This paper establishes a fundamental theory of secure clock synchronization. Accurate clock synchronization is the backbone of systems managing power distribution, financial transactions, telecommunication operations, database services, etc. Some clock synchronization (time transfer) systems, such as the global navigation satellite systems, are based on one-way communication from a master to a slave clock. Others, such as the network transport protocol, and the IEEE 1588 precision time protocol (PTP), involve two-way communication between the master and slave. This paper shows that all one-way time transfer protocols are vulnerable to replay attacks that can potentially compromise timing information. A set of conditions for secure two-way clock synchronization is proposed and proved to be necessary and sufficient. It is shown that IEEE 1588 PTP, although a two-way synchronization protocol, is not compliant with these conditions, and is therefore insecure. Requirements for secure IEEE 1588 PTP are proposed, and a second example protocol is offered to illustrate the range of compliant systems.
The work presented in @cite_11 is perhaps in closest relation to the current paper. upper bound the clock drift between subsequent synchronization signals using a drift model, and perform two-way exchange of timestamps such that the master clock is able to verify the time at the slave. Furthermore, given the maximum clock drift rate and the maximum and minimum propagation delay of the timing signal, they derive an upper bound on the adversarial delay that can go unnoticed. However, with conservative bounds on the maximum clock drift rate and the variation in path delays, the accuracy guarantees derived in @cite_11 may be insufficient for certain applications. Moreover, as will be shown in this paper, they fail to take account of one the necessary conditions for secure synchronization.
@cite_11
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We initiate a study of bounded clock synchronization under a more severe fault model than that proposed by Lamport and Melliar-Smith [1985]. Realistic aspects of the problem of synchronizing clocks in the presence of faults are considered. One aspect is that clock synchronization is an on-going task, thus the assumption that some of the processors never fail is too optimistic. To cope with this reality, we suggest self-stabilizing protocols that stabilize in any (long enough) period in which less than a third of the processors are faulty. Another aspect is that the clock value of each processor is bounded. A single transient fault may cause the clock to reach the upper bound. Therefore, we suggest a bounded clock that wraps around when appropriate.We present two randomized self-stabilizing protocols for synchronizing bounded clocks in the presence of Byzantine processor failures. The first protocol assumes that processors have a common pulse, while the second protocol does not. A new type of distributed counter based on the Chinese remainder theorem is used as part of the first protocol. Recent advances in miniaturization and low-cost, low-power design have led to active research in large-scale networks of small, wireless, low-power sensors and actuators. Time synchronization is critical in sensor networks for diverse purposes including sensor data fusion, coordinated actuation, and power-efficient duty cycling. Though the clock accuracy and precision requirements are often stricter than in traditional distributed systems, strict energy constraints limit the resources available to meet these goals.We present Reference-Broadcast Synchronization, a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts. A reference broadcast does not contain an explicit timestamp; instead, receivers use its arrival time as a point of reference for comparing their clocks. In this paper, we use measurements from two wireless implementations to show that removing the sender's nondeterminism from the critical path in this way produces high-precision clock agreement (1.85 ± 1.28μsec, using off-the-shelf 802.11 wireless Ethernet), while using minimal energy. We also describe a novel algorithm that uses this same broadcast property to federate clocks across broadcast domains with a slow decay in precision (3.68 ± 2.57μsec after 4 hops). RBS can be used without external references, forming a precise relative timescale, or can maintain microsecond-level synchronization to an external timescale such as UTC. We show a significant improvement over the Network Time Protocol (NTP) under similar conditions. Abstract We describe a new fault-tolerant algorithm for solving a variant of Lamport's clock synchronization problem. The algorithm is designed for a system of distributed processes that communicate by sending messages. Each process has its own read-only physical clock whose drift rate from real time is very small. By adding a value to its physical clock time, the process obtaines its local time. The algorithm solves the problem of maintaining closely synchronized local times, assuming that processes' local times are closely synchronized initially. The algorithm is able to tolerate the failure of just under one-third of the participating processes. It maintains synchronization to within a small constant, whose magnitude depends upon the rate of clock drift, the message delivery time and its uncertainty, and the initial closeness of synchronization. We also give a characterization of how far the clocks drift from real time. Reintegration of a repaired process can be accomplished using a slight modification of the basic alborithm. A similar style algorithm can also be used to achieve synchronization initially. The power of two well-known consistency conditions for shared-memory multiprocessors, sequential consistency and linearizability , is compared. The cost measure studied is the worst-case response time in distributed implementations of virtual shared memory supporting one of the two conditions. Three types of shared-memory objects are considered: read write objects, FIFO queues, and stacks. If clocks are only approximately synchronized (or do not exist), then for all three object types it is shown that linearizability is more expensive than sequential consistency. We show that, for all three data types, the