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Intro

Fully Homomorphic Encryption

Noise Grows with Computation

Need to Clean Noise

Bootstrapping Framework [Gentry]

Current State of the Art

Limitations and Tradeoffs

Fundamental Question

Recap of (R)LWE and RGSW

Recap of FHEW-like Bootstrapping

Technical Barriers for SIMD

New Mathematical Framework

Final Solution - Reuse Rings

Instantiations of Tensor Fields/Rings

Summary

Homomorphic Comp of the Framework

Overall Computation Structure

Application to FHEW-like Algorithms

Error Growth for Batch FHEW

Parameters of the Rings

Results and Comparison

High Level Question

(Recursive) Nussbaumer Transform [MS18]

DFT-based Polynomial Multiplications [MS18]

Optimization by Recursion

FHEW with Nussbaumer Transform

Description:

Explore a comprehensive session from Eurocrypt 2023 focused on Fully Homomorphic Encryption (FHE). Delve into the current state of the art, limitations, and tradeoffs of FHE technology. Examine the bootstrapping framework, technical barriers for SIMD, and a new mathematical framework for addressing challenges. Learn about instantiations of tensor fields/rings, homomorphic computation structures, and applications to FHEW-like algorithms. Investigate error growth in batch FHEW, parameter selection for rings, and comparative results. Discover optimizations through recursive Nussbaumer transforms and DFT-based polynomial multiplications. Gain insights into cutting-edge research and advancements in the field of fully homomorphic encryption.

Fully Homomorphic Encryption: Advanced Techniques and Optimizations - Session 2

TheIACR

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#Computer Science #Cryptography #Fully Homomorphic Encryption #High Performance Computing #Parallel Computing #SIMD