Multi Identity and Multi Key Leveled FHE from Learning with Errors

Explore a comprehensive lecture on Multi Identity and Multi Key Leveled Fully Homomorphic Encryption (FHE) based on the Learning with Errors problem. Delve into the Gentry Sahai and Waters (GSW) Identity-Based Fully Homomorphic Encryption (IBFHE) scheme, examining its homomorphic operations and properties. Gain insights into a high-level sketch of a 2-Identity IBFHE and review basic operations and their properties. Investigate the GSW compiler for Identity-Based Encryption (IBE) in the single identity setting, and learn about a compiler for Multi-Identity IBFHE. Understand the intuition behind the abstract compiler scheme and explore concrete constructions of masking systems, including a relaxed version and support for all identities. This 28-minute talk provides a thorough examination of advanced cryptographic concepts and their applications in secure multi-party computation.

Intro
Gentry Sahai and Waters (GSW) IBFHE
GSW Homomorphic Operations
High-Level Sketch of a 2-Identity IBFHE
Review of Basic Operations
Properties of Basic Operations
GSW Compiler for IBE in the Single Identity Setting
A Compiler for Multi-Identity IBFHE Intuition
Our Abstract Compiler: Scheme
Concrete Construction of Masking System: Relaxed version
Concrete Construction of Masking System: Support for all identities