worst-case response time is very sensitive to the assumptions that are made about the timing information available to the system. Under the strong assumption that processes have perfectly synchronized clocks, it is shown that sequential consistency and linearizability are equally costly. We present upper bounds for linearizability and matching lower bounds for sequential consistency. The upper bounds are shown by presenting algorithms that use atomic broadcast in a modular fashion. The lower-bound proofs for the approximate case use the technique of “shifting,” first introduced for studying the clock synchronization problem. Time-based localization approaches attract a lot of interest due to their high accuracy and potentially low cost for wireless sensor networks (WSNs). However, time-based localization is tightly coupled with clock synchronization. Thus, the reliability of timestamps in time-based localization becomes an important yet challenging task to deal with. In this paper, we propose robust time-based localization strategies to locate a target node with the help of anchors (nodes with known positions) in asynchronous networks. Two kinds of asynchronous networks are considered: one only with clock offsets, labeled quasi-synchronous networks, whereas the other with not only clock offsets but also clock skews, labeled fully asynchronous networks. A novel ranging protocol is developed for both networks, namely asymmetric trip ranging (ATR), to reduce the communication load and explore the broadcast property of WSNs. Regardless of the reliability of the timestamp report from the target node, closed-form least-squares (LS) estimators are derived to accurately estimate the target node position. As a result, we counter the uncertainties caused by the target node by ignoring the timestamps from this node. Furthermore, in order to simplify the estimator in fully asynchronous networks, localization and synchronization are decoupled. A simple yet efficient method is proposed to first Calibrate the Clock Skews of the anchors, and then Estimate the Node Position (CCS-ENP). Finally, Cramer-Rao bounds (CRBs) and simulation results corroborate the efficiency of our localization schemes. Recently, a few efficient timing synchronization protocols for wireless sensor networks (WSNs) have been proposed with the goal of maximizing the accuracy and minimizing the power utilization. This paper proposes novel clock skew estimators assuming different delay environments to achieve energy-efficient network-wide synchronization for WSNs. The proposed clock skew correction mechanism significantly increases the re-synchronization period, which is a critical factor in reducing the overall power consumption. The proposed synchronization scheme can be applied to the conventional protocols without additional overheads. Moreover, this paper derives the Cramer-Rao lower bounds and the maximum likelihood estimators under different delay models and assumptions. These analytical metrics serves as good benchmarks for the thus far reported experimental results We introduce the distributed gradient clock synchronization problem. As in traditional distributed clock synchronization, we consider a network of nodes equipped with hardware clocks with bounded drift. Nodes compute logical clock values based on their hardware clocks and message exchanges, and the goal is to synchronize the nodes' logical clocks as closely as possible, while satisfying certain validity conditions. The new feature of gradient clock synchronization (GCS for short) is to require that the skew between any two nodes' logical clocks be bounded by a nondecreasing function of the uncertainty in message delay (call this the distance) between the two nodes. That is, we require nearby nodes to be closely synchronized, and allow faraway nodes to be more loosely synchronized. We contrast GCS with traditional clock synchronization, and discuss several practical motivations for GCS, mostly arising in sensor and ad hoc networks. Our main result is that the worst case clock skew between two nodes at distance d from each other is Ω(d + log D log log D), where D is the diameter1 of the network. This means that clock synchronization is not a local property, in the sense that the clock skew between two nodes depends not only on the distance between the nodes, but also on the size of the network. Our lower bound implies, for example, that the TDMA protocol with a fixed slot granularity will fail as the network grows, even if the maximum degree of each node stays constant. Synchronization and localization are critical challenges for the coherent functioning of a wireless network, which are conventionally solved independently. Recently, various estimators have been proposed for pairwise synchronization between immobile nodes, based on time stamp exchanges via two-way communication. In this paper, we consider a network of mobile nodes for which a novel joint time-range model is presented, treating both unsynchronized clocks and the pairwise distances as a polynomial functions of true time. For a pair of nodes, a least squares solution is proposed for estimating the pairwise range parameters between the nodes, in addition to estimating the clock offsets and clock skews. Extending these pairwise solutions to network-wide ranging and clock synchronization, we present a central data fusion based global least squares algorithm. A unique solution is nonexistent without a constraint on the cost function e.g., a clock reference node. Ergo, a constrained framework is proposed and a new Constrained Cramer–Rao Bound (CCRB) is derived for the joint time-range model. In addition, to alleviate the need for a single clock reference, various clock constraints are presented and their benefits are investigated using the proposed solutions. Simulations are conducted and the algorithms are shown to approach the theoretical limits. In this paper, we describe a global distributed solution that enables the simultaneous performance of time synchronization and positioning in ultra-wideband (UWB) ad hoc networks. On the one hand, the proposed synchronization scheme basically relies on cooperative two-way-ranging time-of-arrival transactions and a diffusion algorithm that ensures the convergence of clock parameters to average