Succinct non-interactive arguments for bounded depth computations

Jawale, Ruta S

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https://hdl.handle.net/2142/116136 Copy

Description

Title

Succinct non-interactive arguments for bounded depth computations

Author(s)

Jawale, Ruta S

Issue Date

2022-04-25

Director of Research (if dissertation) or Advisor (if thesis)

Khurana, Dakshita

Department of Study

Computer Science

Discipline

Computer Science

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• cryptography
• cryptographic protocols
• delegation schemes
• non-interactive
• Fiat-Shamir
• sum-check
• GKR
• PPAD
• lossy
• correlation intractability

Abstract

We construct a succinct non-interactive publicly-verifiable delegation scheme for any logspace uniform circuit under the sub-exponential Learning With Errors (LWE) assumption. For a circuit C : {0, 1}^N → {0, 1} of size S and depth D, the prover runs in time poly(S), the communication complexity is D · polylog(S), and the verifier runs in time (D + N) · polylog(S). To obtain this result, we introduce a new cryptographic primitive: a lossy correlation-intractable hash function family. We use this primitive to soundly instantiate the Fiat-Shamir transform for a large class of interactive proofs, including the interactive sum-check protocol and the Goldwasser-Kalai-Rothblum (GKR) protocol, assuming the subexponential hardness of LWE. Additionally, by relying on the result of Choudhuri et al. (STOC 2019), we establish (sub-exponential) average-case hardness of PPAD, assuming the sub-exponential hardness of LWE.

Graduation Semester

2022-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Ruta Jawale

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