Pre-requisite: An Understanding of Zero-Knowledge Proofs is required which can be obtained from my blog.

In this article, we will be going through the 2 most popular implementations of the zero-knowledge proofs from a practical standpoint which are ZK-SNARKs and ZK-STARKs.

The core difference between them is that STARKS produces scalable and transparent proofs whereas SNARKS produces succinct and non-interactive proofs and both of them are used for the validation of ZK-Proofs.

Now, let’s understand what they are first.

1. ZK SNARKS

   A zk-SNARK also known as Zero-Knowledge Succinct Non-Interactive Argument of Knowledge is a type of zero-knowledge proof system that has the following traits -

   • Zero-Knowledge: The prover can convince the verifier about the truth of a statement without revealing any additional or unnecessary details.

   • Succinctness: The proof is very compact, typically just a few hundred bytes in size.

   • Non-Interactive: The proof can be verified without any back-and-forth communication between the prover and the verifier.

   • Argument of Knowledge: The proof demonstrates that the prover has the knowledge of a witness for the statement being proven.

   • Efficiency: zk-SNARKs in general are very efficient and can generate and verify proofs very quickly making them suitable practically.

   • Scalability: The small proof size allows for the efficient storage and transmission of proofs.

   • Privacy: zk-SNARKs enable privacy-preserving applications by allowing the prover to hide sensitive information.

2. ZK -STARKs

   zk-STARK (Zero-Knowledge Scalable Transparent Argument of Knowledge) is another type of zero-knowledge proof system with the following key characteristics:

   • Zero-Knowledge: Like zk-SNARKs, zk-STARKs allow the prover to convince the verifier of a statement without revealing any additional information.

   • Scalability: zk-STARKs can handle large computations and generate proofs for complex statements.

   • Transparency: zk-STARKs do not require a trusted setup, making the system more transparent and secure.

   • Argument of Knowledge: The proof demonstrates that the prover has the knowledge of a witness for the statement currently being proven.

   • Post-Quantum Security: zk-STARKs are based on hash functions which are known to be resilient against quantum computer attacks.

   • No Trusted Setup: Unlike zk-SNARKs, zk-STARKs do not require a trusted setup phase eliminating a potential security risk or backdoor.

   • Larger Proof Sizes: zk-STARK proofs are generally larger than zk-SNARK proofs, in the range of a few kilobytes.

   • Higher Computational Complexity: Generating and verifying zk-STARK proofs requires more computational resources compared to zk-SNARKs.

   The security of zk-STARKs relies on the hardness of the "Collision-Resistant Hashing" problem, which is believed to be resistant to quantum computer attacks.

   zk-STARKs are used in projects that require scalability, transparency, and post-quantum security, such as

Now, you may be wondering about the point of these and we will be discussing it here.

1. The primary purposes of zk-SNARKs and zk-STARKs are:

   zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge):

   1. Privacy:

      • Enable privacy-preserving applications by allowing the prover to hide sensitive information.

      • Used in blockchain projects like Zcash to enable private and anonymous transactions.

   2. Efficiency and Scalability:

      • Provide efficient and succinct proofs, with proof sizes in the range of a few hundred bytes.

      • Allow for scalable and practical applications that require frequent verification of proofs.

   3. Non-interactivity:

      • The proof can be verified without any back-and-forth communication between the prover and verifier.

      • This makes the system more practical and easier to integrate into various applications.

   zk-STARKs (Zero-Knowledge Scalable Transparent Argument of Knowledge):

   1. Scalability and Transparency:

      • Able to handle large computations and generate proofs for complex statements.

      • Do not require a trusted setup, making the system more transparent and secure.

   2. Post-Quantum Security:

      • Based on hash functions, which are believed to be secure against quantum computer attacks.

      • Provide a higher level of security compared to systems relying on elliptic curve cryptography.

1. Proving System:

   • zk-SNARKs: zk-SNARKs require an initial trusted setup phase involving the development of a Common Reference String (CRS) to generate cryptographic parameters for proof creation. Proofs are generated using this setup data, and verification involves checking these proofs against the CRS.

   • zk-STARKs: In contrast, zk-STARKs do not require a trusted setup phase. They utilize collision-resistant cryptography and public randomness to establish parameters for proof generation. Proofs in zk-STARKs are created without the need for a trusted setup, enhancing transparency and eliminating the risk associated with malicious actors gaining access to setup data.

