On Fulkerson conjecture

If $G$ is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings (a{\em Fulkerson covering}) with the property that every edge of $G$ is contained in exactly two of them. A consequence of the Fulkerson conjecture would be that every bridgeless cubic graph has 3 perfect matchings with empty intersection (this problem is known as the Fan Raspaud Conjecture). A {\em FR-triple} is a set of 3 such perfect matchings. We show here how to derive a Fulkerson covering from two FR-triples. Moreover, we give a simple proof that the Fulkerson conjecture holds true for some classes of well known snarks.Comment: Accepted for publication in Discussiones Mathematicae Graph Theory; Discussiones Mathematicae Graph Theory (2010) xxx-yy

Data-Flow-Based Normalization Generation Algorithm of R1CS for Zero-Knowledge Proof

The communities of blockchains and distributed ledgers have been stirred up by the introduction of zero-knowledge proofs (ZKPs). Originally designed to solve privacy issues, ZKPs have now evolved into an effective remedy for scalability concerns and are applied in Zcash (internet money like Bitcoin). To enable ZKPs, Rank-1 Constraint Systems (R1CS) offer a verifier for bi-linear equations. To accurately and efficiently represent R1CS, several language tools like Circom, Noir, and Snarky have been proposed to automate the compilation of advanced programs into R1CS. However, due to the flexible nature of R1CS representation, there can be significant differences in the compiled R1CS forms generated from circuit language programs with the same underlying semantics. To address this issue, this paper uses a data-flow-based R1CS paradigm algorithm, which produces a standardized format for different R1CS instances with identical semantics. By using the normalized R1CS format circuits, the complexity of circuits' verification can be reduced. In addition, this paper presents an R1CS normalization algorithm benchmark, and our experimental evaluation demonstrates the effectiveness and correctness of our methods.Comment: 10pages, 8 figures, a shorter version is accepted by PRDC 202

ARPA Whitepaper

We propose a secure computation solution for blockchain networks. The correctness of computation is verifiable even under malicious majority condition using information-theoretic Message Authentication Code (MAC), and the privacy is preserved using Secret-Sharing. With state-of-the-art multiparty computation protocol and a layer2 solution, our privacy-preserving computation guarantees data security on blockchain, cryptographically, while reducing the heavy-lifting computation job to a few nodes. This breakthrough has several implications on the future of decentralized networks. First, secure computation can be used to support Private Smart Contracts, where consensus is reached without exposing the information in the public contract. Second, it enables data to be shared and used in trustless network, without disclosing the raw data during data-at-use, where data ownership and data usage is safely separated. Last but not least, computation and verification processes are separated, which can be perceived as computational sharding, this effectively makes the transaction processing speed linear to the number of participating nodes. Our objective is to deploy our secure computation network as an layer2 solution to any blockchain system. Smart Contracts\cite{smartcontract} will be used as bridge to link the blockchain and computation networks. Additionally, they will be used as verifier to ensure that outsourced computation is completed correctly. In order to achieve this, we first develop a general MPC network with advanced features, such as: 1) Secure Computation, 2) Off-chain Computation, 3) Verifiable Computation, and 4)Support dApps' needs like privacy-preserving data exchange

Usalduse vähendamine ja turvalisuse parandamine zk-SNARK-ides ja kinnitusskeemides

Väitekirja elektrooniline versioon ei sisalda publikatsioonezk-SNARK-id on tõhusad ja praktilised mitteinteraktiivsed tõestussüsteemid, mis on konstrueeritud viitestringi mudelis ning tänu kompaktsetele tõestustele ja väga tõhusale verifitseeritavusele on need laialdaselt kasutusele võetud suuremahulistes praktilistes rakendustes. Selles töös uurime zk-SNARK-e kahest vaatenurgast: nende usalduse vähendamine ja turvalisuse tugevdamine. Esimeses suunas uurime kui palju saab vähendada usaldust paaristuspõhiste zk-SNARK-ide puhul ilma nende tõhusust ohverdamata niiviisi, et kasutajad saavad teatud turvataseme ka siis kui seadistusfaas tehti pahatahtlikult või kui avalikustati seadistusfaasi salajane teave. Me pakume välja mõned tõhusad konstruktsioonid, mis suudavad takistada zk-SNARK-i seadistusfaasi ründeid ja mis saavutavad senisest tugevama turvataseme. Näitame ka seda, et sarnased tehnikad võimaldavad leevendada usaldust tagauksega kinnitusskeemides, mis on krüptograafiliste primitiivide veel üks silmapaistev perekond ja mis samuti nõub usaldatud seadistusfaasi. Teises suunas esitame mõned tõhusad konstruktsioonid, mis tagavad parema turvalisuse minimaalsete lisakuludega. Mõned esitatud konstruktsioonidest võimaldavad lihtsustada praegusi TK-turvalisi protokolle, nimelt privaatsust säilitavate nutilepingusüsteemide Hawk ja Gyges konstruktsiooni, ja parandada nende tõhusust. Uusi konstruktsioone saab aga otse kasutada uutes protokollides, mis soovivad kasutada zk-SNARK-e. Osa väljapakutud zk-SNARK-e on implementeeritud teegis Libsnark ja empiirilised tulemused kinnitavad, et usalduse vähendamiseks või suurema turvalisuse saavutamiseks on arvutuslikud lisakulud väikesed.Zero-knowledge Succinct Non-interactive ARguments of Knowledge (zk-SNARKs) are an efficient family of NIZK proof systems that are constructed in the Common Reference String (CRS) model and due to their succinct proofs and very efficient verification, they are widely adopted in large-scale practical applications. In this thesis, we study zk-SNARKs from two perspectives, namely reducing trust and improving security in them. In the first direction, we investigate how much one can mitigate trust in pairing-based zk-SNARKs without sacrificing their efficiency. In such constructions, the parties of protocol will obtain a certain level of security even if the setup phase was done maliciously or the secret information of the setup phase was revealed. As a result of this direction, we present some efficient constructions that can resist against subverting of the setup phase of zk-SNARKs and achieve a certain level of security which is stronger than before. We also show that similar techniques will allow us to mitigate the trust in the trapdoor commitment schemes that are another prominent family of cryptographic primitives that require a trusted setup phase. In the second direction, we present some efficient constructions that achieve more security with minimal overhead. Some of the presented constructions allow to simplify the construction of current UC-secure protocols and improve their efficiency. New constructions can be directly deployed in any novel protocols that aim to use zk-SNARKs. Some of the proposed zk-SNARKs are implemented in Libsnark, the state-of-the-art library for zk-SNARKs, and empirical experiences confirm that the computational cost to mitigate the trust or to achieve more security is practical.https://www.ester.ee/record=b535927

