have an account?【sign in】zero knowledge proofs example:A Simple Example of Zero Knowledge Proofs in Cryptography
hoskinsauthorZero knowledge proofs (ZKP) are a powerful concept in cryptography that allows a prover to demonstrate the existence of certain facts without revealing any information about those facts. This is achieved by using mathematical proofs that are indiscernible from the true proofs, even though the prover does not know the true proofs. ZKP has found applications in various fields, such as secure multiparty computation and anonymous credential authentication. In this article, we will provide a simple example of zero knowledge proofs in cryptography to help readers better understand this concept.
A Simple Example of Zero Knowledge Proofs in Cryptography
Let's consider a scenario where two parties, Alice and Bob, want to prove that they both know the answer to a secret question, without revealing the answer themselves. We will use the concept of zero knowledge proofs to achieve this goal.
1. Pre-sharing secrets
First, Alice and Bob need to pre-share some secrets before the proof begins. Let's say they pre-share a secret binary string X, where X = x1x2...xN, where each xi is either 0 or 1. They can generate this secret string using a secure random number generator.
2. Prover (Alice) generates a proof P
Alice knows the answer to the secret question (say, the binary representation of the number 7), and she wants to prove to Bob that she knows the answer without revealing the actual answer. She generates a proof P = p1p2...pm, where pi is either 0 or 1. Alice knows the actual answer, but she does not know the proof P.
3. Prover (Alice) sends the proof P to Bob
Alice sends the proof P to Bob, who keeps it in his local computer.
4. Bob verifies the proof
Bob uses the secret string X and the proof P to verify the proof. First, he calculates the sum S = s1+s2+...+sm, where si is the binary representation of the number 2^i, for i = 1, 2, ..., N. If S = X, then Bob believes that Alice knows the answer to the secret question.
5. Bob verifies the zero knowledge property
Bob also checks if the proof P is indiscernible from the true proofs. He calculates the sum T = t1+t2+...+tm, where ti is either 0 or 1. Bob needs to prove that, for any string Y = y1y2...ym, where yi is either 0 or 1, there exists at least one index k such that tk = yk. If Bob can prove this property, then he can be sure that the proof P is indeed indiscernible from the true proofs.
6. Bob verifies the answer
Finally, Bob compares the sum S with the secret string X. If S = X, then Bob believes that Alice knows the answer to the secret question.
In this article, we provided a simple example of zero knowledge proofs in cryptography. This example demonstrates how to prove the existence of certain facts without revealing any information about those facts. ZKP has found applications in various fields, such as secure multiparty computation and anonymous credential authentication. However, the practical implementation of ZKP requires advanced cryptographic techniques, such as homomorphic encryption and zero knowledge proofs.