Interactive Proof Research Articles

Research on Blockchain Interactive Zero Knowledge Proof Privacy Protection Scheme Based on Improved Paillier Homomorphic Encryption

In the context of the digital age, data privacy and security issues are increasingly prominent. Blockchain technology plays an important role in data sharing due to its transparency and immutability, but it also brings the risk of privacy leakage. Zero knowledge proof technology provides a solution for verifying data correctness without exposing data content, which is particularly important for blockchain as it can ensure the validity and compliance of transactions while protecting user privacy. Although zero knowledge proof is quite mature in theory, its application in blockchain systems still faces challenges such as computational efficiency, complexity of smart contracts, and system compatibility. This study aims to propose a privacy protection scheme that supports interactive zero knowledge proof by improving the homomorphic encryption Paillier algorithm, in order to enhance the privacy protection capability of blockchain systems and maintain system efficiency and security. The study will adopt an interdisciplinary approach, combining cryptography, computer science, and network security theory, to deeply analyze the application effect of zero knowledge proof technology in blockchain, explore its optimization space and applicability.

Quantum Computational Complexity and Symmetry

Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for BQP (bounded-error quantum polynomial time), QMA (quantum Merlin-Arthur), QSZK (quantum statistical zero-knowledge), QIP(2) (two-message quantum interactive proofs), QIP_EB(2) (two-message quantum interactive proofs restricted to entanglement-breaking provers), and QIP (quantum interactive proofs), thus spanning the prominent classes of the quantum interactive proof hierarchy and forging a non-trivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and QAM, while leaving it as an intriguing open question to determine whether these problems are complete for these classes.

Special Soundness Revisited

We generalize and abstract the problem of extracting a witness from a prover of a special sound protocol into a combinatorial problem induced by a sequence of matroids and a predicate, and present a parametrized algorithm for solving this problem. The parametrization provides a tight tradeoff between the running time and the extraction error of the algorithm, which allows optimizing the parameters to minimize: the soundness error for interactive proofs, or the extraction time for proofs of knowledge. In contrast to previous work we bound the distribution of the running time and not only the expected running time. Tail bounds give a tighter analysis when applied recursively and a concentrated running time.

The Role of Social Network Marketing on Consumer Engagement and Purchase Intention: A Review

This paper explores the influence of social network marketing on consumer engagement and purchase intentions. As a vital component of modern marketing, social network marketing leverages social media platforms to promote products and services, becoming a primary strategy for businesses to attract and interact with consumers. Through a literature review and case studies, this paper delves into the mechanisms by which social network marketing enhances consumer engagement, including the roles of social interaction, user-generated content, and social proof. Additionally, it examines how personalized marketing strategies and social recommendations within social network marketing influence consumers' purchase intentions. Finally, the paper discusses the limitations of current research and proposes future research directions to deepen the understanding of social network marketing's impact.

Exploring modes of microbial interactions with implications for methane cycling.

Methanotrophs are the sole biological sink of methane. Volatile organic compounds (VOCs) produced by heterotrophic bacteria have been demonstrated to be a potential modulating factor of methane consumption. Here, we identify and disentangle the impact of the volatolome of heterotrophic bacteria on the methanotroph activity and proteome, using Methylomonas as model organism. Our study unambiguously shows how methanotrophy can be influenced by other organisms without direct physical contact. This influence is mediated by VOCs (e.g. dimethyl-polysulphides) or/and CO2 emitted during respiration, which can inhibit growth and methane uptake of the methanotroph, while other VOCs had a stimulating effect on methanotroph activity. Depending on whether the methanotroph was exposed to the volatolome of the heterotroph or to CO2, proteomics revealed differential protein expression patterns with the soluble methane monooxygenase being the most affected enzyme. The interaction between methanotrophs and heterotrophs can have strong positive or negative effects on methane consumption, depending on the species interacting with the methanotroph. We identified potential VOCs involved in the inhibition while positive effects may be triggered by CO2 released by heterotrophic respiration. Our experimental proof of methanotroph-heterotroph interactions clearly calls for detailed research into strategies on how to mitigate methane emissions.

