This work presents a mathematical solution to data privacy and integrity issues in Split Learning which uses Homomorphic Encryption (HE) and Zero-Knowledge Proofs (ZKP). It allows calculations to be conducted on encrypted data, keeping the data private, while ZKP ensures the correctness of these calculations without revealing the underlying data. Our proposed system, HavenSL, combines HE and ZKP to provide strong protection against attacks. It uses Discrete Cosine Transform (DCT) to analyze model updates in the frequency domain to detect unusual changes in parameters. HavenSL also has a rollback feature that brings the system back to a verified state if harmful changes are detected. Experiments on CIFAR-10, MNIST, and Fashion-MNIST datasets show that using Homomorphic Encryption and Zero-Knowledge Proofs during training is feasible and accuracy is maintained. This mathematical-based approach shows how crypto-graphic can protect decentralized learning systems. It also proves the practical use of HE and ZKP in secure, privacy-aware collaborative AI.
In their recent breakthrough result, Slofstra and the second author show that there is a two-player one-round perfect zero-knowledge MIP* protocol for RE (STOC'24). We build on their result to show that there exists a succinct two-player one-round perfect zero-knowledge MIP* protocol for RE against dishonest verifiers with polylog question size and O(1) answer size, or with O(1) question size and polylog answer size. To prove our result, we study the three central compression techniques underlying the MIP*=RE proof (Ji et al. '20): question reduction, oracularization, and answer reduction. We show that question reduction preserves the perfect (as well as statistical and computational) zero-knowledge properties of the original protocol against dishonest verifiers, and oracularization and answer reduction preserve the perfect (as well as statistical and computational) zero-knowledge properties of the original protocol against honest verifiers. Secondly, we show that every constraint-constraint binary constraint system (BCS) nonlocal game, which provides a quantum information characterization of MIP*, can be converted to a synchronous constraint-variable BCS game to preserve perfect completeness for our compression. Lastly, we present a parametrized perfect-zero-knowledge transformation of MIP* protocols, which generalizes the transformation in (Slofstra and Kieran STOC'24) . This transformation allows us to preserve the zero-knowledge property against dishonest verifiers in the recursively oracularized protocols in our compression.
Lucien K. L. Ng, Pedro Moreno-Sánchez, Mohsen Minaei, Panagiotis Chatzigiannis · 6 authors
Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) schemes have gained significant adoption in privacy-preserving applications, decentralized systems (e.g., blockchain), and verifiable computation due to their efficiency. However, the most efficient zk-SNARKs often rely on a one-time trusted setup to generate a public parameter, often known as the ``Powers of Tau" (PoT) string. The leakage of the secret parameter, $τ$, in the string would allow attackers to generate false proofs, compromising the soundness of all zk-SNARK systems built on it. Prior proposals for decentralized setup ceremonies have utilized blockchain-based smart contracts to allow any party to contribute randomness to $τ$ while also preventing censorship of contributions. For a PoT string of $d$-degree generated by the randomness of $m$ contributors, these solutions required a total of $O(md)$ on-chain operations (i.e., in terms of both storage and cryptographic operations). These operations primarily consisted of costly group operations, particularly scalar multiplication on pairing curves, which discouraged participation and limited the impact of decentralization In this work, we present Lite-PoT, which includes two key protocols designed to reduce participation costs: \emph{(i)} a fraud-proof protocol to reduce the number of expensive on-chain cryptographic group operations to $O(1)$ per contributor. Our experimental results show that (with one transaction per update) our protocol enables decentralized ceremonies for PoT strings up to a $2^{15}$ degree, an $\approx 16x$ improvement over existing on-chain solutions; \emph{(ii)} a proof aggregation technique that batches $m$ randomness contributions into one on-chain update with only $O(d)$ on-chain operations, independent of $m$. This significantly reduces the monetary cost of on-chain updates by $m$-fold via amortization.
