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A Survey on the Post-Quantum Lattice-Based SNARGs in the Standard Model

Javadi, Mohammad | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58488 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Khazaei, Shahram
  7. Abstract:
  8. In non-interactive succinct argument protocols, the prover is able to produce a short proof for an instance of an NP language that convinces the verifier of the proof’s correctness in significantly less time than would otherwise be required. The advancement of quantum computers on one hand, and the practical applications of this cryptographic primitive in various fields—including privacy-preserving such as verifiable computation, as well as the design of secure distributed systems like blockchains—on the other hand, motivate the design of structures based on this primitive that are post-quantum secure; that is, despite having a classical structure, they remain secure against quantum computers. These structures are mainly designed under the random oracle model and the standard model. Among these, structures designed in the standard model hold greater importance. Such structures are lattice-based. The security of these structures, despite the existence of post-quantum secure lattice-based assumptions that are falsifiable, must be based on post-quantum secure assumptions that are non-falsifiable, which is one of the fundamental challenges in designing such structures. In this thesis, we review the main approaches in schemes constructed based on the framework of the combination of the information-theoretic proof system and cryptographic compiler
  9. Keywords:
  10. Succinct Non-Interactive Arguments (SNARG) ; Encryption Framework ; Lattice-Based Cryptography ; Post-Quantum Cryptography ; Commitment Scheme

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