Fast Proofs for Verifying Computations

Introduction

A proof-system is a protocol that enables a powerful prover to convince a weaker verifier of the validity of a computational statement. Proof-systems have been central to the theory of computing since its inception. Some of the most important results, concepts, and open problems in this field revolve around notions of efficient proof-systems.

Background

In recent years, due to the surging need for large-scale computation coupled with advances such as cloud computing and blockchains, these computational proof-systems, which originated in the theory literature, are now being implemented and deployed also in practice. However, their widespread deployment is impeded by key bottlenecks on the theory side.

Project Goals

The goal of the FASTPROOF project is to identify, study, and mainly to resolve these bottlenecks:

1. Minimizing Interaction
   Minimizing the amount of back-and-forth interaction between the prover and the verifier, aiming at proofs that are non-interactive. Non-interactive proofs offer game-changing advantages: in contrast to their interactive counterparts, such proofs can simply be posted online and shared between different clients.

2. Reducing Proving Time
   In current proof-systems, the time that it takes for a prover to prove the correctness of a computation is significantly longer than the time that it takes to simply perform the computation. The second major challenge is to reduce the complexity of proving correctness to be linear in the computation time.

3. Optimizing Space Complexity
   Making the memory, or space complexity, needed to generate the proof be proportional to the space requirements of the computation, in contrast to most protocols in the literature in which the space required to prove correctness is proportional to the running time of the computation.

Conclusion

The goal of the FASTPROOF project is to resolve these key challenges while relying on well-founded cryptographic assumptions. While the focus of this project is theoretical, we believe that it stands to have an important impact also on the future development of practical proof-systems.