This comprehensive article explores recent advancements in privacy-preserving technologies within artificial intelligence systems, focusing on five key approaches: federated learning, differential privacy, homomorphic encryption, privacy-preserving machine learning (PPML), and zero-knowledge proofs. The article examines how these technologies address critical privacy challenges in machine learning environments while maintaining model performance and utility. The article highlights the implementation of these approaches across various domains, particularly in healthcare and financial services, demonstrating their effectiveness in protecting sensitive data throughout the machine learning lifecycle. The article reveals how these technologies complement each other to create robust privacy protection frameworks while enabling organizations to leverage the power of AI without compromising data confidentiality.
We present a communication-efficient zero-knowledge proof of knowledge for the factorization of Blum integers, a special class of integers of the form n = p q , where p and q are distinct prime numbers satisfying p ≡ q ≡ 3 mod 4 and p ≃ q ≃ n . Existing protocols for proving such statements often incur significant communication costs, especially when demonstrating that p and q are of nearly equal size. We leverage the MPC-in-the-head paradigm, a cryptographic technique that transforms secure multi-party computation protocols into efficient zero-knowledge proof systems. In our protocol, the prover uses additive sharing of p and q over the integers. This approach simplifies proving the size relationship p ≃ q ≃ n and the congruence p ≡ q ≡ 3 mod 4 without requiring costly range proofs. To verify the primality of p and q , we employ the Boneh-Franklin biprimality test. Our protocol achieves a significant reduction in communication complexity. For a 2048-bit integer n and 128-bit security, we construct a proof as small as 12.3 KB, with prover and verifier computational costs comparable to existing protocols that require over 131 KB.
Succinct arguments are proof systems that allow a powerful, but untrusted, prover to convince a weak verifier that an input x belongs to a language \(L \in \mathsf {NP}\) , with communication that is much shorter than the \(\mathsf {NP}\) witness. Such arguments, which grew out of the theory literature, are now drawing immense interest also in practice, where a key bottleneck that has arisen is the high computational cost of proving correctness. In this work, we address this problem by constructing succinct arguments for general computations, expressed as Boolean circuits (of bounded fan-in), with a strictly linear size prover. The soundness error of the protocol is an arbitrarily small constant. Prior to this work, succinct arguments were known with a quasi- linear size prover for general Boolean circuits or with linear-size only for arithmetic circuits, defined over large finite fields. In more detail, for every Boolean circuit \(C=C(x,w)\) , we construct an \(O(\log |C|)\) -round argument-system in which the prover can be implemented by a size \(O(|C|)\) Boolean circuit (given as input both the instance x and the witness w ), with arbitrarily small constant soundness error and using \(\mathrm{poly}(\lambda ,\log |C|)\) communication, where \(\lambda\) denotes the security parameter. The verifier can be implemented by a size \(O(|x|) + \mathrm{poly}(\lambda , \log |C|)\) circuit following a size \(O(|C|)\) private pre-processing step, or, alternatively, by using a purely public-coin protocol (with no pre-processing) with a size \(O(|C|)\) verifier. The protocol can be made zero-knowledge using standard techniques (and with similar parameters). The soundness of our protocol is computational and relies on the existence of collision resistant hash functions that can be computed by linear-size circuits, such as those proposed by Applebaum et al. (ITCS, 2017). At the heart of our construction is a new information-theoretic interactive oracle proof ( \(\mathsf {IOP}\) ), an interactive analog of a \(\mathsf {PCP}\) , for circuit satisfiability, with constant prover overhead. The improved efficiency of our \(\mathsf {IOP}\) is obtained by bypassing a barrier faced by prior \(\mathsf {IOP}\) constructions, which needed to (either explicitly or implicitly) encode the entire computation using a multiplication code.