Lattice-Based Polynomial Commitments: Towards Asymptotic and Concrete Efficiency

Polynomial commitments schemes are a powerful tool that enables one party to commit to a polynomial p of degree d, and prove that the committed function evaluates to a certain value z at a specified point u, i.e. p(u)=z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p(u) = z$$\\end{document}, without revealing any additional information about the polynomial. Recently, polynomial commitments have been extensively used as a cryptographic building block to transform polynomial interactive oracle proofs (PIOPs) into efficient succinct arguments. In this paper, we propose a lattice-based polynomial commitment that achieves succinct proof size and verification time in the degree d of the polynomial. Extractability of our scheme holds in the random oracle model under a natural ring version of the BASIS assumption introduced by Wee and Wu (EUROCRYPT 2023). Unlike recent constructions of polynomial commitments by Albrecht et al. (CRYPTO 2022), and by Wee and Wu, we do not require any expensive preprocessing steps, which makes our scheme particularly attractive as an ingredient of a PIOP compiler for succinct arguments. We further instantiate our polynomial commitment, together with the Marlin PIOP (EUROCRYPT 2020), to obtain a publicly-verifiable trusted-setup succinct argument for Rank-1 Constraint System (R1CS). Performance-wise, we achieve 17\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$17$$\\end{document}MB proof size for 220\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{20}$$\\end{document} constraints, which is 15\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$15$$\\end{document}X smaller than currently the only publicly-verifiable lattice-based SNARK proposed by Albrecht et al.

Live Verification in an Interactive Proof Assistant

Live Verification in an Interactive Proof Assistant

Local Proofs Approaching the Witness Length

Interactive oracle proofs (IOPs) are a hybrid between interactive proofs and PCPs. In an IOP, the prover is allowed to interact with a verifier (like in an interactive proof) by sending relatively long messages to the verifier, who in turn is only allowed to query a few of the bits that were sent (like in a PCP). Efficient IOPs are currently at the core of leading practical implementations of highly efficient proof-systems. In this work we construct, for a large class of NP relations, IOPs in which the communication complexity approaches the witness length. More precisely, for any NP relation for which membership can be decided in polynomial-time with bounded polynomial space (i.e., space n ξ for some sufficiently small constant ξ > 0; e.g., SAT, Hamiltonicity, Clique, Vertex-Cover) and for any constant γ > 0, we construct an IOP with communication complexity (1 + γ) ⋅ n , where n is the original witness length. The number of rounds, as well as the number of queries made by the IOP verifier, are constant. This result improves over prior works on short IOPs/PCPs in two ways. First, the communication complexity in these short IOPs is proportional to the complexity of verifying the NP witness, which can be polynomially larger than the witness size. Second, even ignoring the difference between witness length and non-deterministic verification time, prior works incur (at the very least) a large constant multiplicative overhead to the communication complexity. In particular, as a special case, we also obtain an IOP for CircuitSAT with communication complexity (1 + γ) ⋅ t , for circuits of size t and any constant γ > 0. This improves upon the prior state-of-the-art work of Ben Sasson et al. (ICALP, 2017) who construct an IOP for CircuitSAT with communication length c ⋅ t for a large (unspecified) constant c ≥ 1. Our proof leverages the local testability and (relaxed) local correctability of high-rate tensor codes, as well as their support of a sumcheck-like procedure. In particular, we bypass the barrier imposed by the low rate of multiplication codes (e.g., Reed–Solomon, Reed–Muller, or AG codes)—a key building block of all known short PCP/IOP constructions.

Revolutionizing Cybersecurity with Machine Learning: A Comprehensive Review and Future Directions

In the realm of computing, data science has revolutionized cybersecurity operations and technologies. The key to creating automated and intelligent security systems lies in extracting patterns or insights from cybersecurity data and building data-driven models. Data science, encompassing various scientific approaches, machine learning techniques, processes, and systems, studies real-world occurrences through data analysis. Machine learning techniques, known for their flexibility, scalability, and adaptability to new and unknown challenges, have been applied across many scientific fields. Cybersecurity is rapidly expanding due to significant advancements in social networks, cloud and web technologies, online banking, mobile environments, smart grids, and more. Various machine learning techniques have effectively addressed a wide range of computer security issues. This article reviews several machine learning applications in cybersecurity, including phishing detection, network intrusion detection, keystroke dynamics authentication, cryptography, human interaction proofs, spam detection in social networks, smart meter energy consumption profiling, and security concerns associated with machine learning techniques themselves. The methodology involves collecting a large dataset of phishing and legitimate instances, extracting relevant features such as email headers, content, and URLs, and training a machine learning model using supervised learning algorithms. These models can effectively identify phishing emails and websites with high accuracy and low false positive rates. To enhance phishing detection, it is recommended to continuously update the training dataset to include new phishing techniques and employ ensemble methods that combine multiple machine learning models for improved performance

