The Federated Unified Secure Exchange (FUSE) algorithm represents a breakthrough in computer science and cybersecurity, building upon three foundational elements: Homomorphic Encryption, Zero-Knowledge Proofs, and Federated Learning. By deeply integrating these three pillars, FUSE not only guarantees data integrity and privacy in decentralized environments but also maintains high performance and remarkable scalability. This paper details the architecture, mathematical principles, and real-world applications of FUSE across Internet of Things (IoT), healthcare, finance, and supply chains. In addition, it compares FUSE with several âclassicâ algorithms that have dramatically changed the worldâsuch as QuickSort, RSA, Dijkstra, PageRank, FFT, Backpropagation, SHA, Monte Carlo, Gradient Descent, and Blockchainâhighlighting how FUSE addresses existing limitations in data protection and distributed computation.
As quantum computing advances, classical public-key cryptosystems face escalating risks, driving global standardization efforts by NIST, ETSI, and ISO. This paper provides a comprehensive review of recent developments in post-quantum cryptography (PQC), focusing on lattice-based, hash-based, and multivariate approaches. We examine their security foundations, implementation challenges, and applicability across domains such as finance, blockchain, and the Internet of Things (IoT). A core contribution is the proposed Hybrid Cryptographic Framework (HCF), which combines classical and quantum-resistant primitives to enable a secure and interoperable migration path. The framework integrates hybrid key exchange, dual-signature schemes, and PQC-compatible Merkle trees, and is supported by a discrete multi-objective optimization model for selecting algorithms under real-world constraints. The paper also discusses deployment challenges, including hardware acceleration, side-channel resistance, and legacy compatibility. Real-world case studies illustrate how leading institutions are piloting PQC integration in practice. Finally, we propose a strategic roadmap for PQC adoption, incorporating adaptive triggers based on quantum capabilities and evolving threat models. By aligning cryptographic design with international standards and practical system requirements, this work offers guidance for building resilient, quantum-safe infrastructures.
Machine learning has achieved remarkable results in numerous fields, demonstrating strong momentum and promising prospects for future development. However, machine learning is facing issues related to data security. User data contains a vast amount of sensitive personal information, and once privacy is breached, users may not only suffer from harassment but also face threats to their lives and property security. As a result, usersâ willingness and trust in sharing local raw data are gradually decreasing. In response to this situation, federated learning technology has emerged, which enables efficient training of decentralized data through distributed machine learning methods while protecting usersâ data privacy. Traditional federated learning systems suffer from issues such as single points of failure and lack of trust. Blockchain, as a decentralized, traceable, and tamper-resistant distributed ledger technology, provides a new solution for federated learning. It records every update of the global model, verifies and tracks local updates, and is equipped with a fair incentive mechanism. Based on these ideas, this paper proposes a federated learning framework combined with blockchain, aiming to address data security issues in federated learning.
ObjectiveByzantine Fault-Tolerant (BFT) consensus algorithms in blockchain systems were confronted with two fundamental challenges that significantly impacted their practical implementation: inefficient view changes resulting from dishonest primary nodes and excessive communication overhead during consensus processes.MethodsA novel Dynamic Dual-Master Practical Byzantine Fault Tolerance (DM-PBFT) algorithm was developed to simultaneously overcome these limitations through three key technical innovations. The DM-PBFT architecture was constructed with two tightly integrated components: an optimized consensus process and an intelligent view-change mechanism. To address the critical issue of communication overhead, the algorithm incorporated a dual-primary node framework (designated as B1 and B2) combined with Verifiable Secret Sharing (VSS) to streamline the consensus workflow. In this carefully designed process: (1) client A initiated transactions by sending requests to primary node B1; (2) B1 subsequently broadcast these requests along with A's unique identifier to the network; (3) the secondary primary node B2 distributed cryptographic subkeys and corresponding commitment values to all consensus nodes in set B; (4) each node independently verified the received subkeys using the commitment values to ensure cryptographic integrity; (5) upon successful verification, nodes computed request approval digests incorporating their subkeys and transmitted these digests back to B1; (6) after collecting sufficient subkeys, B1 performed efficient key recovery and compared the results with B2's master key; (7) finally, verification values were broadcast network-wide and persistently stored in all nodes' state databases to complete the consensus process.For optimizing view-change efficiency, a sophisticated reputation evaluation system was implemented