Through the course of the project duration, the ERC funding has enabled the Project HSS team to make tremendous advances in the domain of cryptographic secure computation research, starting from the ground up. Significant steps forward were made across the three core focus directions, moving the field of privacy-preserving computation from high-overhead theoretical constructs toward computationally efficient, scalable reality.
1. Foundations of Homomorphic Secret Sharing (HSS) and Pseudorandom Correlation Generation
The project established new benchmarks for Homomorphic Secret Sharing (HSS) and Function Secret Sharing (FSS), technologies that allow computation to be performed on "shredded" data without ever reassembling the original input. We provided new, faster solutions and expanded the reach of HSS/FSS to efficiently support more complex operations, such as fixed-point arithmetic and branching programs, essential for secure financial and scientific computing. We developed highly optimized constructions of Pseudorandom Correlation Generators (PCG) for generating the "cryptographic raw material" needed for secure protocols, allowing to replace expensive network bandwidth in existing secure computation solutions with cheap local computation. We additionally introduced and demonstrated first feasibility of the strengthened Pseudorandom Correlation Functions (PCF), opening a new flourishing line of research.
2. Succinct and Maliciously Secure Computation
The research focused on making secure computation both highly communication efficient and resilient against active, malicious adversaries. We designed new frameworks for breaking the "circuit-size barrier," enabling parties to perform secure computations on data with communication costs significantly lower than the size of the circuit being computed. Advances included new protocols for specialized tasks like secure sorting and heavy hitters. We introduced a new path for achieving security against strong malicious adversaries with low overhead, via Zero Knowledge Proofs on Distributed Data and "arithmetic sketching." These allow participants to verify that a computation was performed honestly without compromising the underlying secrets, even if some parties act maliciously. We extended protocols to modern network challenges, including topology-hiding communication and straggler-resilient computation, ensuring security remains robust even in unstable or secret network environments.
3. Beyond Secure Computation
The project explored the deep mathematical intersections between cryptography and other fields within theoretical computer science.
We established a powerful synergy between coding theory and pseudorandom correlation generator (PCG) design, leveraging error-correcting code structures and hardness of decoding to build highly optimized PCG constructions. We explored intersections of cryptography with complexity theory, including new HSS-inspired candidate constructions of cryptographic objects in low complexity classes, and mapping out fundamental limits of weak variants of program obfuscation through new connections with learning theory. And, we obtained new results in algorithmic locality-sensitive hashing via HSS construction techniques.
Dissemination of project advancements has taken place via team presentations and participation in both local and international conferences, workshops, visits, and other events. This includes several events of the International Association for Cryptologic Research (IACR), such as annual flagship CRYPTO and EUROCRYPT conferences, the IACR Theory of Cryptography (TCC) and Asiacrypt Conferences; security conference venues such as ACM Conference on Computer and Communications Security (CCS) and IEEE Symposium on Security and Privacy; and broader theory of computer science conferences such as IEEE Symposium on Foundations of Computer Science (FOCS) and Innovations in Theoretical Computer Science (ITCS). Team members gave prestigious invited presentations at 12 workshops, colloquia, and cryptography school events, as well as several invited presentations in regular university seminars.