Examining Schnorrs protocol in the context of zero-knowledge proofs

The rise of technology has brought with it a heightened awareness of the necessity to shield personal data and maintain exclusive access to specific knowledge. A notable solution that emerged from this consciousness is Zero-Knowledge Proofs (ZKPs) and, more specifically, Schnorrs Protocol. Historically, Zero-Knowledge Proofs have a compelling lineage, tracing their roots back to the fervent discussions among cryptographers aiming to achieve a balance between information sharing and privacy. ZKPs are cryptographic methods that allow one party to prove to another that a statement is true, without revealing any specific information about the statement itself. In the midst of these developments, Schnorrs Protocol emerged as a renowned interactive proof system. It possesses an intuitive structure that has made it pivotal in the enhancement of digital security. The typical flow of Schnorrs Protocol begins with the prover sending a commitment to the verifier. The verifier then sends a random challenge back to the prover, who, in turn, produces a response. Whats captivating is that the verifier can ascertain the validity of the proof without gaining insight into the underlying secret. Interactive Schnorrs Protocol involves real-time back-and-forth communication between the prover and verifier. On the other hand, the non-interactive version eliminates this need by using a cryptographic hash function, thereby streamlining the process.

Simultaneous assessment of mechanical and electrical function in Langendorff-perfused ex-vivo mouse hearts.

The Langendorff-perfused ex-vivo isolated heart model has been extensively used to study cardiac function for many years. However, electrical and mechanical function are often studied separately-despite growing proof of a complex electro-mechanical interaction in cardiac physiology and pathology. Therefore, we developed an isolated mouse heart perfusion system that allows simultaneous recording of electrical and mechanical function. Isolated mouse hearts were mounted on a Langendorff setup and electrical function was assessed via a pseudo-ECG and an octapolar catheter inserted in the right atrium and ventricle. Mechanical function was simultaneously assessed via a balloon inserted into the left ventricle coupled with pressure determination. Hearts were then submitted to an ischemia-reperfusion protocol. At baseline, heart rate, PR and QT intervals, intra-atrial and intra-ventricular conduction times, as well as ventricular effective refractory period, could be measured as parameters of cardiac electrical function. Left ventricular developed pressure (DP), left ventricular work (DP-heart rate product) and maximal velocities of contraction and relaxation were used to assess cardiac mechanical function. Cardiac arrhythmias were observed with episodes of bigeminy during which DP was significantly increased compared to that of sinus rhythm episodes. In addition, the extrasystole-triggered contraction was only 50% of that of sinus rhythm, recapitulating the "pulse deficit" phenomenon observed in bigeminy patients. After ischemia, the mechanical function significantly decreased and slowly recovered during reperfusion while most of the electrical parameters remained unchanged. Finally, the same electro-mechanical interaction during episodes of bigeminy at baseline was observed during reperfusion. Our modified Langendorff setup allows simultaneous recording of electrical and mechanical function on a beat-to-beat scale and can be used to study electro-mechanical interaction in isolated mouse hearts.

Education-oriented Proof Assistant Based on Calculational Logic: Proof Theory Algorithms and Assessment Experience

This work presents an interactive proof assistant, based on Dijkstra-Scholten logic, aimed at teaching logic and discrete mathematics in higher education. The assistant interface is web and easy to use, since inferences can be made just with the mouse. The educational experience is presented showing a correlation between the grades of the assessments in class and those made with the application web. Additionally, an algorithm proof theory for the Disjktra-Scholten system are made and the following algorithms are shown: 1) a versatile printing algorithm that allows the administrator to configure the symbols of a theory, by assigning the desired presentation with LaTeX; 2) An algorithm, based on Broda and Damas combinators, for generate monotonic or anti monotonic inferences in the Dijkstra-Scholten logic; 3) An algorithm to generate the proofs of dual theorems in Boolean Algebra theory.

