Blockchain technology is often discussed as if it emerged from nowhere, yet its architectural DNA traces directly to the decentralized computing principles James~N. Gray articulated in 1986. This paper maps the conceptual lineage from Gray's requestor/server model to modern blockchain architectures, showing how his emphasis on modularity, autonomy, data integrity, and standardized communication anticipated the design of systems like Bitcoin and Ethereum, and, more recently, the Web3 movement and Layer-2 scaling architectures. We examine consensus mechanisms, cryptographic foundations, rollup-based Layer-2 protocols, and cross-chain interoperability through this historical lens, identify persistent challenges in scalability and modularity, and outline future directions toward Web4: an intelligent, decentralized internet integrating blockchain, artificial intelligence, and the Internet of Things.
Multi-chain ecosystems suffer from fragmented identity, siloed liquidity, and bridge-dependent token transfers. We present n-VM, a Layer-1 architecture that hosts n heterogeneous virtual machines as co-equal execution environments over shared consensus and shared state. The design combines three components: a dispatcher that routes transactions by opcode prefix, a unified identity layer in which one 32-byte commitment anchors VM-specifific addresses, and a unified token ledger that exposes VM-native interfaces such as ERC-20 and SPL over a common balance store. We formalize routing, identity derivation, and token transfer semantics, and prove cross-VM transfer atomicity and identity isolation under standard cryptographic assumptions. We describe a concrete instantiation with five VMs: a native runtime, EVM, SVM, Bitcoin Script, and TVM. We also present context-based sharding and a write-set scheduler for parallel execution. Under an analytical throughput model, the architecture admits a projected range of about 16,000 to 66,000 transactions per second on commodity hardware.
Peer-discovery protocols within P2P networks are often vulnerable: because creating network identities is essentially free, adversaries can eclipse honest nodes or partition the overlay. This threat is especially acute for blockchains, whose security depends on resilient peer connectivity. We present AetherWeave, a stake-backed peer-discovery protocol that ties network participation to deposited stake, raising the cost of large-scale attacks. We prove that, with high probability, either the honest overlay remains connected or a $(1{-}δ)$-fraction of nodes in every smaller component raise an attack-detection flag -- even against a very powerful adversary. To our knowledge, AetherWeave is the first peer-discovery protocol to simultaneously provide Sybil resistance and privacy: nodes prove they hold valid stake without revealing which deposit they own, and gossiping does not expose peer-table contents. A cryptographic commitment scheme rate-limits discovery requests per round; exceeding the limit yields a publicly verifiable misbehavior proof that triggers on-chain slashing. Beyond deposit and slashing, the protocol requires no on-chain interaction, with per-node communication scaling as $O(s\sqrt{n})$. We validate our design through a mean-field analysis with closed-form convergence bounds, extensive adversarial simulations, and an end-to-end prototype built by forking Prysm, a leading Ethereum consensus client.
Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay creates a conflict window within which overlapping proposals may generate competing branches. This paper derives a density-delay law for such exclusive state progression processes. Under independent proposal arrivals and bounded propagation delay, overlap is approximated by a Poisson model and fork depth is represented by a birth-death process. The analysis shows that maintaining bounded fork depth as the number of participants grows requires the density-delay product $λΔ$ to remain $O(1)$, implying that aggregate proposal intensity must stay bounded and yielding an inverse-scaling law $g(N)=O(1/N)$ at the unit level. Simulation experiments across varying network sizes and propagation delays align with a common density-delay curve, supporting the predicted scaling behavior. The result provides a compact law for stable event-driven state progression in open distributed systems and offers a scaling-based interpretation of Bitcoin-style difficulty adjustment as a decentralized way to regulate effective event density.
Quantum computing provides a feasible multi-layered security challenge to classical blockchain networks. Quantum blockchains that rely on quantum key distribution (QKD) to establish secure channels can address this feasible threat. Whereas, there are still architecture limitations to practical security resulted in the measurement devices while implementing the QKD-secured blockchains in physical layer. This paper presents a quantum-classical hybrid architecture in a distributed blockchain to address the connectivity and distance limitations of the blockchain-embedded quantum networks. A decoupled architecture is designed felicitously so that it pairs a linearly scalable measurement-device-independent (MDI) physical layer with a decentralized consensus. It can optimize the complexity of infrastructure from quadratic to linear scaling, ascribed to leveraging the twin-field (TF) QKD protocol with the MDI-structurized star topology. Additionally, the dual-key stratification strategy transforms symmetric information-theoretic security into publicly auditable forward-secret blockchain evidence. This architecture can integrate the exact information-theoretic security (ITS) with distributed consensus mechanisms, allowing the scalable system to overcome the potential rate-loss limits inherent in classical security-weakened blockchains.