based on an enhanced PeerTrust model. This system incorporated multidimensional confidence factors that dynamically synthesized both local interaction history and global reputation metrics through comprehensive analysis of inter-node verification relationships. The algorithm strategically organized nodes into three distinct operational tiers (primary layer, consensus layer, and non-consensus layer), each with specialized reputation evaluation methodologies. View transitions were executed through continuous hierarchical scoring during consensus rounds, with the system automatically adjusting node classifications based on their evolving reputation scores.The view-change protocol incorporated three carefully designed failure recovery procedures: (1) When primary node B1 was identified as Byzantine, the top-ranked consensus node was automatically promoted to replace it while maintaining operational continuity through B2's consistent subkey management; (2) For failures of B2, a similar replacement protocol was activated with additional safeguards to ensure complete subkey redistribution; (3) In the rare case of simultaneous failure of both primary nodes, the two highest-ranked consensus nodes were promoted to form a new primary pair, with the system automatically reinitializing the consensus process. Within the consensus layer, Byzantine nodes were systematically identified through continuous monitoring and temporarily marked rather than immediately replaced. Replacement was only triggered when the concentration of marked Byzantine nodes reached precisely one-third of the consensus layer's capacity, at which point a corresponding number of top-performing nodes from the non-consensus layer were promoted. This threshold-based approach strategically minimized unnecessary view changes while maintaining rigorous fault tolerance guarantees.Through rigorous algorithmic analysis, DM-PBFT was formally proven to satisfy all critical BFT properties: (1) Request messages and subkeys were cryptographically secured through the combined use of advanced signature algorithms and commitment schemes; (2) Consistency was guaranteed through mathematical proof showing all honest nodes would agree on the same sequence of requests; (3) Liveness was ensured by demonstrating the system would always progress within bounded time, even during view changes; (4) Termination was mathematically verified through analysis of the reputation-based view-change protocol. Communication complexity analysis established that DM-PBFT achieved O(n) complexity, representing a significant improvement over PBFT's O(n²) scaling. Time complexity analysis, conducted under realistic asynchronous network models, confirmed the algorithm's superior temporal efficiency compared to existing approaches.ResultsAn extensive experimental evaluation was conducted to validate DM-PBFT's performance across multiple critical dimensions. The testing framework systematically compared DM-PBFT against three established benchmarks (PBFT, reputation grouping, and HotStuff) while examining consensus latency, communication overhead, throughput, and resilience to network dynamics under various operational conditions.In controlled latency testing with network sizes scaling to 500 nodes, DM-PBFT demonstrated remarkable performance, achieving consensus latency of just 0.46176 seconds. This represented a 400Ă improvement over conventional PBFT (186.44476s), a 100Ă improvement over reputation grouping (46.09653s), and a 56Ă improvement over HotStuff (25.8702s). Detailed analysis revealed that while all tested algorithms exhibited increased latency with network growth, DM-PBFT's hierarchical architecture maintained superior scalability, with latency increasing at a sub-linear rate compared to the polynomial growth observed in other approaches.Communication overhead measurements showed that DM-PBFT achieved stable performance after reaching network stratification thresholds, consistently maintaining O(nân) complexity. In practical terms, this translated to a 62.4% reduction in bandwidth consumption compared to traditional PBFT implementations and measurable improvements over HotStuff's message efficiency. The communication overhead grew gradually with network size until reaching stratification points, after which it remained effectively constant regardless of additional node joins.Throughput benchmarking produced equally impressive results, with DM-PBFT sustaining 3,500 transactions per second (TPS) in large-scale configurations compared to PBFT's 1,200 TPS. While matching HotStuff's peak throughput, DM-PBFT demonstrated significantly better scalability, with throughput improvement rates exceeding those of the reputation grouping approach by substantial margins after crossing stratification thresholds.Additional experiments examined DM-PBFT's resilience under challenging network conditions. Node churn tests confirmed that the frequency of node joins/leaves only impacted performance through net changes in total node count, not through the rate of such changes. Network bandwidth fluctuation tests demonstrated the reputation system's effectiveness in automatically compensating for variable connection quality, with the algorithm maintaining stable performance across diverse bandwidth conditions after several consensus rounds of adaptation.The comprehensive experimental results collectively established DM-PBFT's advantages across three fundamental metrics: (1) Exceptional latency