Multi-scalar multiplication (MSM) is the primary building block in many pairing-based zero-knowledge proof (ZKP) systems. MSM at large scales has become the main bottleneck in ZKP implementations. Inspired by existing SIMD-accelerated work, we are focused on accelerating MSM computing efficiency using SIMD instructions in a single CPU environment. First, we propose a SIMD-accelerated MSM computing architecture with no write conflicts and constant memory overheads. This architecture utilizes multithreading to achieve task-level and loop-level parallelism and employs a three-tier buffer mechanism to maximize the utilization of the SIMD engine. Instanced with AVX512-IFMA instructions, we implement six SIMD elliptic curve arithmetic engines for different point addition in three coordinate systems and two groups. Moreover, we integrate our AVX-MSM implementation into the libsnark library, naming it AVX-ZK. In more detail, point deduplication and “Three-Stage” memory optimization are proposed to address problems existing in practical applications. Based on the RELIC library, our performance results on the BLS12-381 curve show that our AVX-MSM achieves up to 27.86x speedup over the most popular Pippenger algorithm. Compared with libsnark, our AVX-ZK implementation achieves over 11.53x (up to 20.26x) speedup under standard benchmarks.
Xander Pottier, Thomas De Ruijter, Jonas Bertels, Wouter Legiest · 6 authors
The Multi-Scalar Multiplication (MSM) is the main barrier to accelerating Zero-Knowledge applications. In recent years, hardware acceleration of this algorithm on both FPGA and GPU has become a popular research topic and the subject of a multi-million dollar prize competition (ZPrize). This work presents OPTIMSM: Optimized Processing Through Iterative Multi-Scalar Multiplication. This novel accelerator focuses on the acceleration of the MSM algorithm for any Elliptic Curve (EC) by improving upon the Pippenger algorithm. A new iteration technique is introduced to decouple the required buckets from the window size, resulting in fewer EC computations for the same on-chip memory resources. Furthermore, we combine known optimizations from the literature for the first time to achieve additional latency improvements. Our enhanced MSM implementation significantly reduces computation time, achieving a speedup of up to x12.77 compared to recent FPGA implementations. Specifically, for the BLS12-381 curve, we reduce the computation time for an MSM of size 224 to 914 ms using a single compute unit on the U55C FPGA or to 231 ms using four U55C devices. These results indicate a substantial improvement in efficiency, paving the way for more scalable and efficient Zero-Knowledge proof systems.
With the wide application of electric vehicles, smart robots and Internet of Things (IoT) devices, efficient scheduling of mobile charging systems has become an important research direction in smart energy management. However, the traditional cloud computing architecture is difficult to meet the requirements of low latency, high reliability and privacy protection, and the existing scheduling strategies still have challenges in terms of energy optimization, task balancing and dynamic adaptability. To this end, this paper proposes an intelligent mobile charging scheduling method that integrates edge computing and biomechanical modeling, constructs a biomechanical-based charging demand modeling and energy consumption analysis framework, and combines bionic optimization algorithms to achieve efficient path planning. Meanwhile, an edge computing architecture is adopted to optimize resource scheduling, and a federated learning mechanism is designed to enhance cross-domain data processing capability. To safeguard user privacy, a multi-level privacy protection mechanism is proposed, combining differential privacy, homomorphic encryption and zero-knowledge proof to ensure data security. Experimental results show that the method outperforms traditional methods in terms of task response time, energy consumption optimization, load balancing and privacy security, and can significantly improve the charging scheduling efficiency and provide effective technical support for large-scale distributed charging networks. The research results provide a theoretical basis and engineering practice reference for the application of smart charging networks, edge intelligent computing and privacy protection technology.
This Blockchain technology has revolutionized various industries by offering decentralized, secure, and immutable record-keeping. However, its adoption faces challenges such as scalability, energy consumption, and interoperability. As blockchain continues to evolve, researchers and developers have been working on innovative solutions to address these limitations and expand its practical applications. This paper explores recent advancements aimed at enhancing blockchain technology, focusing on key areas such as scalability solutions, energy-efficient consensus mechanisms, and interoperability protocols. It delves into techniques like sharding, Layer 2 solutions, and optimized consensus algorithms that improve transaction speed and reduce congestion. Additionally, it examines alternative consensus mechanisms like Proof-of-Stake (PoS) and Proof-of-Authority (PoA), which offer sustainability and efficiency without compromising security. Furthermore, the paper investigates interoperability solutions that enable seamless data exchange between different blockchain networks, such as atomic swaps, cross-chain communication protocols, and blockchain bridges. The study also highlights emerging trends that are set to shape the future of blockchain, including quantum-resistant cryptography, AI integration, Zero-Knowledge Proofs (ZKPs), and Blockchain-as-a-Service (BaaS). By addressing these enhancements, blockchain technology can achieve greater adoption, enabling new opportunities across various industries such as finance, supply chain, healthcare, governance, and IoT. The paper concludes with an analysis of the broader impact of blockchain innovations, emphasizing the need for continuous research and development to overcome existing barriers and unlock its full potential in modern digital infrastructure.
