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NIWI and New Notions of Extraction for Algebraic Languages

Ganesh, C and Khoshakhlagh, H and Parisella, R (2022) NIWI and New Notions of Extraction for Algebraic Languages. In: 13th International Conference on Security and Cryptography for Networks, SCN 2022, 12 - 14 September 2022, Amalfi, pp. 687-710.

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Official URL: https://doi.org/10.1007/978-3-031-14791-3_30


We give an efficient construction of a computational non-interactive witness indistinguishable (NIWI) proof in the plain model, and investigate notions of extraction for NIZKs for algebraic languages. Our starting point is the recent work of Couteau and Hartmann (CRYPTO 2020) who developed a new framework (CH framework) for constructing non-interactive zero-knowledge proofs and arguments under falsifiable assumptions for a large class of languages called algebraic languages. In this paper, we construct an efficient NIWI proof in the plain model for algebraic languages based on the CH framework. In the plain model, our NIWI construction is more efficient for algebraic languages than state-of-the-art Groth-Ostrovsky-Sahai (GOS) NIWI (JACM 2012). Next, we explore knowledge soundness of NIZK systems in the CH framework. We define a notion of strong f-extractability, and show that the CH proof system satisfies this notion. We then put forth a new definition of knowledge soundness called semantic extraction. We explore the relationship of semantic extraction with existing knowledge soundness definitions and show that it is a general definition that recovers black-box and non-black-box definitions as special cases. Finally, we show that NIZKs for algebraic languages in the CH framework cannot satisfy semantic extraction. We extend this impossibility to a class of NIZK arguments over algebraic languages, namely quasi-adaptive NIZK arguments that are constructed from smooth projective hash functions. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Item Type: Conference Paper
Publication: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to the Springer Science and Business Media Deutschland GmbH.
Keywords: Algebra; Hash functions; Semantics, Algebraic languages; Black boxes; Efficient construction; Extractability; Hartmann; Non black boxes; Non-interactive zero-knowledge proofs; Proof system; Semantics extractions; State of the art, Extraction
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 06 Oct 2022 10:54
Last Modified: 06 Oct 2022 10:54
URI: https://eprints.iisc.ac.in/id/eprint/77243

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