characteristics, delivering 400Ă improvements at scale; (2) Efficient bandwidth utilization, achieving 62.4% reductions compared to conventional approaches; (3) Consistently high throughput maintenance even under adversarial conditions with Byzantine node concentrations up to 30%. The view-change process demonstrated particular efficiency, completing in just 1.2 seconds compared to PBFT's 12.8 seconds - a 90.6% reduction that proved critical for practical deployment scenarios.ConclusionsThe DM-PBFT algorithm represented a significant theoretical and practical advancement in Byzantine fault-tolerant consensus mechanisms through its novel integration of dual-primary node management, verifiable secret sharing, and dynamic reputation-based stratification. The solution demonstrated particular effectiveness for large-scale consortium blockchain implementations, successfully achieving the dual objectives of sub-linear communication growth and rapid fault recovery without compromising security guarantees.The algorithm's architectural innovations, especially its stratified node management framework and intelligent threshold-based view-change protocol, established a new foundation for next-generation consensus protocol design in increasingly complex and adversarial network environments. Future research directions were identified to further enhance the algorithm's practical utility, including: (1) Optimization for real-world deployment scenarios with heterogeneous hardware; (2) Development of cross-shard coordination mechanisms for sharded blockchain architectures; (3) Enhanced security analysis under sophisticated adaptive adversary models; (4) Integration with emerging cryptographic techniques such as zero-knowledge proofs for additional privacy preservation. These advancements promised to extend DM-PBFT's applicability to an even broader range of production blockchain environments while maintaining its fundamental advantages in efficiency, security, and scalability.
A novel identity management concept known as decentralized identity (or self-sovereign identity) has drawn significant interest and extensive development within both academic and industrial circles. Decentralized oracles empower users to demonstrate the origin of data accessed through TLS from a specific website and verify statements concerning that data. This system operates without the reliance on trusted hardware or requiring modifications on the server side. In DECO (CCS 2020), the first decentralized oracle within TLS 1.2 was introduced. It also investigates the methodology of optionally proving statements about this data in a zero-knowledge setting, preserving the confidentiality of the data itself. Furthermore, a separate study proposed an attribute-based anonymous credential system incorporating a commitment scheme (ASIACRYPT 2020), introducing show proofs to verify a set of attributes in a credential to verifiers without disclosing attribute specifics. Building upon these research findings, this thesis presents a series of optimizations and expansions aimed at advancing self-sovereign identity solutions. First, we present DIDO and DIDO+ (decentralized identification oracle), which expands DECO to TLS 1.3. In DIDO, we address several unresolved challenges, encompassing the incorporation of X25519 key exchange, the creation of a round-optimal three-party key exchange, the structuring of a 2PC system for TLS 1.3 key scheduling, and the optimization of circuit design for 2PC protocols. Furthermore, we expand upon DIDO to create DIDO+, which introduces a protocol named selective disclosure. This protocol facilitates the extraction of particular plaintext substrings from websites, enhancing the functionality and flexibility of the system. Our implementation is verified against real-world websites, and a security proof is furnished to validate its integrity. Next, we introduce DEVS (decentralized verification service), the first generic decentralized verification service built on a decentralized oracle. DEVS enhances the traditional single-verifier oracle by incorporating a multi-verifier mechanism. Our aim is to streamline the protocol for reduced communication and computation costs while enabling reusable proofs and maintaining security. DEVS comprises three key components: a reconstructed decentralized oracle to bolster data trust, secure storage for share retention, and a verification process tailored to the needs of verifiers and authorities. Considering 10 verifiers, the reconstruction reduces the running time (approximately 89.1% or 89.6%) in WAN settings and communication bandwidth (approximately 89.1% or 87.8%) of TLS 1.2 or 1.3, it provides a significant improvement when working with multiple verifiers. Lastly, we introduce a unified attribute-based anonymous credential system where users consistently receive credentials in a standardized format from the issuer. This system allows users to opt for efficient multi-use or single-use show proofs, offering a more user-centric perspective compared to current schemes. Technically, we suggest an interactive method for the credential issuance protocol utilizing two-party computation with additive homomorphic encryption. This approach maintains crucial security features such as impersonation resilience, anonymity, and unlinkability. In addition to the interactive protocol, we develop show proofs tailored for efficient single-use credentials that uphold user anonymity throughout the process.
