Periodic Reporting for period 1 - SPP (Secrecy-Preserving Proofs with Solid Foundations)
Reporting period: 2022-10-01 to 2025-03-31
The traditional notion of a proof offers no secrecy — proving the validity of a blockchain transaction would reveal its details, proving qualification for a loan would reveal private financial information, and proving that a system has been hacked could reveal sensitive details about the system. Remarkably,
using cryptography, this problem can be solved. Secrecy-preserving proofs are a class of protocols allowing to prove assertions about secret information, without actually revealing the information. The most prominent notion of such a proof is that of zero knowledge proofs, which reveal no information at all.
Recent years have seen zero knowledge proofs transition from theory to practice. With major investment from industry and governments, they are now being deployed and standardized. Driven by large-scale applications such as blockchains, deployment efforts have put special stress on efficiency, often compromising on the core principle of rigorous security analysis based on solid hardness assumptions. At the same time, the nearing possibility of new threats such as quantum attacks, only requires stronger security.
The goal of the project is secrecy-preserving proofs that meet present day challenges, without compromising on the gold standard of cryptographic security. We envision a world where secrecy-preserving proofs are reliable enough to be used in high-stake applications, and efficient enough to be
used in large-scale applications. The project applies foundational theoretical research to identify barriers and challenges and to develop new techniques to overcome them toward achieving this ultimate goal.
Within this context, the project focuses on three main objectives:
- Constructions of succinct proofs with fast verification.
- Superior constructions of non-interactive proofs in terms of security guarantees, hardness assumptions, and efficiency.
- Security against quantum attackers.
using cryptography, this problem can be solved. Secrecy-preserving proofs are a class of protocols allowing to prove assertions about secret information, without actually revealing the information. The most prominent notion of such a proof is that of zero knowledge proofs, which reveal no information at all.
Recent years have seen zero knowledge proofs transition from theory to practice. With major investment from industry and governments, they are now being deployed and standardized. Driven by large-scale applications such as blockchains, deployment efforts have put special stress on efficiency, often compromising on the core principle of rigorous security analysis based on solid hardness assumptions. At the same time, the nearing possibility of new threats such as quantum attacks, only requires stronger security.
The goal of the project is secrecy-preserving proofs that meet present day challenges, without compromising on the gold standard of cryptographic security. We envision a world where secrecy-preserving proofs are reliable enough to be used in high-stake applications, and efficient enough to be
used in large-scale applications. The project applies foundational theoretical research to identify barriers and challenges and to develop new techniques to overcome them toward achieving this ultimate goal.
Within this context, the project focuses on three main objectives:
- Constructions of succinct proofs with fast verification.
- Superior constructions of non-interactive proofs in terms of security guarantees, hardness assumptions, and efficiency.
- Security against quantum attackers.
During the course of the project so far, progress was made on our project objectives. We studied new methods and models for constructing succinct arguments, which have resulted in new improved constructions as well as implications beyond cryptography to complexity theory. We advanced the state of the art in the construction of non-interactive secrecy-preserving proofs and introduced new routes that can be applied in future constructions. We made progress on the study of secrecy-preserving proofs secure against quantum attackers and their applications.
Our achievements include:
- New models of probabilistic proof systems that take simplicity and efficiency to the limit, and are yet expressive enough for general computations. This has brought about constructions of cryptographic proof systems with extremely short proofs and and extremely simple verification process. In addition, our proof systems have led to new hardness results for approximation algorithms, showing that natural and well studied problem cannot even be approximately solved in exponential under widely believed complexity assumptions.
- We established strong connections between succinct proofs and secrecy-preserving proofs. We provide the first formal barrier on the ability to construct succinct proofs with computational assumptions weaker than collision-resistant hash functions (under which constant-round succinct computationally-sound proofs are known). This has also resulted in new insights in complexity, specifically on the class of languages that have statistical witness-indistinguishable proofs.
- We developed a general hardness amplification techniques for non-interactive secrecy-preserving proofs, turning systems with weak security guarantees into ones with strong security. This approach enables proof combiners to enhance robustness of existing constructions and may also simplify future constructions.
Our achievements include:
- New models of probabilistic proof systems that take simplicity and efficiency to the limit, and are yet expressive enough for general computations. This has brought about constructions of cryptographic proof systems with extremely short proofs and and extremely simple verification process. In addition, our proof systems have led to new hardness results for approximation algorithms, showing that natural and well studied problem cannot even be approximately solved in exponential under widely believed complexity assumptions.
- We established strong connections between succinct proofs and secrecy-preserving proofs. We provide the first formal barrier on the ability to construct succinct proofs with computational assumptions weaker than collision-resistant hash functions (under which constant-round succinct computationally-sound proofs are known). This has also resulted in new insights in complexity, specifically on the class of languages that have statistical witness-indistinguishable proofs.
- We developed a general hardness amplification techniques for non-interactive secrecy-preserving proofs, turning systems with weak security guarantees into ones with strong security. This approach enables proof combiners to enhance robustness of existing constructions and may also simplify future constructions.
The focus of the project is on theoretical foundations.