WHAT IS A COLLABORATIVE ZERO-KNOWLEDGE PROOF?

ZKON Network
8 min readFeb 20, 2024

Discover the cutting-edge technology of Collaborative Zero-Knowledge Proofs (co-ZKPs) in Web3. In this article, we will introduce you to these advanced cryptographic constructions. This is an evolution of traditional Zero-Knowledge Proofs (ZKPs), which have been instrumental in enhancing privacy and security in the digital domain. A key player in this evolution is zk-SNARKs. These publicly verifiable proofs allow a prover to demonstrate possession of secret data (a witness) that satisfies a certain public NP relation, without revealing any information about the secret itself.

One of the core strengths of zk-SNARKs lies in their generality and efficiency. They are capable of proving any relation that can be expressed as a bounded size arithmetic circuit. Moreover, they offer the advantage of easy verification, where the proof size and verification time are significantly smaller than the amount of secret data involved, typically requiring only kilobytes of data and tens of milliseconds to verify. However, it’s crucial to acknowledge the limitations of zk-SNARKs as well. Generating these proofs is computationally expensive, often thousands of times slower than directly checking the relation. Also, the traditional approach to zk-SNARKs requires the secret data to be held by a single party, which restricts their application in scenarios involving distributed secret data.

This development not only boosts privacy and security but also fosters a new level of trust and collaboration in digital transactions, leading to the emergence of collaborative zk-SNARKs. Read on to understand how co-ZKPs are revolutionizing privacy and security.

Origins & Evolution of ZKPs

The foundation of Zero-Knowledge Proofs (ZKPs) was established in the 1980s by Shafi Goldwasser, Silvio Micali, and Charles Rackoff. Their pioneering work introduced a way for a prover to convincingly demonstrate the truth of a statement to a verifier without disclosing any additional information, a concept that has become a cornerstone in the field of cryptography. This groundbreaking idea laid the groundwork for subsequent innovations, including the development of zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge), which are a specific and highly efficient form of ZKP. Building on the traditional ZKP concept, zk-SNARKs offer a more efficient solution. Explore the journey from ZKPs to zk-SNARKs below.

zk-SNARKs, in particular, represent a significant advancement in the realm of cryptographic proofs. These publicly verifiable proofs enable a prover to demonstrate possession of secret data (a witness) that satisfies a certain public NP relation, without revealing anything about the secret data other than its validity. The key strengths of zk-SNARKs are their generality and the ease of verification. They can prove any relation expressible as a bounded size arithmetic circuit and are easily verified, with proof size and verification time being sublinear in the amount of secret data.

Over time, collaborative ZKPs have evolved to address complex challenges in data security and privacy. This collaborative approach is vital in environments where confidentiality is paramount, even among the participants in the process. The ability to verify statements without sharing underlying data is a major advancement, demonstrating the maturity and adaptability of ZKPs in today’s technological landscape.

The Power of Collaboration in ZKPs

Collaboration in Zero-Knowledge Proofs (ZKPs) enables multiple stakeholders to collectively validate a claim without compromising their individual data. This capability is crucial in scenarios where data privacy must be maintained, even among participants. Collaborative zk-SNARKs are a key innovation in this regard, transforming the traditional model of zk-SNARKs to support distributed secrets among multiple parties. Learn how collaboration enhances the power of ZKPs.

In collaborative zk-SNARKs, the secret data, denoted as w = (w1, …, wN), is distributed among N parties, with each party i holding a piece wi. The proof generation process in this model ensures that nothing new about w is revealed to any coalition of parties other than the validity of w. This is achieved by starting with a standard single-prover zk-SNARK and running its proof generation algorithm as a secure multi-party computation (MPC) among the N provers. The MPC framework allows these parties to compute a public function over their secret inputs, revealing only the output and nothing else about each other’s inputs. This method ensures that the privacy of each participant’s data is maintained throughout the process.

ZKON, by applying this technology, becomes a potential key player across all industries. Collaborative ZKPs offer an effective solution for maintaining privacy and security, leveraging these features to facilitate safer and more private interactions, thereby positioning ZKON as a benchmark in modern cryptography.

Key Features & Benefits of Collaborative ZKPs

co-ZKPs representation

Collaborative Zero-Knowledge Proofs (co-ZKPs) are distinguished by their efficiency and ability to ensure the security and privacy of participants. These proofs are uniquely designed to preserve the confidentiality of information, protecting it not only from external parties but also among the participants themselves, without compromising on performance. The robustness of these proofs is rooted in the cryptographic strength of the underlying Zero-Knowledge Proof (ZKP) system, significantly reducing computational and communication burdens and making them practical for real-world applications.

