Homomorphic Encryption in the SPDZ Protocol for MPC

Explore the intricacies of homomorphic encryption in the SPDZ protocol for secure multi-party computation in this 54-minute lecture by Peter Scholl from Aarhus University. Delve into the SPDZ setting, preprocessing model, and additive secret sharing with MACs. Learn about the online phase for securely computing arithmetic circuits and the multiplication of secret-shared values. Examine two main approaches to triple generation, focusing on threshold homomorphic encryption and its distributed decryption protocol. Understand the passive triple generation process and how active security is achieved in two steps. Investigate zero-knowledge proofs in SPDZ, including proving knowledge of short preimages. Discover variations on the basic SPDZ protocol and explore potential areas for improvement, such as enhancing zero-knowledge proofs and noise drowning in distributed decryption. Consider alternative approaches like non-interactive triple generation. Gain valuable insights into the latest developments in lattice-based cryptography and its practical applications in secure multi-party computation.

Intro
Secure Multi-Party Computation
The SPDZ setting
MPC in the preprocessing model
Additive secret sharing with MACS
Reconstructed shared values
SPDZ online phase : securely computing arithmetic circuits
Multiplication of secret-shared values
Triple generation: two main approaches
Threshold homomorphic encryption
Instantiating threshold homomorphic
Distributed decryption protocol
Passive triple generation: basic protocol
Active security in two steps
Zero knowledge proofs in SPDZ
Proving knowledge of short preimages
Variations on the basic SPDZ protocol
Where can we hope to do better?
Improving zero knowledge proofs
A step further removing zero knowledge proofs?
Noise drowning in distributed decryption
Alternative approach: non-interactive triploma generation
Conclusion