Policing “Fake” femininity:Authenticity, accountability, and influencer antifandom

Although social media influencers enjoy a coveted status position in the popular imagination, their requisite career visibility opens them up to intensified public scrutiny and—more pointedly—networked hate and harassment. Key repositories of such critique are influencer “hateblogs”—forums for anti-fandom often dismissed as frivolous gossip or, alternatively, denigrated as conduits for cyberbullying and misogyny. This article draws upon an analysis of a women-dominated community of anti-fans, Get Off My Internets (GOMIBLOG), to show instead how influencer hateblogs are discursive sites of gendered authenticity policing. Findings reveal that GOMI participants wage patterned accusations of duplicity across three domains where women influencers seemingly “have it all”: career, relationships, and appearance. But while antifans’ policing of “fake” femininity may purport to dismantle the artifice of social media self-enterprise, such expressions fail to advance progressive gender politics, as they target individual-level—rather than structural—inequities

Deploying ZKP Frameworks with Real-World Data: Challenges and Proposed Solutions

Zero-knowledge proof (ZKP) frameworks have the potential to revolutionize the handling of sensitive data in various domains. However, deploying ZKP frameworks with real-world data presents several challenges, including scalability, usability, and interoperability. In this project, we present Fact Fortress, an end-to-end framework for designing and deploying zero-knowledge proofs of general statements. Our solution leverages proofs of data provenance and auditable data access policies to ensure the trustworthiness of how sensitive data is handled and provide assurance of the computations that have been performed on it. ZKP is mostly associated with blockchain technology, where it enhances transaction privacy and scalability through rollups, addressing the data inherent to the blockchain. Our approach focuses on safeguarding the privacy of data external to the blockchain, with the blockchain serving as publicly auditable infrastructure to verify the validity of ZK proofs and track how data access has been granted without revealing the data itself. Additionally, our framework provides high-level abstractions that enable developers to express complex computations without worrying about the underlying arithmetic circuits and facilitates the deployment of on-chain verifiers. Although our approach demonstrated fair scalability for large datasets, there is still room for improvement, and further work is needed to enhance its scalability. By enabling on-chain verification of computation and data provenance without revealing any information about the data itself, our solution ensures the integrity of the computations on the data while preserving its privacy

LaBRADOR: Compact Proofs for R1CS from Module-SIS

The most compact quantum-safe proof systems for large circuits are PCP-type systems such as Ligero, Aurora, and Shockwave, that only use weak cryptographic assumptions, namely hash functions modeled as random oracles. One would expect that by allowing for stronger assumptions, such as the hardness of Module-SIS, it should be possible to design more compact proof systems. But alas, despite considerable progress in lattice-based proofs, no such proof system was known so far. We rectify this situation by introducing a Lattice-Based Recursively Amortized Demonstration Of R1CS (LaBRADOR), with more compact proof sizes than known hash-based proof systems, both asymptotically and concretely for all relevant circuit sizes. LaBRADOR proves knowledge of a solution for an R1CS mod $2^{64}+1$ with $2^{20}$ constraints, with a proof size of only 58 KB, an order of magnitude more compact than previous quantum-safe proofs

ZEN: An Optimizing Compiler for Verifiable, Zero-Knowledge Neural Network Inferences

We present ZEN, the first optimizing compiler that generates efficient verifiable, zero-knowledge neural network inference schemes. ZEN generates two schemes: ZEN$_{acc}$ and ZEN$_{infer}$. ZEN$_{acc}$ proves the accuracy of a committed neural network model; ZEN$_{infer}$ proves a specific inference result. Used in combination, these verifiable computation schemes ensure both the privacy of the sensitive user data as well as the confidentiality of the neural network models. However, directly using these schemes on zkSNARKs requires prohibitive computational cost. As an optimizing compiler, ZEN introduces two kinds of optimizations to address this issue: first, ZEN incorporates a new neural network quantization algorithm that incorporate two R1CS friendly optimizations which makes the model to be express in zkSNARKs with less constraints and minimal accuracy loss; second, ZEN introduces a SIMD style optimization, namely stranded encoding, that can encoding multiple 8bit integers in large finite field elements without overwhelming extraction cost. Combining these optimizations, ZEN produces verifiable neural network inference schemes with ${\bf 5.43} \sim {\bf 22.19} \times$ ($15.35 \times$ on average) less R1CS constraints