The first half of the project focused mainly on the first two aforementioned objectives, namely achieving integrity and authenticity of computation performed on untrusted machines. Our work also addressed the last objective by generating, when appropriate, implementations and experiments to assess the costs of our solutions.
With respect to the problem of integrity of computation, we mainly focused on two cryptographic primitives: zero-knowledge succinct non-interactive arguments (aka zkSNARKs) and vector commitments. Both of these primitives are a form of succinct proof systems that enable an untrusted party to prove the correctness of data and computation by providing short and easy to verify proofs. Our most significant advances in these areas have been on expanding our modular design approach and developing techniques for specialize computations in order to build more efficient zkSNARKs, and on studying the foundations of vector commitments.
More specifically, our most significant results in this period are:
- the design of a new framework and techniques to build universal and updatable zkSNARKs with increased efficiency (published at Asiacrypt 2021);
- the proposal of new zkSNARKs for the problem of proving membership of a batch of elements in a large set (published at ACM CCS 2022);
- the design of a new modular framework to construct efficient zkSNARKs for sequential computations with applications to machine learning and image processing (published at ACM CCS 2023);
- the design of a new methodology for the design and analysis of simulation extractable zkSNARKs (published at TCC 2023);
- the construction of proofs of sequential work (published at Eurocrypt 2023);
- the study of vector commitments by proving that a significant class of these schemes is impossible to realize (published at TCC 2022);
- the realization (based on techniques from algebraic vector commitments) of the first registration-based encryption scheme with practical efficiency (published at ACM CCS 2023).
With respect to the problem of authenticity of computation, we focused on homomorphic signatures. Our most significant results in this period are:
- the introduction and realization of a new class of homomorphic signature schemes with increased expressivity and efficiency (published at ACM CCS 2022);
- the proposal of a new approach to build homomorphic signature schemes via functional commitments, and realizations of this primitive (published at Asiacrypt 2022);
- the construction of the first functional commitment schemes that support the evaluation of any circuit of unbounded depth and, given the previous result, the analogous implication for homomorphic signatures (published at TCC 2023);
- a new methodology to build multi-key homomorphic signatures from single-key ones (published in the Theoretical Computer Science journal).