   2.Verification Cost:

   • zk-SNARKs: Verification costs for zk-SNARKs can be higher due to the need for a trusted setup and the computational requirements associated with verifying proofs generated using the CRS.

   • zk-STARKs: zk-STARKs offer more efficiency in verification costs as they do not require a trusted setup. The elimination of this setup phase reduces computational demands, making verification more cost-effective compared to zk-SNARKs.

   3. Setup and Update Frequency:

   • zk-SNARKs: zk-SNARKs necessitate a trusted setup phase, which involves generating and distributing cryptographic parameters. The setup data must be securely maintained to prevent security breaches.

   • zk-STARKs: zk-STARKs do not require frequent setup and updates as they eliminate the need for a trusted setup. The use of collision-resistant cryptography and public randomness ensures that parameters can be established without the complexities associated with regular updates, enhancing the system's robustness against security threats.

   By understanding these technical differences, it becomes evident that zk-STARKs offer advantages in terms of transparency, verification costs, and setup simplicity compared to zk-SNARKs, making them a promising option for cryptographic applications.

4. Performance and Scalability

**      Scalability**

• zk-SNARKs: zk-SNARKs have limitations in scalability as the computational and storage requirements for generating and verifying proofs increase linearly with the size of the underlying computation. This can make it challenging to handle large transaction volumes or complex computations on-chain.

• zk-STARKs: In contrast, zk-STARKs exhibit better scalability characteristics. They utilize a technique called "polynomial commitments" that allows the proving and verification complexity to scale quasi-linearly with the computation complexity. This enables zk-STARKs to handle larger transaction volumes and more complex computations more efficiently than zk-SNARKs.

  Performance

• zk-SNARKs: zk-SNARKs have the advantage of being non-interactive, meaning the proof can be generated and verified without any back-and-forth communication between the prover and verifier. This makes the verification process faster and more efficient compared to interactive proof systems.

• zk-STARKs: While zk-STARKs are more computationally intensive during the proof generation phase, they offer improved performance in terms of verification. The elimination of the trusted setup in zk-STARKs reduces the computational overhead, making the verification process more efficient, especially for large-scale blockchain applications.

In summary, zk-STARKs demonstrate better scalability by handling increased transaction volumes and network sizes more efficiently through their quasi-linear scaling properties. However, zk-SNARKs have an advantage in terms of verification speed and efficiency due to their non-interactive nature. The choice between the two technologies ultimately depends on the specific requirements of the application, balancing the trade-offs between scalability, performance, and other factors.

5. Security and Trust

Security Model:

• zk-SNARKs: The security of zk-SNARKs relies on the assumption of a trusted setup phase, where a group of participants generates a set of cryptographic parameters that must be kept secret. If these parameters are compromised, the security of the entire system is at risk. Additionally, zk-SNARKs are susceptible to quantum computing attacks, as their underlying cryptography may be broken by advancements in quantum computing.

• zk-STARKs: In contrast, zk-STARKs do not require a trusted setup phase, eliminating the risk associated with compromised setup parameters. Instead, they utilize collision-resistant cryptography and public randomness to establish the necessary parameters for proof generation and verification. This approach makes zk-STARKs more resistant to quantum computing attacks and reduces the trust assumptions required for the system's security.

6. Trust and Adoption:

• zk-SNARKs: zk-SNARKs have gained significant traction in the cryptocurrency and blockchain communities, particularly in the context of Layer 2 scaling solutions like zk-Rollups. Projects such as Polygon Hermez, zkSync, and Loopring have successfully implemented zk-SNARKs to improve transaction throughput and reduce gas fees. However, the need for a trusted setup phase has raised concerns about the decentralization and transparency of these systems.

• zk-STARKs: zk-STARKs have emerged as a promising alternative to zk-SNARKs, offering increased transparency and eliminating the need for a trusted setup. Projects like StarkWare's StarkEx, dYdX, and Immutable X have adopted zk-STARK technology to enhance scalability, privacy, and gas efficiency. The community has generally welcomed zk-STARKs as a more decentralized and secure approach to zero-knowledge proofs, though their higher computational requirements may pose challenges for wider adoption.

