have an account?【sign in】Zero-knowledge Proof Simple Example: Understanding Zero-Knowledge Proof in a Simplified Scenario
howarthauthorZero-Knowledge Proof: A Simple Example for Understanding Its Principles
Zero-knowledge proof (ZKP) is a concept in cryptography that enables a party, called the prover, to prove to another party, called the verifier, the existence of a statement without revealing any information about the statement itself. This mechanism is useful in scenarios where the confidentiality of the statement is crucial, such as in privacy-preserving applications like blockchain and encrypted communication. In this article, we will explore a simple example to understand the principles of zero-knowledge proof.
Simple Example: Multiplication of Two Positive Integers
Suppose we want to design a zero-knowledge proof system for the following statement: "The product of two positive integers, a and b, is equal to c." For simplicity, let's assume a and b are known to both the prover and the verifier. The prover wants to prove to the verifier that the product of a and b is equal to c without revealing any information about a, b, or c.
1. Prover generates random numbers r1 and r2, and computes the product p = a * b.
2. Prover generates a random number r3 known only to itself.
3. Prover computes the statement value s = (p, r1, r2, r3).
4. Prover shows the statement value s to the verifier, who checks if the statement is correct based on the known values of a, b, and c.
5. If the verifier is convinced that the statement is correct, the verifier generates a random number r4 known only to itself.
6. The prover shows the value of r4 to the verifier, who checks if the statement is correct based on the known values of a, b, c, and r1, r2, r3, r4.
7. If the verifier is still convinced that the statement is correct, the verifier can generate a random number r5 known only to itself.
8. The prover shows the value of r5 to the verifier, who checks if the statement is correct based on the known values of a, b, c, r1, r2, r3, r4, r5.
9. If the verifier is convinced that the statement is correct, the prover successfully proves that the product of a and b is equal to c. Otherwise, the prover cannot prove the statement.
This simple example demonstrates the principles of zero-knowledge proof. In this scenario, the prover uses random numbers generated by itself to prove the existence of a statement without revealing any information about the statement itself. The verifier can verify the proof based on the known values of the statement and the random numbers generated by the prover.
Zero-knowledge proof is an essential concept in cryptography that enables the proof of existence without revealing any information about the statement itself. This mechanism is useful in various applications, such as privacy-preserving blockchains and encrypted communication, where confidentiality of the statement is crucial. The simple example provided in this article demonstrates the principles of zero-knowledge proof, helping readers understand its concepts and potential applications.