Canonical LST (sTEZ) is an enshrined, protocol-native mechanism designed to mitigate the centralization risks associated with liquid staking intermediaries. Intended to complement direct staking rather than replace it, Canonical LST provides a neutral, public alternative managed directly by the Tezos protocol. It allows any tez holder to participate in aggregated staking without reliance on third-party operators. sTEZ follows an accrual-based design: all slashing events and rewards are reflected in the token's exchange rate to tez, keeping balances fungible while exposing holders to the precise economics of staking. This approach ensures that liquid staking functions as fundamental network infrastructure--with deterministic lifecycle rules, transparent on-chain data, and governance anchored in the amendment process--rather than as a discretionary commercial product. This white paper summarises the motivation for enshrining liquid staking, the core mechanics, exchange-rate model, regulatory touchpoints, risk posture, and forward-looking roadmap for Canonical LST.
Global cryptocurrencies are unbacked and have high transaction cost incurred by global consensus. In contrast, grassroots cryptocurrencies are backed by the goods and services of their issuers -- any person, natural or legal -- and have no transaction cost beyond operating a smartphone. Liquidity in grassroots cryptocurrencies arises from mutual credit via coin exchange among issuers. However, as grassroots coins are redeemable 1-for-1 against any other grassroots coin, the credit-forming exchange must also be 1-for-1, lest prompt redemption after exchange would leave the parties with undue profit or loss. Thus, grassroots coins are incongruent with liquidity through interest-bearing credit. Here we introduce grassroots bonds, which extend grassroots coins with a maturity date, reframing grassroots coins -- cash -- as mature grassroots bonds. Bond redemption generalises coin redemption, allowing the lending of liquid coins in exchange for interest-bearing future-maturity bonds. We show that digital social contracts -- voluntary agreements among persons, specified, fulfilled, and enforced digitally -- can express the full gamut of financial instruments as the voluntary swap of grassroots bonds, including loans, sale of debt, forward contracts, options, and escrow-based instruments, and that classical liquidity ratios are applicable just as well to grassroots bonds. Grassroots bonds may thus allow local digital economies to form and grow without initial capital or external credit, harnessing mutual trust within communities into liquidity. The formal specification presented here was implemented in GLP, a concurrent logic programming language running on Dart for smartphone deployment. The implementation is illustrated by a running multiagent village market scenario in GLP.
Existing high performance blockchains verify one signature per transaction on the critical path, which creates O(N) verification cost, high hardware pressure, and difficult post quantum migration. This paper presents ACE Runtime, a ZKP native execution layer built on identity authorization separation. We replace per transaction signature checks with lightweight HMAC attestations in the hot path, then generate one aggregated zero knowledge finality certificate per block in an asynchronous prove stage. The system is organized as an Attest Execute Prove pipeline with two tier finality: soft finality from BFT voting and hard finality from proof verification. Under standard cryptographic assumptions, we provide formal arguments for attestation unforgeability and hard finality irreversibility. We also define a two phase timeout and backup proving path with witness availability gossip for liveness under builder failure. Quantitative results combine analytical modeling with reference implementation measurements. The prototype shows low CPU orchestration overhead, while model driven analysis projects constant per block verification cost, lower validator hardware requirements for non builders, and better bandwidth efficiency than per transaction signature designs. These results indicate that identity authorization separation is a practical architecture for sub second cryptographic finality with a clear path toward stronger post quantum components.
