A brief introduction to what zero-knowledge proof is.

Zero-Knowledge Proof (ZKP) is a cryptographic protocol that allows one party (the prover) to prove to another party (the verifier) ​​that a statement is true without revealing any specific information about the statement. The concept of zero-knowledge proof was proposed by Shafi Goldwasser, Silvio Micali and Charles Rackoff in 1985 and has been widely used in cryptography and computer science.

Three major properties of zero-knowledge proof

1. Completeness:

• If the statement is true, an honest prover can convince an honest verifier.

2. Soundness:

• If the statement is false, the probability that a non-cheating prover can convince an honest verifier is very small (usually negligible).

3. Zero-Knowledge:

• If the statement is true, the verifier does not obtain any additional information beyond the statement.

Types of Zero-Knowledge Proofs

1. Interactive Zero-Knowledge Proofs:

• The prover and the verifier prove the truth of a statement through multiple rounds of interaction.

2. Non-Interactive Zero-Knowledge Proofs (NIZK):

• The prover generates a single proof that can be verified by any verifier without further interaction.

The application of zero-knowledge proofs, to put it bluntly, is the process of knowing that you are awesome but not knowing how you are awesome. The token worth paying attention to in this field is zkSync~

Zero-knowledge proofs have a wide range of applications in many fields, including but not limited to:

1. Blockchain and cryptocurrency:

• Zero-knowledge proofs are used to ensure the privacy and security of transactions, such as the application of zk-SNARKs and zk-STARKs technology in Zcash and other privacy coins.

2. Authentication:

• Verify the identity of the user without exposing the user's password or other sensitive information.

3. Secure multi-party computation:

• Multiple parties perform joint computation without disclosing their private data.

4. Data privacy protection:

• Protect data privacy and ensure that sensitive information is not disclosed when sharing or processing data.

Example

Example of interactive zero-knowledge proof: map coloring problem

Suppose there is a map, and the prover claims that the map can be colored with four colors so that the colors of adjacent regions are different. The verifier wants to verify this claim, but does not want to know the specific coloring scheme.

1. The prover first colors the map with four colors.

2. The prover masks the color of each region and randomly swaps the color labels.

3. The prover shows the swapped map to the verifier.

4. The verifier randomly selects a pair of adjacent regions and asks the prover to reveal the colors of these regions.

5. The prover reveals the colors, and the verifier checks whether the colors of this pair of adjacent regions are different.

6. Repeat the above steps multiple times, and the verifier selects a different pair of adjacent regions each time.

If the prover can correctly reveal the colors each time and the colors are different, then the verifier can have a high degree of confidence that the prover does have a correct coloring scheme without knowing the specific scheme.

Summary

Zero-knowledge proof is a powerful cryptographic tool that can prove the authenticity of certain statements without leaking information. It has broad application prospects in fields such as blockchain, identity authentication, and data privacy protection.