Notes by Rafael Pass and Abhi Shelat.

Lecture notes by Yevgeniy Dodis

Lecture notes by Chris Peikert

Lecture notes by Boaz Barak.

Slides by Stefan Dziembowski.

Slides,Notes by Gil Segev.