Zero-Knowledge Proofs (ZKPs) are cryptographic tools that have been impacting data privacy within blockchain.

At its core, blockchain embraces transparency as one of its key principles; however, there is a subtle balance required between transparency and confidentiality. ZKPs emerge as a crucial tool in achieving this equilibrium, allowing participants to verify ownership or compliance without exposing unnecessary details.

Among the most significant ZKP protocols are zk-SNARKs, zk-STARKs, and Bulletproofs. This article will explore the structure, use cases, and security considerations of these three ZKP types, highlighting how each can power applications in finance, privacy, and security with their unique features.

Understanding Zero-Knowledge Proofs

ZKPs enable one party (the prover) to convince another (the verifier) that a statement is true without disclosing any unnecessary information. Since their introduction in the 1980s, ZKPs have evolved significantly and now support many of the applications working on privacy-preserving solutions.

They adhere to three core principles:

• Completeness: If the statement is true, an honest prover can convince the verifier.
• Soundness: If the statement is false, a cheating prover cannot deceive an honest verifier.
• Zero-Knowledge: The verifier learns nothing beyond the statement’s truthfulness.

In blockchain, ZKPs help increase transaction efficiency by offloading proofs to layer-2 networks, allowing blockchains to remain secure and scalable without compromising user privacy. Some examples of protocols that use ZKPs are Immutable X, dYdX and Polygon.

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zk-SNARKs

zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge) are widely used in privacy-focused applications like Zcash and Ethereum-based zk-rollups. They enable secure, non-interactive proofs but require a “trusted setup” to generate initial public parameters (Common Reference String or CRS), which, if compromised, could lead to security risks.

How zk-SNARKs Work

SNARKs use elliptic curve cryptography to generate compact proofs where a single verifier can validate information without multiple rounds of back-and-forth communication. This makes SNARKs ideal for applications requiring rapid, high-frequency transactions. However, the reliance on elliptic curves adds a layer of vulnerabilities to them.

Pros of zk-SNARKs:

• Small Proof Size: Compact proofs reduce bandwidth consumption.
• Fast Verification: Ideal for high-speed environments.
• Versatile: Efficiently supports a wide range of cryptographic applications.

Cons of zk-SNARKs:

• Trusted Setup Requirement: A vulnerable setup can compromise security.
• Not Post-Quantum Secure: zk-SNARKs are not resistant to quantum attacks.

zk-STARKs

zk-STARKs (Zero-Knowledge Scalable Transparent Arguments of Knowledge) are another type of proof that addresses some SNARKs limitations by adding improvements on  quantum resistance and eliminating the need for a trusted setup. STARKs leverage hash functions to achieve scalability and transparency, making them more suitable for large-scale computations, particularly in solutions like StarkNet’s L2 rollup.

How zk-STARKs Work

STARKs rely on polynomial commitments and hash functions rather than elliptic curves, meaning that their structure enables them to handle larger computations securely while providing robustness against quantum threats. However, STARK proofs are generally larger, which can affect storage and bandwidth requirements.

Pros of zk-STARKs:

• No Trusted Setup: Improved transparency and reduced setup risks.
• Post-Quantum Security: Resilient against quantum computing attacks.
• Scalable for Complex Calculations: Suitable for data-intensive applications.

Cons of zk-STARKs:

• Larger Proof Size: Potentially increases bandwidth usage.
• Higher Computational Load: Proof generation can be resource-intensive.

Bulletproofs

Bulletproofs are non-interactive ZKPs without trusted setups that were initially developed for efficient range proofs in confidential transactions. Used by privacy-focused blockchains like Monero, Bulletproofs enhance blockchain privacy by enabling zero-knowledge validation of transaction amounts.

How Bulletproofs Work

Bulletproofs rely on the discrete logarithm problem and the Fiat-Shamir heuristic, which converts interactive proofs into a non-interactive format using digital signatures. These proofs use Pedersen commitments to confirm values within specific ranges, maintaining privacy by preventing the disclosure of transaction amounts.

Pros of Bulletproofs:

• No Trusted Setup: Reduced risk compared to protocols requiring CRS.
• Small Proofs: Bulletproofs are compact, saving storage and transaction fees.
• Efficiency in Confidential Transactions: Bulletproofs enable Monero’s Confidential Transactions, reducing data size and costs by up to 80%​.

Cons of Bulletproofs:

• Longer Verification Time: Compared to SNARKs, Bulletproofs take longer to verify.
• Range Limitations: Bulletproofs are best suited for range proofs, limiting their broader use cases.

Practical Use Cases

Zero-knowledge proofs have become essential tools across various industries, with an increasing number of applications implementing their different types, such as:

Confidential Transactions: SNARKs, STARKs, and Bulletproofs all enhance privacy in financial transactions by concealing transaction data from public view. For instance, SNARKs power Zcash's shielded transactions, while Bulletproofs enable Monero’s confidential transfers, obscuring transaction amounts without trusted setups​.

Identity Verification: STARKs are ideal for large-scale applications requiring robust data privacy, such as KYC (Know Your Customer) verification systems. Using zk-STARKs, institutions can validate user identities without storing sensitive data, ensuring regulatory compliance and user privacy.