Mahmoud Hafez, Eman Ouda, Mohammed A. Mohammed Eltoum, Khaled Salah · 5 authors
Aircraft engine blade maintenance relies on inspection records shared across manufacturers, airlines, maintenance organizations, and regulators. Yet current systems are fragmented, difficult to audit, and vulnerable to tampering. This paper presents BladeChain, a blockchain-based system providing immutable traceability for blade inspections throughout the component life cycle. BladeChain is the first system to integrate multi-stakeholder endorsement, automated inspection scheduling, AI model provenance, and cryptographic evidence binding, delivering auditable maintenance traceability for aerospace deployments. Built on a four-stakeholder Hyperledger Fabric network (OEM, Airline, MRO, Regulator), BladeChain captures every life-cycle event in a tamper-evident ledger. A chaincode-enforced state machine governs blade status transitions and automatically triggers inspections when configurable flight hour, cycle, or calendar thresholds are exceeded, eliminating manual scheduling errors. Inspection artifacts are stored off-chain in IPFS and linked to on-chain records via SHA-256 hashes, with each inspection record capturing the AI model name and version used for defect detection. This enables regulators to audit both what defects were found and how they were found. The detection module is pluggable, allowing organizations to adopt or upgrade inspection models without modifying the ledger or workflows. We built a prototype and evaluated it on workloads of up to 100 blades, demonstrating 100% life cycle completion with consistent throughput of 26 operations per minute. A centralized SQL baseline quantifies the consensus overhead and highlights the security trade-off. Security validation confirms tamper detection within 17~ms through hash verification.
Joel Lidin, Amir Sarfi, Erfan Miahi, Quentin Anthony · 9 authors
Recently, there has been increased interest in globally distributed training, which has the promise to both reduce training costs and democratize participation in building large-scale foundation models. However, existing models trained in a globally distributed manner are relatively small in scale and have only been trained with whitelisted participants. Therefore, they do not yet realize the full promise of democratized participation. In this report, we describe Covenant-72B, an LLM produced by the largest collaborative globally distributed pre-training run (in terms of both compute and model scale), which simultaneously allowed open, permissionless participation supported by a live blockchain protocol. We utilized a state-of-the-art communication-efficient optimizer, SparseLoCo, supporting dynamic participation with peers joining and leaving freely. Our model, pre-trained on approximately 1.1T tokens, performs competitively with fully centralized models pre-trained on similar or higher compute budgets, demonstrating that fully democratized, non-whitelisted participation is not only feasible, but can be achieved at unprecedented scale for a globally distributed pre-training run.
In high-speed rail (HSR) systems, federated learning (FL) enables cross-departmental flow prediction without sharing raw data. However, existing schemes suffer from two key limitations: (1) insufficient incentives, leading to free-riding and model poisoning; and (2) centralized aggregation, which introduces a single point of failure. We propose a secure and efficient framework SI-ChainFL that addresses these issues by combining contribution-aware incentives with decentralized aggregation. First, we quantify client contributions using a Shapley value metric that jointly considers rare-event utility, data diversity, data quality, and timeliness. To reduce computational overhead, we further develop a rare positive driven client clustering strategy to accelerate Shapley estimation. Moreover, we design a blockchain-based consensus protocol for decentralized aggregation, where aggregation eligibility is tied to Shapley incentives. This design motivates clients to submit high-quality updates and enables efficient and secure global aggregation. Experiments on MNIST, CIFAR 10 and CIFAR 100, and a HSR flow dataset show that SI ChainFL remains effective under 90% malicious clients in PA attacks, achieving 14.12% higher accuracy than RAGA. Theoretical analysis further guarantees an upper bound on performance
In post-quantum blockchain settings, objects that require validity proofs (e.g., blob roots, execution-layer or consensus-layer signature aggregates) must be broadcast through mempool and relay networks. Recursive STARKs have been proposed to aggregate such proofs so that each node forwards one proof per tick plus objects without proofs, capping per-node proof bandwidth at roughly 128 KB degree per tick. We observe that propagation does not inherently require validity proofs on the path-only a lightweight assurance that an object is eligible for relay. We present AR-ACE (ACE-GF-based Attestation Relay for PQC), in which relay nodes forward objects plus compact attestations (e.g., identity-bound signatures or commitments) and do not generate, hold, or forward any full validity proof. Only the builder (or final verifier) performs a single aggregated validity proof over the set of objects it includes. This proof-off-path design removes proof overhead from the propagation path entirely, yielding an order-of-magnitude reduction in proof-related relay bandwidth relative to proof-carrying propagation. When instantiated with ACE-GF-derived attestation keys, AR-ACE preserves a unified identity story with on-chain authorization and is PQC-ready. We specify a protocol model, state design goals and security considerations, define security games, and provide a structural bandwidth comparison with recursive-STARK-based propagation.