  • Privacy: Collaborative ZKPs protect each participant’s information, keeping it confidential even among those involved in the process. This is achieved by ensuring that the proof generation process does not reveal any new information about the secret data to any coalition of parties, other than the validity of the data.
  • Security: These proofs provide robust cryptographic guarantees, based on the security of the underlying ZKP system. Collaborative ZKPs are constructed by lifting conventional zk-SNARKs into secure protocols among multiple provers to jointly produce a single proof over a distributed witness. This approach ensures that security against a malicious minority of provers can be achieved with approximately the same runtime as a single prover, and security against nearly all malicious provers requires only a 2x slowdown.
  • Efficiency: Designed to minimize computational and communication burdens, Collaborative ZKPs facilitate real-world applications. Techniques like parallelism and multi-threading are applied to enhance performance. In most cases, parallelism accelerates Fourier transforms and multi-scalar multiplications, operations that are performed locally within our protocols, thus maintaining similar performance benefits as seen in single-prover setups.

These features suggest the importance of MPC (Multi-Party Computation) ‘friendliness’ as a new criterion for evaluating zk-SNARKs, highlighting the need for optimizations that cater to the collaborative nature of these proofs.

Applications and Use Cases for co-ZKPs

co-ZKPs have a wide range of applications, particularly due to their ability to verify claims without disclosing sensitive information, making them extremely useful in domains like financial transactions, voting systems, and supply chain transparency:

  • In Financial Transactions: They enhance privacy and security through multi-party verification, allowing for secure, private transactions where all involved parties can verify the truth of a claim without revealing the underlying data.
  • In Voting Systems: co-ZKPs can guarantee the integrity of the voting process while preserving voter anonymity. This is crucial for maintaining the democratic process’s credibility by ensuring that votes are both counted correctly and remain confidential.
  • In Supply Chain Management: They enable the verification of product authenticity and compliance without exposing proprietary information. This fosters trust between different links in the supply chain, as parties can verify certain properties (like origin, quality, or compliance with standards) without revealing sensitive business information.

A particularly insightful real-world application is in the domain of Healthcare Statistics. Here, collaborative proofs offer a clean solution for handling sensitive healthcare data. For instance, healthcare providers can publish Merkle commitments to their provided services. Regulators can then request aggregate statistics over these services without revealing individual patient data. Providers compute the aggregate statistic via an MPC and publish a collaborative proof that the claimed result is consistent with all of their local commitments. This approach protects patient privacy while ensuring the integrity of the aggregate data. Such a system can be extended to other areas requiring aggregate statistics computation over sensitive data, like criminal justice statistics.

Here are some practical examples of ZKP applications possible using ZKON technology:

The Future of Collaborative ZKPs

Looking towards the future, collaborative ZKPs have the potential to revolutionize the way we manage and protect information in a digital world. As our reliance on technology and digital transactions increases, the need for advanced cryptographic solutions like co-ZKPs becomes even more critical.

Collaborative ZKPs, particularly collaborative zk-SNARKs, have shown immense promise in experiments and implementations. They have been successfully adapted into secure protocols among multiple provers to jointly produce a single proof over a distributed witness. This process involves optimizing the proof generation algorithm in pairing-based zk-SNARKs using algebraic techniques for multiparty computation (MPC). One of the remarkable findings in the implementation of collaborative zk-SNARKs is the achievement of security against a malicious minority of provers with approximately the same runtime as a single prover. Even more impressive is that securing against nearly all (N-1) malicious provers requires only a 2x slowdown in performance. This level of efficiency is unusual, as most computations significantly slow down when securely distributed. The ability of collaborative ZKPs to maintain efficiency while offering robust security makes them well-suited for real-world applications and scalable for widespread use.

These technologies could be critical for creating more secure and private systems. Their uses range from online banking and digital identity verification to extensive institutional applications in areas like government, healthcare, and education. They are also relevant in emerging fields such as decentralized energy management and smart city infrastructure, particularly important given the rise in sophisticated cyber threats. The adaptability and efficiency of co-ZKPs in managing distributed secrets and providing verifiable proofs, all while maintaining privacy, make them an essential tool in our increasingly digital society.

Conclusion

Collaborative Zero-Knowledge Proofs represent a remarkable ongoing innovation in the field of cryptography and information security. They skillfully maintain a balance between privacy and collaboration. This paves the way for secure and efficient applications, not only in current Web3 paradigms, but also in traditional Web2 or Web2.5 sectors. This balance is especially critical in all industries as we progress towards a more digitized future. The demand for privacy, security, and collaborative functionality in digital interactions is continually growing.

As we continue to develop and refine these technologies, it becomes increasingly vital to understand and adopt them. Their applications in all fields, ranging from finance and healthcare to government systems, are a testament to their versatility and effectiveness. The efficiency of collaborative ZKPs, particularly collaborative zk-SNARKs, has been demonstrated to be practical for real-world applications. Most applications that can tolerate the cost of a single-prover proof should also be able to manage the cost of a collaborative proof, making them a feasible and attractive option for many current and future digital systems.

As the digital landscape evolves, so does ZKON approach to security and privacy. Collaborative ZKPs are at the forefront of this evolution, offering a blend of privacy, efficiency, and collaboration that is well-suited to the demands of our increasingly interconnected world.

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ZKON Network

ZKON enables multi-party creation of zk-SNARK proofs over distributed secrets, ensuring server integrity and decentralized MPC signing.