1- Setup Phase

Function-hiding functional commitment Scheme

1- A univariate polynomial commitment scheme

2- A proof of function relation (PFR)

A proof of function relation shows that a committed relation is a function.

3- An algebric holographic proof (AHP)

In the following section, we will review the setup phase of the protocol. We also provide an example to clarify the method.

1-1- PFR and AHP Setup

1-2- Example

References

[1] Boneh, Dan, Wilson Nguyen, and Alex Ozdemir. "Efficient functional commitments: How to commit to a private function." Cryptology ePrint Archive (2021).

[2] Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., & Ward, N. (2020). Marlin: Preprocessing zkSNARKs with universal and updatable SRS. In Advances in Cryptology–EUROCRYPT 2020: 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings, Part I 39 (pp. 738-768). Springer International Publishing.‏‏

[3] de Castro, Leo, and Chris Peikert. "Functional commitments for all functions, with transparent setup and from SIS." Annual International Conference on the Theory and Applications of Cryptographic Techniques. Cham: Springer Nature Switzerland, 2023.‏

[4] Gabizon, Ariel, and Zachary J. Williamson. "plookup: A simplified polynomial protocol for lookup tables." Cryptology ePrint Archive (2020).‏

[5] Wee, Hoeteck, and David J. Wu. "Lattice-based functional commitments: Fast verification and cryptanalysis." International Conference on the Theory and Application of Cryptology and Information Security. Singapore: Springer Nature Singapore, 2023.

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