Tutorial on Homomorphic Encryption

Dive into the second part of a comprehensive tutorial on homomorphic encryption presented by Shai Halevi at Crypto 2011 in Santa Barbara, CA. Explore advanced concepts such as Learning with Errors (LWE), the BV'11b construction, dimension reduction techniques, and the transition from Somewhat Homomorphic Encryption (SWHE) to Fully Homomorphic Encryption (FHE). Examine key topics including modulus switching, the BGV'11 leveled FHE, and current status of homomorphic encryption constructions. Gain insights into optimization techniques and variants in this 58-minute in-depth exploration of cutting-edge cryptographic methods.

Intro
Learning with Errors (LWE) Regev 2005 Hard to solve linear equations with noise
The (BV'11b) Construction
Homomorphism
Multiplying More than once?
Reducing the Dimension
An Attempt that Almost Works
Dimension Reduction (Key-Switching)
Security
The (BV'11b) "Leveled SWHE"
From SWHE to FHE
Modulus Switching - Main Lemma
How Does Modulus-Switching Help?
Putting It All Together
The (BGV'11) Leveled FHE
Variants and Optimizations
Current Status of HE constructions