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Knowledge Hub

May 4, 2023

Mathematical magic behind Zero-Knowledge Proof

The Zero-Knowledge Proof process is easy to understand but requires complex mathematical operations in the background that need to be designed to enable a particular proof to be created. There are various ZKP algorithms, each with its unique possible implementation.However, the general outline of the mathematical operations involved in creating a Zero-Knowledge Proof should follow the pattern:

1. Commitment

The user creates a commitment in the ZKP-enabled wallet, which is a value generated from the date of birth and a random number (called a nonce). The commitment is designed to conceal the date of birth while allowing the prover to perform mathematical operations.

2. Challenge

The verifier generates a challenge for the user. Usually, the challenge is a random number or a hash of the commitment. It ensures the user cannot reuse a previously computed proof, as the challenge would change, rendering the old proof invalid.

3. Response

The wallet calculates a response based on the challenge, date of birth in our example, and the random nonce used in the commitment. This response demonstrates knowledge of the secret information without revealing it directly.

4. Verification

The verifier checks the response provided by the user against the commitment and the challenge. If the response is valid, the verifier can conclude that the user has certain age (possesses the secret information) without learning any details like full date of birth or any other information that can be read from the officially issued ID. Therefore, users can maintain privacy by using ZKPs for age verification while proving eligibility for age-restricted services. This innovative cryptographic technique offers a secure and privacy-preserving solution for age verification in the digital world.

ZKP mathematical operations use advanced cryptographic techniques, such as modular arithmetic, elliptic curve cryptography, or homomorphic encryption. Different Zero-Knowledge Proof algorithms might use distinct methods and operations to achieve the same goal of privacy-preserving proof generation. Some popular ZKP schemes include Schnorr protocol, zk-SNARKs, and zk-STARKs. Each ZKP scheme has its unique approach and set of mathematical operations.

These techniques ensure that the proof remains secure and user’s age is not revealed during the process.

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