This systematic literature review compares two leading selective-disclosure primitives for decentralised identity-BBS+ signatures and Selective-Disclosure JSON Web Tokens (SD-JWT)-to clarify their suitability for privacypreserving credentials. Following Kitchenham's protocol, 226 records from 2017-2025 were screened across IEEE, ACM, SpringerLink, ScienceDirect, IETF and W3C repositories, yielding 31 primary studies with empirical data. Quantitative synthesis shows that BBS+ derived proofs remain constant-size at roughly 140 bytes and verify in about 12 ms on consumer hardware, whereas SD-JWT presentations grow with the number of revealed claims but still verify in under 10 ms for typical twoclaim use cases. Qualitative analysis confirms BBS+ provides strong unlinkability, predicate proofs and zero-knowledge disclosure, while SD-JWT offers seamless integration with existing JOSE/OAuth infrastructures yet carries correlation risk due to stable salted digests. Standardisation progress is comparable: the BBS+ cryptosuite reached W3C Candidate Recommendation in April 2025, and SD-JWT is in late-stage IETF review. The review concludes that privacy-critical scenarios such as age-gated services favour BBS+, whereas high-throughput web applications benefit from SD-JWT; consequently, hybrid wallet support for both formats is recommended. Future research should tackle scalable revocation, post-quantum migration and multi-credential aggregation to sustain long-term trust and interoperability.
Atoms and photons, two things so different but yet so alike. The former, the building block of matter, something we learn about in school and imagine it as some tiny marbles encircled by other tinier marbles. The latter, an electromagnetic wave, a light particle or an excitation of the electromagnetic field. Quantum mechanics tells us about the properties of these two entities. And even if it sounds, looks and writes counter-intuitive, it has proven right for over a century now. In this work, I elaborate on how we tested the laws of quantum mechanics and how we used them learn more about the tiny building blocks of nature and the fields they use to talk to each other. The atoms we use, are artificial. Superconducting qubits, small electrical circuits with quantized energy levels behave like electrons that transition between different orbitals in an atom. One of the qubits' advantages, is also a big disadvantage. We design the circuits' energy levels and fabricate them in a cleanroom. This allows for arbitrary spaced energy levels but in contrast to real atoms, prevents two superconducting qubits from being alike. Still, this qubit platform is one of the frontrunners for future quantum computing technology and testing fundamental physics due to their scalability. We interface superconducting qubits, which operate in the GHz regime, with microwave photons. We use 3D aluminum cavities as mediators between qubits and photons. The cavities allow for non-destructive readout of the qubit state, they shield the qubits from noise at the qubit frequency and they give us an easy way to frequency-tune these joint systems. We need to operate superconducting qubits and their cavities at millikelvin temperatures in dilution refrigerators. At higher temperatures, superconductivity suffers and even worse, the environment is filled with thermal noise photons. This poses a fundamental limitation on the scalability of superconducting qubit devices. Also connecting multiple devices in different fridges does not work over room temperature links because the microwave photons used for this purpose will be covered in noise and the quantum information they carry, will be unusable. Infrared photons do not suffer from this noise problem since there are close to zero thermal noise photons at their frequencies at room temperature. We cannot simply interface superconducting devices with optical photons due their frequency mismatch and the destructive effect of optical photons on superconductors. Therefore, we use microwave-to-optics transducers that allow to convert microwave photons into optical ones and vice-versa. The transducers that we use are macroscopic electro-optic transducers using the Pockels effect in a disk-shaped Lithium Niobate whispering gallery mode resonator. By using a strong optical pump, photons from the two frequency domains experience a beam-splitter interaction and get converted from one to the other. We measure the generated optical photons using elaborate optical setups, optical heterodyning and single photon detectors to gain knowledge about the qubit state or the converted microwave photons. Bridging the microwave and the optical world allows us to take advantage of both of their strengths but it also requires deep knowledge about both of their working principles. In this work, we describe two experiments that our group conducted to showcase the opportunities that arise from interfacing superconducting qubits with optical photons but also the pitfalls, one may encounter on the way. In the first experiment, we managed to all-optically read out a superconducting qubit. We show that the assignment fidelity, the probability that a measurement of the qubit state matches the prepared state, is close to equal for all-optical, microwave-to-optics and conventional microwave readout. We show T1 and T2 measurements for all three readout types and give an analysis of the noise caused by the optics. Finally, we show that the infrared light does not affect the qubit performance in a negative way but that the heating it causes does. This is an important insight that we used in the next experiment. The second experiment is the upconversion of itinerant single microwave photons to the optical domain. We show that we can generate single microwave photons from a qubit-cavity system. We upconvert these single photons, measure them with a single photon detector and reconstruct their shape. By conducting a single photon Rabi measurement, we show correlations between the microwave and the optical domain. And by thorough signal-to-noise measurements and noise analysis, we find that we can generate single infrared photons with high signal-to-noise ratio 5.1 and low transducer added noise (<0.012 quanta). We show that this measurement creates a path towards entanglement of a superconducting qubit and an optical photon and what parameters need to be improved to achieve it. Additionally, this experiment is a proof of principle for an on-demand infrared single photon source. More generally, it allows to link microwave quantum technology in general to the optical domain.