Supply Chain Transparency: STARKs can authenticate data across complex supply chains without exposing business-sensitive information. With STARK proofs, parties can validate the provenance of goods, ensuring transparency without revealing trade secrets.

Technical Comparison of the Features of SNARKs, STARKs, and Bulletproofs

When evaluating zk-SNARKs, zk-STARKs, and Bulletproofs, several performance and security aspects stand out, making each of these ZKPs suitable for different types of blockchain applications.

1. Algorithmic Complexity
   • Prover Complexity: Both SNARKs and Bulletproofs operate with O( N × log⁡ ( N )) complexity, which is efficient for many applications. STARKs, however, achieve even greater scalability with O(N×poly-log(N)) complexity, handling larger computations more effectively.
   • Verifier Complexity: SNARKs are the most efficient in verification, with constant O(1) complexity, allowing fast validation. STARKs scale with O(poly-log(N)), while Bulletproofs are less efficient, with a linear O(N) complexity.
2. Proof Size
   • SNARKs produce the smallest proofs (~200 bytes per transaction), ideal for low-bandwidth environments. zk-STARKs generate significantly larger proofs (~45 kB per transaction), and Bulletproofs sit between them, with a compact 1.5 kB proof size.
   • For larger datasets (e.g., 10,000 transactions), SNARKs require an extensive setup (key size of ~500 GB), while STARKs and Bulletproofs maintain relatively manageable proof sizes (135 kB and 2.5 kB, respectively).
3. Gas Costs
   • SNARKs are less gas-intensive on Ethereum (estimated ~600k gas), making them preferable for applications on EVM-compatible blockchains. STARKs, while scalable, have higher gas costs (~2.5 million gas), and Bulletproofs are not yet optimized for Ethereum.
4. Trusted Setup Requirement
   • SNARKs require a trusted setup, which involves security risks if the setup process is compromised. Both STARKs and Bulletproofs eliminate this need, enhancing transparency and security.
5. Post-Quantum Security
   • STARKs are the only post-quantum secure option, relying on collision-resistant hashes instead of elliptic curve cryptography, which are susceptible to quantum attacks. SNARKs and Bulletproofs, dependent on discrete log assumptions, end up being vulnerable to these future threats.
6. Cryptographic Assumptions
   • SNARKs use strong cryptographic assumptions related to elliptic curves. STARKs rely on simpler, well-understood assumptions around collision-resistant hashes, while Bulletproofs use discrete log assumptions.

Importance of Security Auditing for ZKPs

With the growing complexity and application scope of ZKPs, the importance of reliable security auditing cannot be overstated. Audits help identify vulnerabilities early, preventing protocols from launching flawed contracts that could be susceptible to exploits, potentially resulting in catastrophic financial or data losses. As highlighted in the September 2024 PenPie hack, overlooking vulnerabilities in smart contracts can lead to significant damage, with millions being drained from the protocol and eroding user trust.

In ZKP-based systems, rigorous audits help ensure that:

• Trusted Setups Remain Secure: For protocols like zk-SNARKs, auditing the trusted setup ceremony is crucial to prevent backdoors.
• Non-Trivial Vulnerabilities Are Addressed: Techniques like reentrancy guards and input validation ensure that external contracts cannot exploit system functions, a critical safeguard shown by the PenPie incident​.
• Real-Time Monitoring Complements Pre-Deployment Audits: Continuous monitoring tools can detect anomalies in real time, adding an extra layer of security.

Effective auditing requires both automated and manual code reviews, especially for protocols handling significant funds or sensitive data. Combining automated scanning with expert code assessments, as provided by firms like AuditOne, ensures comprehensive vulnerability detection and mitigation​ by combining automated scanning with expert code assessment ensures comprehensive vulnerability detection and mitigation. Audit One can help provide this exact service in a trusted and secure environment, want to know more? learn about our services!

Future Outlook of ZKP Technology

ZKP technology will likely continue evolving in response to both quantum computing threats and rising privacy demands. zk-STARKs and Bulletproofs may gain prominence as quantum-resistant solutions, while zk-SNARKs might adopt hybrid approaches to mitigate risks associated with trusted setups. As the technology matures, developers may leverage hybrid models that integrate the best attributes of SNARKs, STARKs, and Bulletproofs for versatile applications across finance, healthcare, supply chains, and more.

Conclusion

The ZKPs presented in this article each address unique privacy, scalability, and security needs, forming the foundations of many cryptographic applications today. By understanding their respective strengths and vulnerabilities, developers and organizations can make informed decisions, guaranteeing privacy, efficiency, and security in their applications, and comprehensive audits are a critical component of maintaining ZKP-based protocols’ security, helping to safeguard against vulnerabilities that could otherwise compromise user data and funds.

As ZKPs evolve, they hold immense promise for enhancing digital privacy and trust, ensuring data integrity without exposing sensitive information. This technology is poised to reshape privacy standards across industries, from blockchain to traditional data management.

Protecting your Web3 project is essential for growth and user trust. Start by using our free Smart Contract Security Checklist Tool to identify any potential vulnerabilities. Or, book a free 30 min. consultation with us to explore advanced protection options tailored to your project.

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