Abstract Privacy is one of the major security concerns. The zero-knowledge proof enables the transmission of data from the sender to the receiver without disclosing the actual content of the data. The proposed work uses the ZK-STARK (Zero-Knowledge Scalable Transparent ARgument of Knowledge) Algorithm for transaction privacy in the organic jaggery supply chain. The paper emphasizes a detailed mathematical model, involving two key participants: the prover (food processor) and the verifier (distributor). The prover calculates the polynomial for the problem, its composition polynomial, and provides its Merkle proof to the verifier. The verifier conducts queries to confirm and validate the accuracy of the information. Using the fast reed-solomon interactive oracle proofs protocol, the proof is validated. It measures performance as proof generation and verification time, proof size, and throughput. Plans involve increasing the domain size of this algorithm, varying the polynomial interpolation, and evaluating its performance measures by integrating it into Blockchain.
Open access
Blockchain Technology Applications and Security
Cryptography and Data Security
Advanced Steganography and Watermarking Techniques
This is the NIST Threshold Call, calling for public submissions of multi-party threshold schemes, and other related crypto-systems, to support the United States’ National Institute of Standards and Technology (NIST) in gathering a public body of reference materials unadvanced cryptography. In a threshold scheme, a reference cryptographic primitive (e.g., signing, encryption, decryption, key generation) is computed in a distributed manner, while its private/secret key is or becomes secret-shared across various parties. The threshold schemes submitted in reply to this call will be interchangeable with a reference no threshold primitive of interest, in the sense that their outputs can be used interchangeably in a subsequent operation. The primitives of interest are organized into various categories, across two classes: Class N, for selected NIST-specified primitives; and Class S, for special primitives that are not specified by NIST but are threshold friendly or have useful functional features. The scope of Class S also includes fully homomorphic encryption, zero-knowledge proofs, and auxiliary gadgets. This document specifies submission phases, and the requirements for submitting a package, including a technical specification, a reference implementation, and a report on experimental evaluation. A subsequent phase of public analysis will support the elaboration of a characterization report, which may help assess new interests beyond the cryptographic techniques currently standardized by NIST, and may include recommendations for future processes.
This publication presents a novel cryptographic commit scheme named DFTWS which is used to enable deterministic, fair, and transparent winner selection in an open source Proof-of-Useful-Work blockchain for High Energy Physics (HEP) called gophy. In gophy, instead of spamming hashing operations to mine blocks, miners are running computationally expensive Monte Carlo simulations to support a real-world HEP experiment with necessary data required to conduct the experiment. To preserve the usefulness property, block problems are defined over time by a Root Authority which is coordinated by a representative of a real-world HEP experiment. In order to be able to provide a transparent mechanism that allows for fair block winner selection from a list of eligible miners that solved a block problem, DFTWS is employed to achieve consensus between nodes. A strength of this approach is that every node is able to verify the fairness of the winner selection process. This publication provides an in-depth description and theoretical fairness analysis of DFTWS, a practical evaluation of its performance under real-world conditions and considerations of potential bottlenecks that can potentially occur as the node network scales. It also discusses a deployment strategy for using DFTWS on top of existing blockchain infrastructure like the Ethereum network. Additionally, theoretical performance aspects of DFTWS are compared with various state-of-the-art cryptographic commitment schemes and Zero-Knowledge Proof systems.