Verifiable Delay Functions (VDFs) introduced by Boneh et al. (CRYPTO'18) are functions that require a prescribed number of sequential steps T to evaluate, yet their output can be verified in time much faster than T. Since their introduction, VDFs have gained a lot of attention due to their applications in blockchain protocols, randomness beacons, timestamping and deniability. This thesis explores the theory and applications of VDFs, focusing on enhancing their soundness, efficiency and practicality. The only practical VDFs known to date are based on repeated squaring in hidden order groups. Consider the function VDF(x,T)=x^(2^T). The iterated squaring assumption states that, for a random group element x, the result of VDF cannot be computed significantly faster than performing T sequential squarings if the group order is unknown. To make the result verifiable a prover can compute a proof of exponentiation (PoE) \pi. Given \pi, the output of VDF can be verified in time much less than T. We first present new constructions of statistically sound proofs of exponentiation, which are an important building block in the construction of SNARKs (Succinct Non-Interactive Argument of Knowledge). Statistical soundness means that the proofs remain secure against computationally unbounded adversaries, in particular, it remains secure even when the group order is known. We thereby address limitations in previous PoE protocols which either required (non-standard) hardness assumptions or a lot of parallel repetitions. Our construction significantly reduces the proof size of statistically sound PoEs that allow for a structured exponent, which leads to better efficiency of SNARKs and other applications. Secondly, we introduce improved batching techniques for PoEs, which allow multiple proofs to be aggregated and verified with minimal overhead. These protocols optimize communication and computation complexity in large-scale blockchain environments and enable scalable remote benchmarking of parallel computation resources. We then construct VDFs with enhanced properties such as zero-knowledge and watermarkability. It was shown by Arun, Bonneau and Clark (ASIACRYPT'22) that these features enable new cryptographic primitives called short-lived proofs and signatures. The validity of such proofs and signatures expires after a predefined amount of time T, i.e., they are deniable after time T. Our constructions improve upon the constructions by Arun, Bonneau and Clark in several dimensions (faster forging times, arguably weaker assumptions). Finally, we apply PoEs in the realm of primality testing, providing cryptographically sound proofs of non-primality for large Proth numbers. This work gives a surprising application of VDFs in the area of computational number theory. Together, our contributions advance both the theoretical foundations and the real-world usability of VDFs in general and in particular of PoEs, making them more adaptable and secure for current and emerging cryptographic applications.
