Loading...

Designing a Succinct Argument System Based on GKR Protocol Via Polynomial Commitment Schemes

Shirzad, Alireza | 2023

93 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56369 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Eghlidos, Taraneh
  7. Abstract:
  8. With the dramatic advancements in information technology and the industry requirements for security and privacy, proof systems play a crucial role in cryptography. Among the vast variety of proof systems, succinct non-interactive arguments (SNARG) seem to be the most appealing class of proof systems, due to their attractive properties. SNARGs are usually made up of two constructive components, namely the information theoretic part and the cryptographic part. The GKR protocol was introduced as a proof system for a tractable family of languages called “log-Space Uniform Circuits”. The log-space uniformity is a necessary condition for the protocol to be succinct. Hence, it is not possible to design SNARGs based on the original GKR proof system, without the log-space uniformity condition. In this thesis, we leverage holography in GKR protocol to build SNARGs for nonuniform family of circuits. The proposed holography is created using polynomial commitment schemes, allowing the verifier to delegate the computation of wiring predicates to the prover. As showcases, first, we make the PST polynomial commitment scheme more efficient for multi-linear polynomials and use it as a polynomial delegation tool to build a designated-verifier SNARG. Then, to generalize our SNARG to a publicly verifiable SNARG, we use a transparent polynomial commitment scheme called Dory. The proposed SNARGs can be efficiently transformed into SNARKs and zk-SNARKs
  9. Keywords:
  10. Secure Computation ; Succinct Non-Interactive Arguments (SNARG) ; Verifiable Computing ; GKR Protocol ; Polynomial Commitment Scheme ; Proof System ; Privacy Preserving

 Digital Object List

 Bookmark

...see more