Active Learning (AL) is a machine learning technique where the model selectively queries the most informative data points for labeling by human experts. Integrating AL with crowdsourcing leverages crowd diversity to enhance data labeling but introduces challenges in consensus and privacy. This poster presents CrowdAL, a blockchain-empowered crowd AL system designed to address these challenges. CrowdAL integrates blockchain for transparency and a tamper-proof incentive mechanism, using smart contracts to evaluate crowd workers' performance and aggregate labeling results, and employs zero-knowledge proofs to protect worker privacy.
Dong Liu, Juan S. Giraldo, Peter Pálenský, Pedro P. Vergara
Model-free power flow calculation, driven by the rise of smart meter (SM) data and the lack of network topology, often relies on artificial intelligence neural networks (ANNs). However, training ANNs require vast amounts of SM data, posing privacy risks for households in distribution networks. To ensure customers' privacy during the SM data gathering and online sharing, we introduce a privacy preserving PF calculation framework, composed of two local strategies: a local randomisation strategy (LRS) and a local zero-knowledge proof (ZKP)-based data collection strategy. First, the LRS is used to achieve irreversible transformation and robust privacy protection for active and reactive power data, thereby ensuring that personal data remains confidential. Subsequently, the ZKP-based data collecting strategy is adopted to securely gather the training dataset for the ANN, enabling SMs to interact with the distribution system operator without revealing the actual voltage magnitude. Moreover, to mitigate the accuracy loss induced by the seasonal variations in load profiles, an incremental learning strategy is incorporated into the online application. The results across three datasets with varying measurement errors demonstrate that the proposed framework efficiently collects one month of SM data within one hour. Furthermore, it robustly maintains mean errors of 0.005 p.u. and 0.014 p.u. under multiple measurement errors and seasonal variations in load profiles, respectively.
Abstract As machine learning technologies advance rapidly across various domains, concerns over data privacy and model security have grown significantly. These challenges are particularly pronounced when models are trained and deployed on cloud platforms or third-party servers due to the computational resource limitations of users’ end devices. In response, zero-knowledge proof (ZKP) technology has emerged as a promising solution, enabling effective validation of model performance and authenticity in both training and inference processes without disclosing sensitive data. Thus, ZKP ensures the verifiability and security of machine learning models, making it a valuable tool for privacy-preserving AI. Although some research has explored the verifiable machine learning solutions that exploit ZKP, a comprehensive survey and summary of these efforts remains absent. This survey paper aims to bridge this gap by reviewing and analyzing all the existing Zero-Knowledge Machine Learning (ZKML) research from June 2017 to August 2025. We begin by introducing the concept of ZKML and outlining its ZKP algorithmic setups under three key categories: verifiable training, verifiable inference, and verifiable testing. Next, we provide a comprehensive categorization of existing ZKML research within these categories and analyze the works in detail. Furthermore, we explore the implementation challenges faced in this field and discuss the improvement works to address these obstacles. Additionally, we highlight several commercial applications of ZKML technology. Finally, we propose promising directions for future advancements in this domain.
With the widespread adoption of Zero-Knowledge Proof systems, particularly ZK-SNARK, the efficiency of proof generation, encompassing both the witness generation and proof computation phases, has become a significant concern. While substantial efforts have successfully accelerated proof computation, progress in optimizing witness generation remains limited, which inevitably hampers overall efficiency. In this paper, we propose Yoimiya, a scalable framework with pipeline, to optimize the efficiency in ZK-SNARK systems. First, Yoimiya introduces an automatic circuit partitioning algorithm that divides large circuits of ZK-SNARK into smaller subcircuits, the minimal computing units with smaller memory requirement, allowing parallel processing on multiple units. Second, Yoimiya decouples witness generation from proof computation, and achieves simultaneous executions over units from multiple circuits. Moreover, Yoimiya enables each phase scalable separately by configuring the resource distribution to make the time costs of the two phases aligned, maximizing the resource utilization. Experimental results confirmed that our framework effectively improves the resource utilization and proof generation speed.