Flexible Instruction-Set Semantics via Abstract Monads (Experience Report)

Instruction sets, from families like x86 and ARM, are at the center of many ambitious formal-methods projects. Many verification, synthesis, programming, and debugging tools rely on formal semantics of instruction sets, but different tools can use semantics in rather different ways. The best-known work applying single semantics across diverse tools relies on domain-specific languages like Sail, where the language and its translation tools are specialized to the realm of instruction sets. In the context of the open RISC-V instruction-set family, we decided to explore a different approach, with semantics written in a carefully chosen subset of Haskell. This style does not depend on any new language translators, relying instead on parameterization of semantics over type-class instances. We have used a single core semantics to support testing, interactive proof, and model checking of both software and hardware, demonstrating that monads and the ability to abstract over them using type classes can support pleasant prototyping of ISA semantics.

Fiat–Shamir Transformation of Multi-Round Interactive Proofs (Extended Version)

The celebrated Fiat–Shamir transformation turns any public-coin interactive proof into a non-interactive one, which inherits the main security properties (in the random oracle model) of the interactive version. While originally considered in the context of 3-move public-coin interactive proofs, i.e., so-called varSigma -protocols, it is now applied to multi-round protocols as well. Unfortunately, the security loss for a (2mu + 1)-move protocol is, in general, approximately Q^mu , where Q is the number of oracle queries performed by the attacker. In general, this is the best one can hope for, as it is easy to see that this loss applies to the mu -fold sequential repetition of varSigma -protocols, but it raises the question whether certain (natural) classes of interactive proofs feature a milder security loss. In this work, we give positive and negative results on this question. On the positive side, we show that for (k_1, ldots , k_mu )-special-sound protocols (which cover a broad class of use cases), the knowledge error degrades linearly in Q, instead of Q^mu . On the negative side, we show that for t-fold parallel repetitions of typical (k_1, ldots , k_mu )-special-sound protocols with t ge mu (and assuming for simplicity that t and Q are integer multiples of mu ), there is an attack that results in a security loss of approximately frac{1}{2} Q^mu /mu ^{mu +t}.

Interactive cryptographic proofs of quantumness using mid-circuit measurements

Interactive cryptographic proofs of quantumness using mid-circuit measurements

A Machine Proof System of Point Geometry Based on Coq

An important development in geometric algebra in recent years is the new system known as point geometry, which treats points as direct objects of operations and considerably simplifies the process of geometric reasoning. In this paper, we provide a complete formal description of the point geometry theory architecture and give a rigorous and reliable formal verification of the point geometry theory based on the theorem prover Coq. Simultaneously, a series of tactics are also designed to assist in the proof of geometric propositions. Based on the theoretical architecture and proof tactics, a universal and scalable interactive point geometry machine proof system, PointGeo, is built. In this system, any arbitrary point-geometry-solvable geometric statement may be proven, along with readable information about the solution’s procedure. Additionally, users may augment the rule base by adding trustworthy rules as needed for certain issues. The implementation of the system expands the library of Coq resources on geometric algebra, which will become a significant research foundation for the fields of geometric algebra, computer science, mathematics education, and other related fields.

Guest Column: New ways of studying the BPP = P conjecture

What's new in the world of derandomization? Questions about pseudorandomness and derandomization have been driving progress in complexity theory for many decades. In this survey we will describe new approaches to the BPP = P conjecture from recent years, as well as new questions, algorithmic approaches, and ways of thinking. For example: Do we really need pseudorandom generators for derandomization, or can we get away with weaker objects? Can we prove free lunch theorems, eliminating randomness with zero computational overhead? What hardness assumptions are necessary and sufficient for derandomization? And how do new advances in this area interact with progress in cryptography and in interactive proof systems?

