Modern computational environments are highly distributed. Users’ data is collected, combined, and stored across multiple entities, raising significant privacy and integrity concerns. These scenarios are naturally addressed by the powerful framework of Secure Multiparty Computation (MPC). This framework enables a group of parties to jointly compute a function without revealing any additional information about their private inputs. In its most general form, MPC can be viewed as a "complete" cryptographic primitive that subsumes many specific cryptographic tasks, such as zero-knowledge proofs, electronic voting, and even foundational primitives like encryption and digital signatures.
This project primarily focuses on Information-Theoretic (IT) MPC that provides security against computationally unbounded adversaries. The IT setting has several important useful features: It does not rely on the validity of unproven computational intractability assumptions, it is robust to the exact computational model of the adversary (e.g. classical vs. quantum), and it offers everlasting security against adversaries that gather data during the protocol's execution and later invest huge amounts of resources in order to extract information from the collected data. Importantly, for many cryptographic problems, the best existing solutions are based on an information-theoretic core construction that is enhanced with a simple cryptographic tool. Taking a broader view, many central problems that deal with ``fault-tolerance'' from areas like coding theory, distributed computing and computational complexity can be formulated as concrete instances of IT-MPC problems.
Despite its foundational importance, our understanding of IT-MPC remains limited. This project addresses this fundamental question through three complementary, yet independently motivated, research directions: First, we aim to improve the complexity of general secret sharing schemes. Such schemes can be viewed as the information-theoretic analog of encryption schemes, and accordingly they have numerous applications for distributed storage of static data. Our second objective is to improve the efficiency and extend the applicability of Secure Non-Interactive Reductions -- a powerful tool that allows to securely represent a complicated computational task by a simpler one. Finally, our third objective is to expand our theoretical understanding of constant-round information-theoretic protocols, optimize their round complexity, and study their computational complexity. The project bridges across different regions of computer science such as coding theory, cryptography, computational complexity, and communication complexity. It is expected to impact central problems in cryptography, while enriching the general landscape of theoretical computer science.