Paula Heess, Stefanie Holly, Marc-Fabian Körner, Astrid Nieße · 9 authors
Abstract The need to harness the flexibility of small-scale assets for system stabilization, including redispatch, is growing rapidly with the increasing prevalence of distributed generation, such as photovoltaic systems and heavy loads, in particular heat pumps and electric vehicles. Integrating these resources into the redispatch process presents special requirements: On the one hand, building trust with the owners of such assets requires privacy and a reasonable degree of autonomy and engagement. On the other hand, besides the system’s scalability and robustness, the verifiability and traceability of provided data are essential for grid operators who depend on the reliable provision of redispatch services. To date, research and practice have encountered significant challenges in defining a system that enables the inclusion of decentralized flexibilities while satisfying necessary requirements. To that end, we present a novel conceptual system design that addresses these challenges by combining a multi-agent system (MAS) approach with verifiable information flows through digital self-sovereign identities (SSIs) and Zero-Knowledge-Proofs (ZKPs). Single agents, as edge devices, operate locally and autonomously, respecting customer preferences, while MAS provide the ability to design robust, reliable, and scalable systems. SSI enables agents to manage their data autonomously, while ZKPs are used to protect users’ privacy through selective data disclosure which allows the verification of the correctness of information without disclosing the underlying data. To validate the feasibility of this design, a case study is included to demonstrate the functionality of key sub-processes, such as baseline optimization, aggregation, and disaggregation, in a realistic scenario. This case study, supported by a prototype implementation, provides initial evidence of the concept’s soundness and lays the groundwork for future evaluation through extensive simulations and field testing. Together, the technologies included in the conceptual system design balance full transparency for grid operators with autonomy and data economy for asset owners.
This research introduces FoReChain (Fog-based Re-Encryption Chain), a blockchain-enabled proxy re-encryption (PRE) framework designed for secure, low-latency data sharing in fog-based IoT networks. The framework addresses key challenges related to data security, privacy, and performance in distributed environments, where traditional models face issues like high latency, limited scalability, and inefficient key management. FoReChain integrates blockchain with ECC-based proxy re-encryption to secure data without exposing original content. A delegated Practical Byzantine Fault Tolerance (d-PBFT) consensus mechanism ensures efficient transaction validation. The framework processes data at fog nodes, reducing delays commonly found in cloud-dependent models. Key management relies on time-based key updates stored immutably on the blockchain, while zero-knowledge proofs support secure, anonymous data sharing. The study evaluates FoReChain against FE-PRE and PREA models using metrics such as latency, throughput, scalability, blockchain consensus time, and adaptive policy effectiveness. Results show lower latency, higher throughput, and better adaptability in FoReChain, especially under heavy network conditions like smart healthcare and industrial IoT setups. FoReChain demonstrates secure data sharing, efficient resource utilization, and reliable key management in dynamic IoT environments. It offers consistent performance under varying loads, with improved scalability and data integrity maintained through decentralized validation.
This comprehensive technical article explores the evolution and architectural landscape of Decentralized Finance (DeFi), examining its transformation from initial implementations to the more sophisticated DeFi 2.0 ecosystem. It investigates the fundamental technical components, including smart contract infrastructure, consensus mechanisms, and cross-chain interoperability solutions that form the backbone of modern DeFi systems. Through a detailed examination of Layer-2 scaling solutions, risk management protocols, and AI-driven analytics, the article highlights how DeFi aggregators are revolutionizing user interactions with decentralized protocols. It further delves into emerging technologies such as zero-knowledge proofs and quantum-resistant cryptography, while addressing critical challenges in security, scalability, and mainstream adoption. By examining both technical innovations and integration challenges, this article provides insights into how DeFi is reshaping traditional financial systems through decentralized protocols and smart contracts while emphasizing the importance of balancing innovation with security and regulatory compliance in the evolving blockchain landscape.
Blockchain technology, with its decentralization as well as tamper-proof characteristics, has achieved wide application in major fields in recent years. However, because of the potential of privacy leakage that comes with its transparency, privacy protection technology has emerged as a key area of current blockchain research. The first step involves reviewing the blockchain's architecture and selecting a summary of the privacy threats posed by the four layers of the blockchain: data, network, transaction, and application. Next, it concentrates on describing the two more significant types of blockchain privacy protection technology: zero-knowledge proof and homomorphic encryption. The former is developed from its fundamental ideas, application scenarios in the blockchain, and performance and security analysis. Conversely, zero-knowledge proof is derived from three from three aspects of its basic concept, application in blockchain, and technical challenges; finally, the privacy protection technology in blockchain is summarized and a prediction of its future research direction development is made.
