🏝️Fiat-Shamir transformation (or Fiat-Shamir heuristic)
The Fiat-Shamir transformation (or Fiat-Shamir heuristic) is a cryptographic technique used to transform an interactive proof system (where a prover and a verifier exchange multiple messages) into a non-interactive one (where only a single message is sent from the prover to the verifier). This technique is especially useful in zero-knowledge proofs.
Here's a simplified breakdown of the process:
Interactive Proof:
Commit: The prover sends a commitment to the verifier.
Challenge: The verifier sends a random challenge back to the prover.
Response: Based on the challenge, the prover responds with an answer.
The verifier checks the prover's answer and decides if the proof is valid.
Fiat-Shamir Transformation:
Instead of waiting for a challenge from the verifier, the prover uses a cryptographic hash function to generate the challenge themselves.
Commit: The prover generates a commitment.
Challenge: The prover uses a cryptographic hash function to hash the commitment and generates a challenge.
Response: The prover computes a response based on this self-generated challenge.
The prover then sends the commitment and the response to the verifier.
The verifier, upon receiving the commitment and response, independently computes the challenge (by hashing the received commitment) and checks the validity of the response.
The security of this non-interactive transformation relies on the assumption that the hash function used is cryptographically secure. If the prover cannot predict the output of the hash function before generating the commitment, then they cannot cheat by adjusting their commitment after seeing the challenge.
This transformation is widely used in the design of non-interactive zero-knowledge proofs (NIZKs) and is fundamental in many modern cryptographic protocols, especially in privacy-preserving mechanisms on blockchain platforms like zk-SNARKs.
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