Summary:

For the FRI protocol, the complexity of the verification satisfies the logarithmic relationship. The algorithm ensures that the round consistency verifications can be passed if and only if the initial polynomial satisfies . The actual implementation may vary slightly. For more information, please refer to the DEEP-FRI paper. In comparison to FRI, DEEP-FRI increases the system’s reliability while maintaining an optimal level of proof and verification complexity.

The ZK-STARK algorithm can be summarized as follows:

1. The algorithm is divided into two parts: Arithmeticalization and LDT.

2. Arithmeticalization converts the issue to polynomial equality and polynomial LDT issue.

3. The FRI protocol is used in the LDT stage to ensure the complexity of linear proof and the complexity of logarithmic verification

4. The zero-knowledge attribute ensures that the verifier cannot access the points in the trajectory polynomial and that the trajectory polynomial contains privacy values.

5. Simultaneously, to ensure the zero-knowledge attribute, random values for rows must be added to the trajectory polynomial, which is determined by the verifier and prover after negotiation.

6. CRS is not required as a third party throughout the process.

7. The entire process does not depend on any mathematical problems.

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