Currently, PAKE (Password Authenticated Key Exchange) protocols on lattice using a single-server architecture are widely applied. However, such protocols are vulnerable to server leakage attacks, dictionary attacks, and other threats. To address these issues, researchers have proposed multi-server and two-server architecture-based PAKE protocols. However, PAKE protocols in a multi-server architecture require the use of complex cryptographic primitives such as signatures, and zero-knowledge proofs to ensure security, which reduces the execution efficiency of the protocol. To tackle these challenges, we propose two new multi-server password authentication key exchange protocols based on the MLWE (Module learning with errors) problem. Both protocols rely on MLWE instances, using Peikert's error coordination technique to enable two parties with similar values to compute the same result. Furthermore, we introduce the error pairing assumption and proves its security within random oracle model. The proposed protocol divides the password information into different shares and stores them on separate servers. In protocol 1, all servers and user collaboratively generate session keys, making it suitable for high-security application scenarios. In protocol 2, both user and servers generate session keys individually, which is ideal for high-efficiency application scenarios. Compared to similar protocols, both protocols lower computation and communication costs, better addressing practical application needs while providing protection against quantum computing attacks and server leakage threats.
With the continuous development of blockchain technology, an increasing number of scholars have begun to consider the harm of data leakage during on-chain transactions and the requirement for privacy data protection. Zero-knowledge range proof, as a cryptographic technology, can perform legitimacy verification of data while hiding private data, effectively realizing the protection of private data on the blockchain, so it is increasingly used to protect blockchain privacy. The mainstream construction methods for range proofs can be mainly divided into two categories: n-ary decomposition and square decomposition. This paper introduces and analyzes the advantages and disadvantages of these construction methods in detail. Then, based on these two methods, a zero-knowledge range proof scheme based on multibit split square decomposition (ZKRPMSSD) is proposed, which requires no trusted third-party setting and can achieve range proofs for arbitrary ranges. The proposed ZKRPMSSD scheme processes the original data based on the multibit split idea, and the acquisition method of secret value components is optimized so that the acquisition of components does not depend on the scale of the original problem. Additionally, the algorithms for proof generation and verification in the ZKRPMSSD scheme are redesigned based on the \(\Sigma\) protocol and Pedersen commitments, effectively reducing the computational cost of the proof generation and verification process. Finally, typical n-ary decomposition and square decomposition zero-knowledge range proof construction schemes are taken for comparative analysis. Under 256-bit security and the same problem scale, experimental results indicate that ZKRPMSSD has advantages in proof and verification time costs.
Open access
Cryptography and Data Security
Digital Filter Design and Implementation
Advanced Steganography and Watermarking Techniques
Phuc-Hung Pham Le, Trung-Tin Tran, Toan Q. Dinh, Quy N.
As end-to-end encryption (E2EE) becomes the standard for secure communication, ensuring message authenticity while maintaining user privacy poses significant challenges.This paper introduces the BL0K-ME protocol, a novel cryptographic solution that combines Zero-Knowledge Proofs (ZKP), RSA encryption, and Bloom filters to authenticate individual messages within E2EE conversations.RSA encryption is employed to secure the transmission of messages between users, ensuring that only the intended recipient can decrypt the content, while ZKP enables third-party verification of specific message content without exposing the entire conversation.By leveraging Bloom filters, the protocol provides efficient logging and verification of message existence, balancing privacy protection with legal and regulatory requirements for digital evidence.BL0K-ME addresses a critical gap in current messaging systems by allowing service providers to verify message authenticity for legal investigations without compromising the confidentiality of unrelated communications.This research demonstrates the potential of integrating RSA encryption, ZKP, and Bloom filters to offer a scalable, secure solution for message authentication in E2EE systems, safeguarding both user privacy and the integrity of digital evidence.