Secure machine learning paradigms have emerged as compelling solutions to address growing concerns of large-scale data collection in modern Machine Learning (ML) systems. These paradigms leverage secure computation techniques to enable the execution of ML applications without the necessity to share raw data, models or predictions to be shared between parties, offering strong, formal privacy guarantees. Recent advances have significantly enhanced both the scalability and expressiveness of these secure paradigms, facilitating their deployment in real-world scenarios across a variety of privacy-sensitive domains. However, the very mechanisms that provide these privacy guarantees also introduce new challenges to robustness, trust, and accountability. To ensure secrecy, secure ML systems conceal the processes of training and inference, making them difficult to inspect, validate, or audit. This intrinsic opacity creates a fundamental tension between privacy and accountability: hiding data and models to protect usersâ privacy can also obscure failures and enable undetectable manipulation. Furthermore, in many secure ML frameworks, multiple, potentially untrusted parties collaboratively contribute to computations, thereby amplifying risks. Traditional threat models in adversarial ML often depend on transparent access to data, models, or outputsâassumptions that do not hold in secure settings. As a result, these systems become vulnerable to new and sometimes more potent attack vectors. Without dedicated integrity mechanisms, these privacy-preserving systems cannot be safely deployed in high-stakes domains such as healthcare, finance, or critical infrastructure. Realizing the full potential of secure ML requires a comprehensive understanding of the unique threats these systems face, the development of new integrity mechanisms, and their integration into these systems in a way that is efficient and preserves the privacy guarantees they provide. This dissertation advances accountability in secure ML through two complementary directions. First, it develops an understanding of the robustness challenges that arise in secure settings. We investigate the role of memorization and system-level dynamics in exposing secure systems to targeted manipulation. Based on these insights, we then introduce new cryptographic building blocks to strengthen the robustness and transparency of secure ML. We present RoFL, a system for privacy-preserving input validation in secure Federated Learning; Arc, the first framework for end-to-end auditing of secure ML pipelines; and Artemis, a new construction for generating efficient zero-knowledge proofs for real-world ML models. Together, these contributions lay the foundation for secure ML systems that are not only private, but also accountable and trustworthy in practice.
éç俥ćŻććŻç忍éĺĺąďźć°ćŽĺŽĺ ¨ĺç¨ćˇçéç§čśĺĺĺ°éč§ăćŹććĺşäşä¸ç§ĺżĺ莤čŻĺŻéĽäş¤ć˘(Anonymous Key Exchange, AKE)ĺ莎ďźć¨ĺ¨ä¸şĺťçĺşćŻä¸çĺťçć°ćŽĺ ąäşŤĺćŁč 躍䝽éç§ćäžĺŽĺ ¨ĺéç§çäżć¤ă诼ćšćĄéčżä˝żç¨ç´Żĺ ĺ¨ăéśçĽčŻčŻćĺĺ łčć°ćŽĺ ĺŻçććŻďźĺŽç°ç¨ćˇĺżĺç莤čŻĺĺŽĺ ¨çäźčŻĺŻéĽĺĺďźććé˛ć˘ćć寚äşç¨ćˇĺĺťç¨çŠčç˝čŽžĺ¤çćťĺťďźčżč˝ćľĺžĄčŻĺŽä¸ĺĽ˝ĺĽçĺťçćşć寚ćŁč 躍䝽ççćľăç¸čžäşç°ćçćšćĄćäžäşć´ĺźşçéç§ĺŽĺ ¨äżć¤ďźĺšśä¸ĺžĺĽ˝ĺ°ĺšłčĄĄäşć§č˝ĺĺŽĺ ¨ć§ďźĺ ˇćéčŚçç莺䝡ĺźĺćäšăWith the rapid development of information technology, data security and user privacy have been paid more and more attention. This paper proposes an Anonymous authenticated Key Exchange (AKE) protocol to provide security and privacy protection for medical data sharing and patient identity privacy in medical scenarios. By using accumulator, zero-knowledge proof and associated data encryption technology, the scheme realizes anonymous user authentication and secure session key agreement, which effectively prevents adversaries from attacking users and medical IoT devices, and can resist honest and curious medical institutions from guessing the patientâs identity. Compared with the existing schemes, it provides stronger privacy security protection, and a good balance between performance and security, which has important theoretical value and significance.
