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. Read more