In summary, the security models of zk-SNARKs and zk-STARKs differ significantly, with zk-STARKs offering a more transparent and quantum-resistant approach. While zk-SNARKs have gained traction in the cryptocurrency and blockchain space, the trust concerns associated with their trusted setup phase have led to the emergence of zk-STARKs as a promising alternative, though their higher computational demands may present adoption challenges.

• Application in Blockchain and Smart Contracts

  • zk-SNARKs: In blockchain technology, zk-SNARKs are utilized to enhance privacy and scalability, particularly in the context of smart contracts. They enable the verification of off-chain transactions on the main chain, leading to increased throughput and scalability while maintaining the security of the main chain. zk-SNARKs reduce computation on the base blockchain, resulting in faster transactions and lower gas fees.

  • zk-STARKs: Similarly, zk-STARKs play a crucial role in blockchain applications, offering transparent and scalable zero-knowledge proofs. They are applied to validate computations and data off-chain, reducing the computational load on the main chain and they also eliminate the need for a trusted setup, enhancing decentralization and security in blockchain systems.

• Use Cases

  • Privacy-Preserving Voting Systems: Both zk-SNARKs and zk-STARKs have been implemented in privacy-preserving voting systems to ensure the confidentiality of votes while allowing for public verification of the election results. These zero-knowledge proof systems enable voters to prove the validity of their votes without revealing their choices, enhancing the integrity and privacy of the voting process.

  • Confidential Transactions: zk-SNARKs and zk-STARKs are utilized in blockchain applications to facilitate confidential transactions, where the details of the transaction are kept private while still ensuring the validity and integrity of the transaction. By using zero-knowledge proofs, parties can verify transactions without disclosing sensitive information, enhancing privacy and security in financial transactions.

In summary, zk-SNARKs and zk-STARKs play vital roles in blockchain technology, particularly in smart contracts and privacy-preserving transactions. These zero-knowledge**-**proof systems offer innovative solutions for enhancing privacy, scalability, and security in various blockchain applications, making them essential tools for building efficient and secure decentralized systems.

Let’s now perform a deep comparison of the key features and differences between zk-SNARKs and zk-STARKs:

• zk-SNARKs: Require an initial trusted setup phase to generate a Common Reference String (CRS) containing cryptographic parameters. Proofs are generated and verified using this CRS.

• zk-STARKs: Do not require a trusted setup. They use collision-resistant cryptography and public randomness to establish the parameters for proof generation and verification.

• zk-SNARKs: Verification costs can be higher due to the computational requirements of checking proofs against the CRS.

• zk-STARKs: Verification costs are generally lower as they do not require a trusted setup, reducing the computational overhead.

• zk-SNARKs: Require a trusted setup that must be securely maintained to prevent security breaches. The setup data needs to be updated periodically.

• zk-STARKs: Do not require a trusted setup, eliminating the need for regular updates and reducing the risk of security vulnerabilities.

• zk-SNARKs: There are limitations in scalability as the computational and storage requirements for generating and verifying proofs increase linearly with the size of the underlying computation.

• zk-STARKs: Exhibit better scalability characteristics, with the proving and verification complexity scaling quasi-linearly with the computation complexity.

• zk-SNARKs: Have the advantage of being non-interactive, making the verification process faster and more efficient.

• zk-STARKs: While more computationally intensive during the proof generation phase, they offer improved performance in verification due to the elimination of the trusted setup.

• zk-SNARKs: Rely on the assumption of a trusted setup, where the secrecy of the generated parameters is crucial. They are also susceptible to quantum computing attacks.

• zk-STARKs: Do not require a trusted setup, eliminating the risk associated with compromised setup parameters. They are more resistant to quantum computing attacks.

• zk-SNARKs: Have gained significant traction in the cryptocurrency and blockchain communities, particularly in Layer 2 scaling solutions, but the need for a trusted setup has raised concerns about decentralization and transparency.

• zk-STARKs: Have emerged as a promising alternative, offering increased transparency and eliminating the need for a trusted setup, though their higher computational requirements may pose challenges for wider adoption.

In summary, zk-STARKs offer advantages in terms of transparency, scalability, and security model, while zk-SNARKs excel in verification speed and efficiency. The choice between the two technologies ultimately depends on the specific requirements of the application and the trade-offs between these key features.