The correctness of a computation can be efficiently verified in a privacy-preserving manner without re-execution using zero-knowledge succinct non-interactive arguments of knowledge (zkSNARKs). With short transcript sizes and fast verification times, zkSNARKs enable the potential deployment of computationally intensive algorithmsâsuch as machine learning modelsâon the blockchain, making them efficiently verifiable through short proofs. However, the prover time for matrix computations in these settings often fails to scale efficiently with increasing model complexity and data size. We are the first to systematically address zkSNARKs for general matrix computations with practical prover efficiency. We achieve an $O(N + nM)$ prover time, asymptotically faster than the unverified matrix computation, for computations involving $M$ matrix operations on $n \times n$ matrices with $N$ total non-zero entries. Starting with a single dense matrix multiplication, we propose zkMatrix, a special-purpose zkSNARK for verifying committed $n \times n$ matrix multiplication through their projections onto random vectors. Among zkSNARKs with $O(\log n)$ transcript size and verifier time, zkMatrix is the first to achieve $O(n^2)$ prover time and $O(n^2)$ RAM usage. Batching multiple proofs together reduces the prover time for each additional multiplication to $O(n)$ group operations. Next, we design zkSNARKs for sparse matrix multiplication with $N$ non-zero entries. zkSmart reduces the prover time from $O(n^2)$ to $O(N + n)$, relying on an $O(N + n)$-prover vector-matrix-vector product argument, achieved by improving Bulletproofs. Moreover, \zksmart formulates verifiable computation represented as a matrix circuit of $M$ nodes, each denoting a matrix operation. Sparse matrix multiplication translates the matrix circuit satisfiability (Mat-Circ-SAT) problem into the high-dimensional rank-1 constraint system (HD-R1CS), a matrix-circuit version of the rank-1 constraint system (R1CS), traditionally used for arithmetic circuits. Using zkSmart, we achieve $O(N + nM)$ prover time for general matrix computations. To reduce the cost of committing to intermediate variable matrices in zkSmart, we introduce Evalyn, which generates proofs using a pre-order tree traversal on the abstract syntax tree (AST) of a matrix expression. Evalyn ensures output and input consistency in serial matrix computations by linking randomness for zkSNARKs between parent and child nodes, eliminating the need to commit to the nodes and significantly improving prover efficiency. Our prover for R1CS outperforms state-of-the-art general-purpose zkSNARKs. As a foundational component of our framework, we optimize Bulletproofs to construct the fastest known inner product argument (IPA). Additionally, we propose a zero-knowledge transformation that commits to transcript elements with only logarithmic overheadâwhile maintaining compatibility with post-quantum secure, non-homomorphic commitment schemes. We apply our framework to zero-knowledge machine learning (zkML), providing zkSNARKs for neural networks. We translate floating-point truncations and non-linear activation functions into linear algebra equations that can be verified by our framework. We utilize our framework to generate efficient proofs for the attention layer in large language models (LLMs). After resolving all these challenges, we have thoroughly addressed the design of efficient zkSNARKs for matrix computations.
S Remya, Manu J. Pillai, Preethi Ann Jacob, Sruthi Suresh ¡ 5 authors
Certificateless Proxy Re-Encryption (CL-PRE) eliminates certificate management and private key exposure risks for blockchain data sharing, but existing schemes have critical security vulnerabilities and performance limitations. This research work presents comprehensive security analysis and performance evaluation of CL-PRE schemes for blockchain applications. The primary contribution is discovering a critical public key replacement attack against Wang et al.âs CL-PRE scheme, where Type I adversaries completely compromise message confidentiality by substituting legitimate public keys with adversary-controlled keys, enabling ciphertext decryption without private keys and violating IND-CCA security. The systematic performance evaluation of pairing-free PRE schemes for blockchain environments is conducted through extensive benchmarking of three schemes implemented in Go. Results show self PRE achieves superior security but incurs 13.7% higher execution time than certificateless schemes. To address vulnerabilities, this work proposes a secure CL-PRE framework with enhanced validation mechanisms. The Ethereum implementation reduces on-chain storage by 40% while maintaining provable security. The framework achieves 14.1% better performance than existing secure schemes and reduces gas costs by 14.3%. These findings establish security benchmarks and practical guidelines for blockchain developers, emphasizing rigorous cryptographic analysis importance for decentralized access control advancement.
