Verifiable computation schemes enable a client to outsource the computation of a function F on various inputs to an untrusted worker, and then verify the correctness of the returned results. Critically, the outsourcing and verification procedures must be more efficient than performing the computation itself.
In more detail, we introduce and formalize the notion of Verifiable Computation, which enables a computationally weak client to "outsource" the computation of an arbitrary function F on various dynamically-chosen inputs x_1,...,x_k to one or more workers. The workers return the result of the function evaluation, e.g., y_i=F(x_i), as well as a proof that the computation of F was carried out correctly on the given value x_i. The primary constraint is that the verification of the proof should require substantially less computational effort than computing F(x_i) from scratch.
- Antoine Delignat-Lavaud, Cedric Fournet, Markulf Kohlweiss, and Bryan Parno, Cinderella: Turning Shabby X.509 Certificates into Elegant Anonymous Credentials with the Magic of Verifiable Computation, IEEE – Institute of Electrical and Electronics Engineers, May 2016.
- Craig Costello, Cedric Fournet, Jon Howell, Markulf Kohlweiss, Benjamin Kreuter, Michael Naehrig, Bryan Parno, and Samee Zahur, Geppetto: Versatile Verifiable Computation, in Proceedings of the IEEE Symposium on Security and Privacy, IEEE – Institute of Electrical and Electronics Engineers, 18 May 2015.
- George Danezis, Cedric Fournet, Markulf Kohlweiss, and Bryan Parno, Pinocchio Coin: Building Zerocoin from a Succinct Pairing-based Proof System, in Workshop on Language Support for Privacy Enhancing Technologies, ACM – Association for Computing Machinery, 4 November 2013.
- Rosario Gennaro, Craig Gentry, Bryan Parno, and Mariana Raykova, Quadratic Span Programs and Succinct NIZKs without PCPs, in Proceedings of the IACR Eurocrypt Conference, International Association for Cryptologic Research, 30 May 2013.
- Bryan Parno, Craig Gentry, Jon Howell, and Mariana Raykova, Pinocchio: Nearly Practical Verifiable Computation, in Proceedings of the IEEE Symposium on Security and Privacy, IEEE, 21 May 2013. Best Paper Award
- Srinath Setty, Benjamin Braun, Victor Vu, Andrew J. Blumberg, Bryan Parno, and Michael Walfish, Resolving the Conflict Between Generality and Plausibility in Verified Computation, in Proceedings of the ACM European Conference on Computer Systems (EuroSys), ACM, 15 April 2013.
- Rosario Gennaro, Craig Gentry, and Bryan Parno, Non-Interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers, in Proceedings of the International Cryptology Conference (CRYPTO), Springer Verlag, August 2010.
Pinocchio's source code.