Creating zk-STARKs

The creation of zk-STARKs revolves around the formulation of a proof for a given computation or function without revealing the specifics of the data that led to the resultant outcome.

Steps:

1. Specifying a Computation: Decide on the specific computation you want to generate a proof for.

2. Transformation: Transform this computation into a series of polynomial equations.

3. Generating the Proof: Using algorithms and tools like the Arithmetization process, produce a zk-STARK for the given computation.

Constructing a zk-STARK

1. Execution Trace:

• Begin with an execution trace that details the computation steps.

• Transform the computation's logic gates into a trace table.

2. Arithmetization:

• Convert the execution trace into polynomial representations.

• The polynomial should evaluate to zero if the trace correctly represents the computation.

3. Merkleizing the Trace:

• Generate a Merkle tree from the trace. This offers a succinct representation and allows for easy commitments to specific values without revealing the whole trace.

4. Composition & Proof:

• Using the Composition function, obtain a single polynomial from the various generated polynomials.

• The prover and verifier then engage in the proof system (commitment, challenge, response, and verification).

Implementing zk-STARKs in code

The implementation of zk-STARKs involves a deep understanding of cryptographic principles, polynomial algebra, and efficient computational practices.

Key Considerations:

1. Language Choice: zk-STARKs can be implemented in various programming languages, but Rust, C++, and Python are popular choices due to their efficiency and extensive cryptographic libraries.

2. Library Utilization: There are several zk-STARK libraries available, such as StarkWare, which simplify the implementation process.

Basic Code Structure (Pseudocode):

import zkSTARK_library

function main():
    // Specify the computation
    computation = defineComputation()

    // Generate zk-STARK proof
    proof = zkSTARK_library.generateProof(computation)

    // Verify the proof (usually by another party)
    isValid = zkSTARK_library.verifyProof(proof)

    if isValid:
        print("Proof is valid!")
    else:
        print("Proof is invalid!")

Example Implementations

1. zk-rollups in Blockchain: zk-STARKs can be used to batch multiple transactions into a single proof on blockchains, reducing data storage and increasing throughput.

2. Private Voting Systems: zk-STARKs can validate that a user's vote is legitimate without revealing the specific vote, ensuring privacy and integrity.

3. Secure Data Validation: In systems where data privacy is crucial (like medical systems), zk-STARKs can confirm the correctness of computations on private data without revealing the data itself.