The increasing number of blockchain projects introduced annually has led to a pressing need for secure and efficient interoperability solutions. Currently, the lack of such solutions forces end-users to rely on centralized intermediaries, contradicting the core principle of decentralization and trust minimization in blockchain technology. We propose a decentralized and efficient interoperability solution (aka Bridge Protocol) that operates without additional trust assumptions, relying solely on the Byzantine Fault Tolerance (BFT) properties of the two chains being connected. In particular, relayers (actors that exchange messages between networks) are permissionless and decentralized, hence eliminating any single point of failure. We introduce Random Sampling, a novel technique for on-chain light clients to efficiently follow the history of PoS blockchains by reducing the signature verifications required. Here, the randomness is drawn on-chain, for example, using Ethereumâs RANDAO. We analyze the security of the bridge from a crypto- economic perspective and provide a framework to derive the security parameters. This includes handling subtle concurrency issues and randomness bias in strawman designs. While the protocol is applicable to various PoS chains, we demonstrate the protocolâs practical feasibility by showcasing an instantiated bridge between Polkadot and Ethereum (currently deployed), and discuss some practical security challenges. Furthermore, we evaluate the efficiency of our on-chain light client verifier (implemented as an Ethereum smart contract) against SNARK-based approaches, demonstrating significantly lower gas costs for signature verification - even for validator sets up to 10âś.
Online voting promises greater convenience and accessibility, but moving from supervised polling places to unsupervised settings magnifies the risk of coercion and vote buying. A compelling strategy is to give voters fake credentials: credentials that look and behave like real voting credentials but whose ballots are silently excluded from the tally. Despite its conceptual appeal, practical realizations and usability evidence for fake credentials have remained limited. This dissertation presents Votegral, the first end-to-end verifiable, coercion-resistant online voting system with empirical evidence towards practical usability. Votegral has two components: TRIP and VLT. TRIP is a trust-limited, in-person registration scheme that issues voters a real credential and any number of fake credentials on paper, without trusted hardware. TRIP embeds an interactive zero-knowledge proof into the physical printing process so that real credentials carry sound proof transcripts while fake credentials carry identically formatted but unsound proof transcripts -- distinguishable only by the voter during issuance and not transferable thereafter. VLT is a tallying scheme that constrains ballots to registrar-issued credentials to enable linear-time filtering of fake ballots. VLT also introduces standing votes: a voter facing extreme coercion can, at registration, delegate their voting rights to a publicly registered political party and leave the booth with only fake credentials. Tallying then credits the party's ballot by the number of such delegations and publishes publicly auditable proofs, resulting in both transparency and coercion evidence -- evidence that an aggregate number of voters felt unsafe to leave the registrar with a real credential. Our prototype tallies 1 million ballots in about 14 hours on a 128 core, 256 GB RAM machine; this puts Votegral on par with modern end-to-end verifiable systems such as Swiss Post, while significantly outperforming prior JCJ-style systems such as Civitas. TRIP's end-to-end, voter-observable registration session completes in under 20 seconds on resource-constrained hardware. In our main user study with 150 demographically diverse participants recruited in Boston, Massachusetts, 83% successfully registered and cast a ballot in our mock election. Among the 120 participants exposed to fake credentials, 96% correctly understood the purpose of fake credentials. These promising results suggest a path for practical viability of coercion-resistant, end-to-end verifiable online voting using fake credentials.
Digital supply chain payments increasingly rely on automated and distributed platforms, yet existing solutions struggle to balance transparency with the confidentiality required by commercial and financial stakeholders. While blockchain-based smart contracts enable tamper-evident settlement and traceability, they often expose sensitive transaction metadata, contractual terms, and risk indicators, limiting adoption in multi-party supply chain environments. This paper presents a privacy-preserving smart and secure contract framework for digital supply chain payments that separates correctness verification from information disclosure. The proposed model combines a permissioned or consortium blockchain with off-chain encrypted data storage, cryptographic commitment schemes, and zero-knowledge proofs to ensure that payment obligations, milestone fulfillment, and financing conditions can be verified without revealing proprietary business details. Tokenized payment obligations represent invoices and receivables on the ledger, while milestone-based smart contracts coordinate delivery confirmation, early financing, dispute resolution, and settlement. Sensitive financial data and documents remain off-chain, anchored to the ledger only through hashes, commitments, and succinct proofs. Optional confidential computing components further enable secure evaluation of dynamic pricing or credit logic. A comprehensive security analysis demonstrates resistance to unauthorized state modification, double financing, insider misuse, and inference attacks under both honest-but-curious and malicious adversary models. Performance evaluation shows that the computational and communication overhead introduced by privacy-preserving mechanisms remains practical for real-world supply chain payment workflows, with low latency, efficient storage growth, and scalable operation across multi-tier ecosystems. The results indicate that the proposed framework provides a viable foundation for secure, privacy-aware, and auditable digital supply chain finance.