What are zk-SNARKs and zk-STARKs and how are they different?

Introduction to Zero-Knowledge Proofs

Zero-knowledge proofs (ZKPs) are cryptographic methods that allow one party to prove to another that a statement is true without revealing any additional information. In the world of cryptocurrencies, ZKPs are particularly valuable for enhancing privacy and security. Two prominent types of ZKPs are zk-SNARKs and zk-STARKs. These technologies enable transactions to be validated without disclosing the transaction details, making them crucial for privacy-focused blockchains like Zcash.

Understanding zk-SNARKs

zk-SNARKs, which stands for Zero-Knowledge Succinct Non-Interactive Argument of Knowledge, are a type of ZKP that allows one party to prove possession of certain information without revealing it. The key features of zk-SNARKs include their succinctness and non-interactivity, meaning the proof can be verified quickly and without further communication between the prover and verifier.

In the context of cryptocurrencies, zk-SNARKs are used to validate transactions on the blockchain without revealing the sender, receiver, or the amount transferred. This is achieved through a complex mathematical process that involves generating a proof that can be verified by anyone on the network.

To understand how zk-SNARKs work, consider the following steps:

• Setup Phase: A common reference string (CRS) is generated, which is used to create and verify proofs. This phase is crucial and must be done securely to prevent vulnerabilities.
• Proof Generation: The prover uses the CRS to generate a proof that a certain statement is true. This proof is succinct and can be generated without revealing the underlying data.
• Verification: The verifier uses the CRS to check the proof. If the proof is valid, the verifier can be confident that the statement is true without knowing the details.

Understanding zk-STARKs

zk-STARKs, or Zero-Knowledge Scalable Transparent ARguments of Knowledge, are another type of ZKP that offers similar privacy benefits but with different technical characteristics. The key features of zk-STARKs include their scalability and transparency, meaning they do not require a trusted setup and can handle larger computations more efficiently.

In the cryptocurrency space, zk-STARKs are used to enhance the privacy and scalability of blockchain transactions. They are particularly useful for applications that require high throughput and low latency.

The process of using zk-STARKs involves the following steps:

• Proof Generation: The prover generates a proof that a certain computation was performed correctly. This proof is scalable and can handle large computations.
• Verification: The verifier checks the proof using publicly available information. The verification process is transparent and does not require a trusted setup.

Key Differences Between zk-SNARKs and zk-STARKs

While both zk-SNARKs and zk-STARKs provide zero-knowledge proofs, there are several key differences between them:

• Trusted Setup: zk-SNARKs require a trusted setup phase, which can be a potential security risk if not done correctly. In contrast, zk-STARKs do not require a trusted setup, making them more transparent and secure.
• Scalability: zk-STARKs are more scalable and can handle larger computations more efficiently than zk-SNARKs. This makes them suitable for applications that require high throughput.
• Proof Size and Verification Time: zk-SNARKs typically have smaller proof sizes and faster verification times compared to zk-STARKs. However, the difference in verification time becomes less significant as the size of the computation increases.
• Cryptographic Assumptions: zk-SNARKs rely on elliptic curve cryptography, which is based on certain mathematical assumptions. zk-STARKs, on the other hand, rely on hash functions and are considered to be post-quantum secure.

Applications in Cryptocurrencies

Both zk-SNARKs and zk-STARKs have been implemented in various cryptocurrencies to enhance privacy and scalability. For example, Zcash uses zk-SNARKs to enable private transactions, while StarkWare leverages zk-STARKs to improve the scalability of Ethereum.

In Zcash, users can choose to shield their transactions using zk-SNARKs, which allows them to prove that a transaction is valid without revealing any details. This feature has made Zcash a popular choice for users who prioritize privacy.

StarkWare, on the other hand, uses zk-STARKs to create scalable solutions for Ethereum. Their technology, known as StarkNet, allows for the execution of complex computations off-chain and the submission of proofs on-chain, significantly increasing the throughput of the Ethereum network.

Technical Implementation of zk-SNARKs and zk-STARKs

Implementing zk-SNARKs and zk-STARKs in a cryptocurrency involves several technical steps. Here is a detailed look at how these technologies are integrated into blockchain systems:

• zk-SNARKs Implementation:

  • Setup: Generate a common reference string (CRS) using a secure multi-party computation protocol. This step is crucial to ensure the security of the system.
  • Circuit Design: Define the computation that needs to be proven as a circuit. This involves converting the computation into a series of logical gates.
  • Proof Generation: Use the circuit and the CRS to generate a proof. This involves solving a complex mathematical problem that can be verified succinctly.
  • Verification: Implement a verification algorithm that checks the proof using the CRS. This algorithm should be efficient and able to verify the proof quickly.

• zk-STARKs Implementation:

  • Circuit Design: Similar to zk-SNARKs, define the computation as a circuit. However, zk-STARKs use a different type of circuit known as an arithmetic circuit.
  • Proof Generation: Generate a proof using the arithmetic circuit. This involves creating a series of commitments and proofs that can be verified transparently.
  • Verification: Implement a verification algorithm that checks the proof using publicly available information. This algorithm should be scalable and able to handle large computations efficiently.

Frequently Asked Questions

Q: Can zk-SNARKs and zk-STARKs be used together in a single blockchain system?

A: Yes, it is possible to use both zk-SNARKs and zk-STARKs in a single blockchain system, depending on the specific requirements of the application. For example, a blockchain could use zk-SNARKs for smaller, more frequent transactions and zk-STARKs for larger, more complex computations.

Q: Are there any cryptocurrencies that use both zk-SNARKs and zk-STARKs?

A: While most cryptocurrencies use one or the other, there are projects exploring the use of both technologies. For instance, some layer-2 scaling solutions for Ethereum are considering integrating both zk-SNARKs and zk-STARKs to optimize performance and privacy.

Q: How do zk-SNARKs and zk-STARKs impact the overall security of a blockchain?

A: Both technologies enhance the security of a blockchain by enabling private transactions and reducing the risk of data breaches. However, the security of zk-SNARKs depends on the trusted setup phase, while zk-STARKs offer a more transparent and potentially more secure approach due to their lack of a trusted setup.

Q: What are the computational requirements for generating and verifying proofs using zk-SNARKs and zk-STARKs?

A: The computational requirements for zk-SNARKs and zk-STARKs vary. zk-SNARKs typically require less computational power for verification but more for proof generation. zk-STARKs, on the other hand, require more computational power for verification but can handle larger computations more efficiently.