September 2022 Summaries

Fully Homomorphic Encryption (FHE) enables computations on encrypted data, and its adoption is growing across public and private sectors due to recent advancements. A paper presented at CHES 2022 explores TFHE, a torus-based FHE scheme, and its implementation on a discretized torus, emphasizing programmable bootstrapping techniques. The study categorizes FHE schemes into two families based on plaintext encoding positions and highlights the use of the discretized torus for LWE-based schemes, which supports various message formats and clarifies the absence of native ciphertext multiplication. The paper suggests using a scheme like TGSW for integer-based plaintexts and stresses the importance of efficient external product operations to manage noise propagation. Additionally, it provides a detailed explanation of bootstrapping, referencing Gentry’s 'recryption' technique, and identifies the rounding operation during LWE decryption as a potential area for optimization to enhance bootstrapping performance, ultimately facilitating functional circuits through programmable bootstrapping.

Zama's research blog introduces their latest paper on Spooky Encryption, a concept initially proposed by Dodis et al., which allows computation on encrypted data to yield results in the clear, contrasting with traditional homomorphic encryption that provides encrypted results. The paper, co-authored with researchers from Aarhus University and KU Leuven, simplifies the concept by likening it to a Scooby-Doo scenario where a secret setup explains the spooky behavior. This innovative approach facilitates the creation of Homomorphic Secret Sharing (HSS), a new cryptographic concept with potential applications, especially in enabling seamless transitions from Fully Homomorphic Encryption (FHE) to Multi-Party Computation applications. While further research is needed to commercialize this technology, it highlights the expanding possibilities of FHE technology being developed by Zama and its collaborators.