Fully Homomorphic Encryption, 10 Years Later - Definitions and Open Problems

Explore a comprehensive lecture on Fully Homomorphic Encryption (FHE) and its evolution over the past decade. Delve into key definitions, open problems, and the latest developments in this cutting-edge field of cryptography. Examine the FHE timeline, lattice-based encryption, and the Gentry bootstrapping technique. Analyze the differences between traditional and fully composable homomorphic encryption schemes. Investigate the relationship between FHE, circular security, and CFHE. Gain insights into approximate encryption schemes and their potential applications in modern cryptography.

Fully Homomorphic Encryption 10 years later definitions and open problems
Fully Homomorphic Encryption Encryption: used to protect data at rest or in transit
FHE Timeline
Lattice Cryptography at Simons
Today • Fully Homomorphic Encryption
Lattice-based Encryption
Additive Homomorphism
Gentry bootstrapping Technique to reduce the amount of error in a lattice- based ciphertext: - Assume (Gen, Enc,Dec, Eval) supports the evaluation of
Composition • Perform two computations in sequence
Correctness of Encryption
Fully Composable HE
Comparing the two definitions
Bootstrapping revisited Gentry's bootstrapping theorem can be formulated in terms of the new CFHE definition • Theorem: FHE+circular security = CFHE - (Gen, Enc,Dec, Eval): FHE supporting the evaluation of
CFHE without circular security?
Approximate Encryption Scheme