have an account?【sign in】Zero-knowledge proof simple example:A Simple Example of Zero-Knowledge Proofs in Cryptography
hosmerauthorA Simple Example of Zero-Knowledge Proofs in Cryptography
Zero-knowledge proofs (ZKP) are a powerful cryptographic technique that allows a prover to demonstrate the existence of a statement without revealing any information about that statement. This is useful in scenarios where a party, the prover, wants to prove their knowledge of a secret without revealing the secret itself. One common example of ZKP is a proof of ownership, where a user wants to prove they own a private key without revealing the key itself. In this article, we will explore a simple example of ZKP in cryptography.
The Example
We will use the XOR function, which is defined by XORing two bits or integers. The XOR of two integers is the bitwise XOR of their binary representations. In other words, the XOR of two integers is the result of exchanging every bit in one integer with the corresponding bit in the other integer. For example, the XOR of 5 (binary: 0101) and 10 (binary: 1010) is 1 (binary: 1101).
Our ZKP proof will involve two pieces of data, A and B, and a public value K. The prover (P) will generate a secret value S, and then compute a proof P of knowledge, which is a function of S, A, and B. The verifier (V) will check the proof P using the known function and the values A, B, and K. If the verifier is able to generate a valid proof P, then they know that P = f(S, A, B) and can conclude that P knows A and B. However, P cannot reveal any information about S, the secret value used to generate the proof.
Step 1: Generate a Secret Value S
The first step is to generate a secret value S, which will be used to generate the proof P. S could be any value, as long as it is known only to P.
Step 2: Generate a Proof P of Knowledge
Once S is generated, P can compute a proof P of knowledge using the function f(S, A, B, K). In our example, f(S, A, B, K) = A XOR B XOR K. P = f(S, A, B, K) will be a function of S, A, B, and K.
Step 3: Provide the Proof P to V
Once P is generated, P can be provided to V. V will check the proof P using the known function f(S, A, B, K) and the values A, B, and K. If V is able to generate a valid proof P, then they know that P = f(S, A, B, K) and can conclude that P knows A and B.
Step 4: Conclude
If V is able to generate a valid proof P, then they know that P knows A and B. However, P cannot reveal any information about S, the secret value used to generate the proof. This is a simple example of zero-knowledge proofs in cryptography, which can be applied to a wide range of scenarios where a party needs to prove their knowledge of a statement without revealing the statement itself.
Zero-knowledge proofs are a powerful tool in cryptography that allow a prover to demonstrate the existence of a statement without revealing any information about that statement. In this article, we explored a simple example of ZKP, using the XOR function and a proof of knowledge generated using a known function. While this example is relatively straightforward, the concept of ZKP can be applied to more complex scenarios, such as proof of ownership in cryptocurrency or verification of a user's identity.