Machine Learning in Cybersecurity: Techniques and Challenges

In the computer world, data science is the force behind the recent dramatic changes in cybersecurity's operations and technologies. The secret to making a security system automated and intelligent is to extract patterns or insights related to security incidents from cybersecurity data and construct appropriate data-driven models. Data science, also known as diverse scientific approaches, machine learning techniques, processes, and systems, is the study of actual occurrences via the use of data. Due to its distinctive qualities, such as flexibility, scalability, and the capability to quickly adapt to new and unknowable obstacles, machine learning techniques have been used in many scientific fields. Due to notable advancements in social networks, cloud and web technologies, online banking, mobile environments, smart grids, etc., cyber security is a rapidly expanding sector that requires a lot of attention. Such a broad range of computer security issues have been effectively addressed by various machine learning techniques. This article covers several machine-learning applications in cyber security. Phishing detection, network intrusion detection, keystroke dynamics authentication, cryptography, human interaction proofs, spam detection in social networks, smart meter energy consumption profiling, and security concerns with machine learning techniques themselves are all covered in this study. The methodology involves collecting a large dataset of phishing and legitimate instances, extracting relevant features such as email headers, content, and URLs, and training a machine-learning model using supervised learning algorithms. Machine learning models can effectively identify phishing emails and websites with high accuracy and low false positive rates. To enhance phishing detection, it is recommended to continuously update the training dataset to include new phishing techniques and to employ ensemble methods that combine multiple machine learning models for better performance.

A Flexible Approach to Multi-party Business Process Execution on Blockchain

In modern business scenarios, more and more organisations have to deal with the critical requirements of trustworthiness and flexibility, when collaborating in multi-party business processes. This calls for new kinds of systems able to manage collaborative processes in untrusted and dynamic environments. Concerning the collaborative perspective, the Business Process Management discipline has provided effective and standardised solutions for a long time, now. Regarding the trustworthiness perspective, blockchain is advocated as one of the most prominent technologies to guarantee trust in a multi-party setting. However, while the immutability of blockchain provides transparent and secure proof of past business interactions, it hinders the flexibility of the business process execution, as the business logic regulating the process execution is immutably stored in the blockchain. On the other hand, flexibility is a property that is becoming crucial in such a setting due to the high dynamism of the business scenarios. In fact, it permits to modify a process at run-time to deal with internal or external changes. In this paper, we face this issue by proposing an architecture for the flexible blockchain-based execution of multi-party business processes. In our approach, business processes are modelled by BPMN choreography diagrams translated into code, whose execution state is then stored in the blockchain. Flexibility is achieved by decoupling the business process’s logic from its execution state, thus allowing run-time changes to the process execution without losing the fundamental properties of trust provided by the blockchain. To show the effectiveness of our approach, we provide a prototypical implementation, called FlexChain, and we use it on a case study from the healthcare application domain. The results obtained by the analysis of cost for the reported case study show the feasibility of the approach. In particular, major costs to sustain relate to one-time operations, such as the deployment and the run-time update of the model, while the most frequent actions are quite efficient.

Proof Automation for Linearizability in Separation Logic

Recent advances in concurrent separation logic enabled the formal verification of increasingly sophisticated fine-grained ( i.e. , lock-free) concurrent programs. For such programs, the golden standard of correctness is linearizability , which expresses that concurrent executions always behave as some valid sequence of sequential executions. Compositional approaches to linearizability (such as contextual refinement and logical atomicity) make it possible to prove linearizability of whole programs or compound data structures ( e.g. , a ticket lock) using proofs of linearizability of their individual components ( e.g. , a counter). While powerful, these approaches are also laborious—state-of-the-art tools such as Iris, FCSL, and Voila all require a form of interactive proof. This paper develops proof automation for contextual refinement and logical atomicity in Iris. The key ingredient of our proof automation is a collection of proof rules whose application is directed by both the program and the logical state. This gives rise to effective proof search strategies that can prove linearizability of simple examples fully automatically. For more complex examples, we ensure the proof automation cooperates well with interactive proof tactics by minimizing the use of backtracking. We implement our proof automation in Coq by extending and generalizing Diaframe, a proof automation extension for Iris. While the old version (Diaframe 1.0) was limited to ordinary Hoare triples, the new version (Diaframe 2.0) is extensible in its support for program verification styles: our proof search strategies for contextual refinement and logical atomicity are implemented as modules for Diaframe 2.0. We evaluate our proof automation on a set of existing benchmarks and novel proofs, showing that it provides significant reduction of proof work for both approaches to linearizability.