Post-quantum signature schemes impose kilobyte-scale on-chain artifacts. Verifying them inside ZK circuits merely relocates the cost via expensive lattice arithmetic in prover circuits. We present ZK-ACE (Zero-Knowledge Authorization for Cryptographic Entities), which replaces transaction-carried signature objects with identity-bound ZK statements. Given a deterministic identity derivation primitive (DIDP) as a black box, the prover demonstrates in zero knowledge that an identity consistent with an on-chain commitment authorized the transaction; no signature object is produced or verified on-chain. We provide game-based definitions and reduction-based proofs for authorization soundness, replay resistance, substitution resistance, and cross-domain separation, under knowledge soundness, collision resistance, and DIDP recovery hardness. Structural data accounting shows an order-of-magnitude reduction in per-transaction authorization data versus direct PQC deployment. A reference implementation offers two backends: Circle STARK (341 active rows / 361 AIR constraint expressions, 14.5 ms prove, 1.1 ms verify, approx. 107 KB proofs, transparent setup, post-quantum-oriented) and Groth16/BN254 (2,155 R1CS constraints, 37.3 ms prove, 128-byte proofs). Both are roughly 500--2,300x smaller than in-circuit PQC signature verification. Under mandatory per-block STARK aggregation, per-transaction consensus-visible data is approx. 160 bytes.
Cross-chain token standards enable fungible tokens that exist across multiple blockchains with a unified total supply model. This paper presents a comprehensive comparative analysis of five leading cross-chain token standards and frameworks: the xERC20 standard (implementing ERC-7281), the Omnichain Fungible Token (OFT) standard, the Native Token Transfers (NTT) framework, the Cross-Chain Token (CCT) standard, and the SuperchainERC20 standard (implementing ERC-7802). We examine each standard's distinguishing properties and technical design, including architecture, message-passing mechanisms, interoperability scope, chain compatibility, and security features. Our analysis reveals that while all these standards share the goal of seamless cross-chain fungibility, they differ significantly in implementation approach, trust model, and target ecosystem.
We introduce LegalEdge, an edge intelligence-driven framework that integrates Federated Learning (FL) and Deep Q-Networks (DQN) to optimize electric vehicle (EV) charging infrastructure. LegalEdge contracts are novel smart contracts deployed on the blockchain to manage dynamic pricing and incentive mechanisms transparently and autonomously. By leveraging FL, multiple edge devices such as EV charging stations collaboratively train DQN agents without sharing raw data, preserving user privacy while reducing communication costs. These edge-deployed agents learn optimal charging strategies in real time based on local conditions and global policy updates. LegalEdge ensures low-latency decisions, high contract integrity, and efficient energy allocation. Our experimental results demonstrate significant improvements in learning convergence, transaction speed, and operational transparency, establishing LegalEdge as a scalable, intelligent, and accountable solution for next-generation EV charging networks.
Patrick Spiesberger, Nils Henrik Beyer, Hannes Hartenstein
Ethereum's ideal of censorship resistance, together with related fairness properties, is undermined in practice, motivating fairness mechanisms that aim to restore these properties. Several of these mechanisms hand control over block contents to a committee of proposers under a 1-of-n honest assumption: at least one committee member complies with the mechanism even when deviating would increase personal revenue. We refer to such proposers as altruistic. Yet prior work shows that roughly 91 percent of blocks are constructed by centralized block-building services that demonstrably take user-adverse actions for financial gain; the responsible proposers sign these blocks blindly, without any means of intervention. A common reading of this figure is that 9 percent of proposers forgo these gains and act altruistically. Our empirical analysis of the full year 2025 shows that this share is far smaller: at most 1.55 percent of proposers can plausibly be regarded as altruistic, whereas the remaining 98.45 percent of proposers exhibit observable non-altruistic behavior. We interpret 1.55 percent as an upper bound on the prevalence of altruistic proposers. These results imply that committee-based fairness mechanisms that rely on altruistic members would require substantially larger committees than currently proposed. This raises concerns about their practical viability and motivates mechanisms in which fair behavior is the rational choice.