Based on our current knowledge of the key features and differences between these technologies, let’s find out for which use cases which technology shines.

1. Blockchain Applications Prioritizing Decentralization and Transparency: zk-STARKs are the preferred choice, as their elimination of the trusted setup and improved security model align better with the core principles of blockchain technology.

2. Blockchain Applications Focused on Verification Speed: zk-SNARKs may be the better option, as their non-interactive nature allows for faster and more efficient verification, which can be crucial in certain blockchain use cases.

3. Blockchain Applications Requiring Scalability: zk-STARKs are the more suitable choice, as their superior scalability characteristics enable them to handle larger transaction volumes and more complex computations on-chain.

Ultimately, the choice between zk-SNARKs and zk-STARKs will depend on the specific requirements and priorities of the blockchain application. As the technology continues to evolve, it is likely that we will see further advancements and hybridization of these zero-knowledge-proof systems, potentially offering the best of both worlds in the future.

• Recursive zk-SNARKs: Researchers are exploring the concept of recursive zk-SNARKs, which could enable new possibilities for SNARK proofs, blockchain consensus, decentralized applications, and data integration with technologies like IPFS.

• Improvements in zk-STARK Efficiency: Ongoing research is focused on enhancing the efficiency of zk-STARKs, particularly in terms of reducing the computational overhead for proof generation and verification. This could further improve the scalability and adoption of zk-STARK-based applications.

• Programming Languages for zk-Proofs: The introduction of specialized programming languages like Cairo by StarkWare simplifies the development of zk-rollup solutions, making it easier for developers to create applications leveraging zk-SNARKs and zk-STARKs.

• Widespread Adoption in Blockchain: Both zk-SNARKs and zk-STARKs are expected to play an increasingly important role in the future of blockchain technology. As Layer 2 scaling solutions and zk-rollups continue to gain traction, the demand for efficient and secure zero-knowledge proofs will grow, driving further advancements in these technologies.

• Expansion into Other Domains: Beyond blockchain, the potential applications of zk-SNARKs and zk-STARKs extend to various industries, including finance, healthcare, supply chain management, and data privacy. As the technology matures, experts predict that zk-proof generation will become a $10 billion market by 2030, with widespread adoption across diverse sectors.

• Interdisciplinary Innovations: The future of zk-SNARKs and zk-STARKs may involve collaborations between experts from different fields, such as cryptographers, blockchain developers, AI researchers, and economists. This cross-pollination of ideas could lead to entirely new use cases and disruptive applications for zero-knowledge proofs.

In summary, the ongoing research and innovation in zk-SNARKs and zk-STARKs, coupled with their growing adoption in blockchain and beyond, suggest a promising future for these zero-knowledge**-**proof systems. As they continue to evolve and become more efficient and accessible, zk-SNARKs and zk-STARKs are poised to revolutionize various industries, enhancing privacy, security, and scalability in the digital landscape.

In the realm of zero-knowledge proof systems, the comparison between zk-SNARKs and zk-STARKs reveals a nuanced landscape of trade-offs and advantages. zk-SNARKs, with their efficiency and non-interactive nature, have been instrumental in enhancing privacy and scalability in blockchain applications. However, the reliance on a trusted setup and potential security vulnerabilities pose challenges that need to be carefully considered.

On the other hand, zk-STARKs offer a compelling alternative with their transparency, scalability, and quantum resistance. By eliminating the need for a trusted setup and leveraging collision-resistant cryptography, zk-STARKs provide a robust security model that aligns well with the principles of decentralization and transparency in blockchain technology.

As the blockchain ecosystem continues to evolve, the choice between zk-SNARKs and zk-STARKs will depend on the specific use case requirements and priorities of users. Both technologies represent cutting-edge advancements in zero-knowledge-proof systems, actively being researched and refined to address the evolving needs of privacy, security, and scalability in decentralized networks.

In conclusion, the journey of zk-SNARKs vs zk-STARKs showcases the dynamic nature of cryptographic innovations, offering diverse solutions to empower the future of blockchain technology and beyond. The decision between these two technologies ultimately rests on a careful evaluation of their unique features and how they align with the goals and values of the applications they seek to enhance.