Ligero

Ames, Scott; Hazay, Carmit; Ishai, Yuval; Venkitasubramaniam, Muthuramakrishnan

doi:10.1145/3133956.3134104

Cited by 201 publications

(7 citation statements)

References 38 publications

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“…Finally, we obtain linear efficiency in the size of circuit. Despite being less efficient than state of the art post-quantum zero-knowledge proofs, such as [2,4,8] whose proofs sizes are sublinear or even polylogarithmic in the size of the witness, our approach still improves on the naive construction from one-way functions and provides a first general purpose zero-knowledge proof from isogenies.…”

Section: Discussion and Further Workmentioning

confidence: 99%

Malleable Commitments from Group Actions and Zero-Knowledge Proofs for Circuits Based on Isogenies

Chen,

Lai,

Laval

et al. 2024

Lecture Notes in Computer Science

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Zero-knowledge proofs for NP statements are an essential tool for building various cryptographic primitives and have been extensively studied in recent years. In a seminal result from Goldreich, Micali and Wigderson [17], zero-knowledge proofs for NP statements can be built from any one-way function, but this construction leads very inefficient proofs. To yield practical constructions, one often uses the additional structure provided by homomorphic commitments. In this paper, we introduce a relaxed notion of homomorphic commitments, called malleable commitments, which requires less structure to be instantiated. We provide a malleable commitment construction from the ElGamal-type isogeny-based group action from Eurocrypt'22 [5]. We show how malleable commitments with a group structure in the malleability can be used to build zero-knowledge proofs for NP statements, improving on the naive construction from one-way functions. We consider three representations: arithmetic circuits, rank-1 constraint systems and branching programs. This work gives the first attempt at constructing a post-quantum generic proof system from isogeny assumptions (the group action DDH problem). Though the resulting proof systems are linear in the circuit size, they possess interesting features such as non-interactivity, statistical zero-knowledge, and online-extractability.

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Section: Discussion and Further Workmentioning

confidence: 99%

Malleable Commitments from Group Actions and Zero-Knowledge Proofs for Circuits Based on Isogenies

Chen,

Lai,

Laval

et al. 2024

Lecture Notes in Computer Science

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“…Verifiable computation is universally used to verify the correctness of outsourced computation tasks to apply outsourced computing resources. Various cryptographic methods, e.g., interactive proofs (IPs) [41], succinct non-interactive arguments of knowledge (SNARK) [42,43], and Authenticated Data Structure (ADS) [44] have become the mainstream methods of constructing verifiable outsourced computations to provide computational integrity. IPs are implemented according to the sum-check protocol and are often converted to circuits for proof.…”

Section: Verifiable Outsourced Computationmentioning

confidence: 99%

Achieving Verifiable Decision Tree Prediction on Hybrid Blockchains

Fu,

Zhang,

et al. 2023

Entropy

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Machine learning has become increasingly popular in academic and industrial communities and has been widely implemented in various online applications due to its powerful ability to analyze and use data. Among all the machine learning models, decision tree models stand out due to their great interpretability and simplicity, and have been implemented in cloud computing services for various purposes. Despite its great success, the integrity issue of online decision tree prediction is a growing concern. The correctness and consistency of decision tree predictions in cloud computing systems need more security guarantees since verifying the correctness of the model prediction remains challenging. Meanwhile, blockchain has a promising prospect in two-party machine learning services as the immutable and traceable characteristics satisfy the verifiable settings in machine learning services. In this paper, we initiate the study of decision tree prediction services on blockchain systems and propose VDT, a Verifiable Decision Tree prediction scheme for decision tree prediction. Specifically, by leveraging the Merkle tree and hash function, the scheme allows the service provider to generate a verification proof to convince the client that the output of the decision tree prediction is correctly computed on a particular data sample. It is further extended to an update method for a verifiable decision tree to modify the decision tree model efficiently. We prove the security of the proposed VDT schemes and evaluate their performance using real datasets. Experimental evaluations show that our scheme requires less than one second to produce verifiable proof.

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“…The main drawback is that they are still concretely inefficient, especially as far as prover complexity is concerned. In the same family, [22,30,2] build on the MPC-in-the-head paradigm [29] and share similar properties. The most efficient one is Ligero [2] which, while having good concrete efficiency, has communication complexity O λ ( |C|) which can be bad for moderately large computations.…”

Section: Related Workmentioning

confidence: 99%

Updateable Inner Product Argument with Logarithmic Verifier and Applications

Daza

Ràfols

Zacharakis

2020

Lecture Notes in Computer Science

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We propose an improvement for the inner product argument of Bootle et al. (EUROCRYPT'16). The new argument replaces the unstructured common reference string (the commitment key) by a structured one. We give two instantiations of this argument, for two different distributions of the CRS. In the designated verifier setting, this structure can be used to reduce verification from linear to logarithmic in the circuit size. The argument can be compiled to the publicly verifiable setting in asymmetric bilinear groups. The new common reference string can easily be updateable. The argument can be directly used to improve verification of Bulletproofs range proofs (IEEE SP'18). On the other hand, to use the improved argument to prove circuit satisfiability with logarithmic verification, we adapt recent techniques from Sonic (ACM CCS'19) to work with the new common reference string. The resulting argument is secure under standard assumptions (in the Random Oracle Model), in contrast with Sonic and recent works that improve its efficiency (Plonk, Marlin, AuroraLight), which, apart from the Random Oracle Model, need either the Algebraic Group Model or Knowledge Type assumptions.

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Ligero

Cited by 201 publications

References 38 publications

Malleable Commitments from Group Actions and Zero-Knowledge Proofs for Circuits Based on Isogenies

Malleable Commitments from Group Actions and Zero-Knowledge Proofs for Circuits Based on Isogenies

Achieving Verifiable Decision Tree Prediction on Hybrid Blockchains

Updateable Inner Product Argument with Logarithmic Verifier and Applications

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