Blockchains are diverse in the way they handle communications between their nodes to disseminate information, mitigate attacks, and agree on the next block. While security vulnerabilities have been identified, they rely on an attack custom-made for a specific blockchain communication protocol. To our knowledge, the vulnerabilities of multiple blockchain communication protocols to adversarial conditions have never been compared. In this paper, we compare empirically the vulnerabilities of the communication protocols of five modern in-production blockchains, Algorand, Aptos, Avalanche, Redbelly and Solana, when attacked in five different ways. We conclude that Algorand is vulnerable to packet loss attacks, Aptos is vulnerable to targeted load attacks and leader isolation attacks, Avalanche is vulnerable to transient failure attacks, Redbelly's performance is impacted by packet loss attacks and Solana is vulnerable to stopping attacks and leader isolation attacks. Our system is open source.
In this paper, we analyze the finality of the Filecoin network, focusing on dynamic probabilistic guarantees of tipset permanence in the canonical chain. Our approach differs from static analyses that consider only the worst-case scenario; instead, we dynamically compute the error probability at each round using the live chain history, providing a more accurate and efficient assessment. We provide a practical algorithm that only requires visibility into the blocks produced by honest participants, which can be implemented by clients or off-chain applications without any change to Filecoin's consensus mechanisms.We demonstrate that, under typical operating conditions, the sought-after error probability of $2^{-30}$ is achievable in approximately 30 rounds, a 30x improvement over the 900 rounds that the network currently encodes as a fixed threshold. This finding immediately expedites transactions and enhances usability of the Filecoin network, while laying the foundation for further analysis of other DAG-structured blockchains.
Yue Li, Lei Wang, Kaixuan Wang, Zhiqiang Yang · 7 authors
The rapid proliferation of autonomous AI agents is driving a shift toward agentic commerce, where agents are expected to autonomously invoke and pay for services. While blockchain-based payments offer a programmable foundation for such interactions, the recently proposed x402 standard fails to enforce end-to-end atomicity across service execution, payment, and result delivery. In this paper, we present A402, a trust-minimized payment architecture that securely binds cryptocurrency payments to service execution. A402 introduces Atomic Service Channels (ASCs), a new channel protocol that integrates service execution into payment channels, enabling real-time, high-frequency micropayments for agentic commerce. Within each ASC, A402 employs an atomic exchange protocol based on TEE-assisted adaptor signatures, ensuring that payments are finalized if and only if the requested service is correctly executed and the corresponding result is delivered. To further ensure privacy, A402 incorporates a TEE-based Liquidity Vault that privately manages the lifecycle of ASCs and aggregates their settlements into a single on-chain transaction, revealing only aggregated balances. We implement A402 and evaluate it against x402 with integrations on both Bitcoin and Ethereum. Our results show that A402 delivers orders-of-magnitude performance and on-chain cost improvements over x402 while providing trust-minimized security guarantees.
Autonomous software agents on blockchains solve distributed-coordination problems by reading shared ledger state instead of exchanging direct messages. Liquidation keepers, arbitrage bots, and other autonomous on-chain agents watch balances, contract storage, and event logs; when conditions change, they act. The ledger therefore functions as a replicated shared-state medium through which decentralized agents coordinate indirectly. This form of indirect coordination mirrors what Grassé called stigmergy in 1959: organisms coordinating through traces left in a shared environment, with no central plan. Stigmergy has mature formalizations in swarm intelligence and multi-agent systems, and on-chain agents already behave stigmergically in practice, but no prior application-layer framework cleanly bridges the two. We introduce Indirect coordination grounded in ledger state (Coordinación indirecta basada en el estado del registro contable) as a ledger-specific applied definition that maps Grassé's mechanism onto distributed ledger technology. We operationalize this with a state-transition formalism, identify three recurring base on-chain coordination patterns (State-Flag, Event-Signal, Threshold- Trigger) together with a Commit-Reveal sequencing overlay, and work through a State-Flag task-board example to compare ledger-state coordination analytically with off-chain messaging and centralized orchestration. The contribution is a reusable vocabulary, a ledger-specific formal mapping, and design guidance for decentralized coordination over replicated shared state at the application layer.
Federated learning (FL) enables collaborative model training over distributed private data. However, sustaining open participation requires incentive mechanisms that compensate contributors for their resources and risks. Enabled by Web3 primitives, especially blockchains, recent FL proposals incorporate incentive mechanisms for open participation, yet most focus primarily on algorithmic design and overlook system-level challenges, including coordination efficiency, secure handling of model updates, and practical usability. We present FWeb3, a practical Web3-enabled FL framework for incentive-aware training in open environments. FWeb3 adopts a modular architecture that separates FL functions from Web3 support services, decoupling the off-chain training and data plane from on-chain settlement while preserving verifiable incentive execution. The framework supports pluggable aggregation and contribution evaluation methods and provides a browser-native DApp interface to lower the participation barrier. We evaluate FWeb3 in real-world settings and show that it supports end-to-end incentive-aware FL with transaction and data-transfer overheads of only 21.3% and 3.4% in WAN; FWeb3 also deploys from zero configuration in under 3 minutes and enables user onboarding in under 1 minute.
Sybil resistance is a key requirement of decentralized consensus protocols. It is achieved by introducing a scarce resource (such as computational power, monetary stake, disk space, etc.), which prevents participants from costlessly creating multiple fake identities and hijacking the protocol. Quantum states are generically uncloneable, which suggests that they may serve naturally as an unconditionally scarce resource. In particular, uncloneability underlies quantum position-based cryptography, which is unachievable classically. We design a consensus protocol that combines classical hybrid consensus protocols with quantum position verification as the Sybil resistance mechanism, providing security in the standard model, and achieving improved energy efficiency compared to hybrid protocols based on Proof-of-Work. Our protocol inherits the benefits of other hybrid protocols, namely the faster confirmation times compared to pure Proof-of-Work protocols, and resilience against the compounding wealth issue that plagues protocols based on Proof-of-Stake Sybil resistance. We additionally propose a spam prevention mechanism for our protocol in the Random Oracle model.
Byzantine Fault Tolerant (BFT) consensus forms the foundation of many modern blockchains striving for both high throughput and low latency. A growing bottleneck is transaction execution and validation on the critical path of consensus, which has led to modular decoupled designs that separate ordering from execution: Consensus orders only metadata, while transactions are executed and validated concurrently. While this approach improves performance, it can leave invalid transactions in the ledger, increasing storage costs and enabling new forms of strategic behavior. We present the first systematic study of this setting, providing a formal framework to reason about the interaction between consensus and execution. Using this framework, we show that the decoupled design enables a previously unidentified attack, which we term gaslighting. We prove a fundamental trade-off between resilience to this attack and resource capacity utilization, where both are impossible to achieve deterministically in the decoupled model. To address this trade-off, we discuss an intermediate model for leader-based protocols that is robust to gaslighting attacks while achieving high throughput and low latency.
Zero-knowledge proof generation imposes stringent timing and reliability constraints on blockchain systems. For ZK-rollups, delayed proofs cause finality lag and economic loss; for Ethereum's emerging L1 zkEVM, proofs must complete within the 12-second slot window to enable stateless validation. The Ethereum Foundation's Ethproofs initiative coordinates multiple independent zkVMs across proving clusters to achieve real-time block proving, yet no principled orchestration framework addresses the joint challenges of (i) strict head-of-chain ordering, (ii) sub-slot latency bounds, (iii) fault-tolerant task reassignment, and (iv) prover-agnostic workflow composition. We present push0, a cloud-native proof orchestration system that decouples prover binaries from scheduling infrastructure. push0 employs an event-driven dispatcher--collector architecture over persistent priority queues, enforcing block-sequential proving while exploiting intra-block parallelism. We formalize requirements drawn from production ZK-rollup operations and the Ethereum real-time proving specification, then demonstrate via production Kubernetes cluster experiments that push0 achieves 5 ms median orchestration overhead with 99--100% scaling efficiency at 32 dispatchers for realistic workloads--overhead negligible (less than 0.1%) relative to typical proof computation times of 7+ seconds. Controlled Docker experiments validate these results, showing comparable performance (3--10 ms P50) when network variance is eliminated. Production deployment on the Zircuit zkrollup (14+ million mainnet blocks since March 2025) provides ecological validity for these controlled experiments. Our design enables seamless integration of heterogeneous zkVMs, supports automatic task recovery via message persistence, and provides the scheduling primitives necessary for both centralized rollup operators and decentralized multi-prover networks.