reference values in each node. Although the described solution is generic at first sight, its sensitivity to time-of-arrival accuracy imposes the choice of an impulse-radio ultra-wideband physical layer in the very context. On the other hand, a distributed algorithm coupled with this synchronization scheme mitigates the impact of non-line-of-sight ranging errors on positioning accuracy without any additional protocol hook. More particularly, the realistic UWB ranging error models we use take into account UWB channel effects, as well as detection noises and relative clock drifts. Then, it is demonstrated that a cooperative and distributed maximization of the log-likelihood of range estimates can reduce the uncertainty on estimated positions in comparison with classical distributed weighted least squares approaches. Finally, the proposed distributed maximum log-likelihood algorithm proves to preserve a reasonable level of complexity in each node by approximating asynchronously the positive gradient direction of the log-likelihood function. For both distributed synchronization and positioning algorithms, simulation results are provided to illustrate the relevance of such a solution. With increasing prevalence of mobile wireless devices with WiFi and Bluetooth capability, new applications that can make use of limited contact opportunities when the devices are physically close are emerging. Proximity-based social networking, and location specific dissemination of advertisements and events, are some such applications. Discovering such services is a challenging problem due to energy budget limitations, user mobility, and nonuniformity and the time-varying nature of energy budgets across users. It is important to rapidly discover such mobile services to make use of limited contact opportunities. To support such applications, we seek to design a localized discovery scheme that can minimize the expected contact latency between mobile phones with limited energy budgets. All the existing neighbor discovery schemes assume lack of any time synchronization. However, in practice sufficiently accurate time synchronization can be achieved with existing time synchronization techniques. We propose Recursive Binary Time Partitioning (RBTP), a scheme that determines how the devices should wake up and sleep to achieve minimal contact latency with other nearby devices. RBTP achieves provable performance bound and outperforms state-of-the-art asynchronous protocols for smartphones. When compared with the optimum scheme, the contact latency is shown to be within a factor of (9 8) in the expected case and 2 in the worst case. In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the consensus algorithm able to synchronize a family of double integrators. Since the various clocks may have different drifts, the algorithm needs to be designed so that it can work also in case of heterogeneous double integrators. Through a robust control analysis it is possible to determine the maximum admissible level of heterogeneity yielding synchronization. The first part of the paper is devoted to the analysis of an unrealistic synchronous implementation of the algorithm. However, in the last part of the paper we propose a realistic pseudo-synchronous implementation which is proved to be a perturbation of the synchronous one. From arguments related the center manifold theorem, the stability of the pseudo-synchronous is finally proved. We present a distributed clock synchronization algorithm that guarantees an exponentially improved bound of O(log D) on the clock skew between neighboring nodes in any graph G of diameter D. In light of the lower bound of Omega(log D log log D), this result is almost tight. Moreover, the global clock skew between any two nodes, particularly nodes that are not directly connected, is bounded by O(D), which is optimal up to a constant factor. Our algorithm further ensures that the clock values are always within a linear envelope of real time. A better bound on the accuracy with respect to real time cannot be achieved in the absence of an external timer. These results all hold in a general model where both the clock drifts and the message delays may vary arbitrarily within pre-specified bounds. The goal of this paper is to determine the data routes, subchannel schedules, and power allocations that maximize a weighted-sum rate of the data communicated over a generic OFDMA wireless network in which the nodes are capable of simultaneously transmitting, receiving and relaying data. Two instances are considered. In the first instance, subchannels are allowed to be time-shared by multiple links, whereas in the second instance, each subchannel is exclusively used by one of the links. Using a change of variables, the first problem is transformed into a convex form. In contrast, the second problem is not amenable to such a transformation and results in a complex mixed integer optimization problem. To develop insight into this problem, we utilize the first instance to obtain efficiently computable lower and upper bounds on the weighted-sum rate that can be achieved in the absence of time-sharing. Another lower bound is obtained by enforcing the scheduling constraints through additional power constraints and a monomial approximation technique to formulate the design problem as a geometric program. Numerical investigations show that the obtained rates are higher when time-sharing is allowed, and that the lower bounds on rates in the absence of time-sharing are relatively tight. Suppose a discrete-time signal S(t), 0 spl les t<N, is a superposition of atoms taken from a combined time-frequency dictionary made of spike sequences 1 sub t= spl tau and sinusoids exp 2 spl pi iwt N spl radic N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discrete-time signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l sup 1 norm of the coefficients among all decompositions. Here "highly sparse" means that N sub t +N sub w < spl radic N 2 where N sub t is the number of time atoms, N sub w is the number of frequency atoms, and N is the length of the discrete-time signal. Underlying this result is a general l sup 1 uncertainty principle which says that if two bases are mutually incoherent, no nonzero signal can have a sparse representation in both bases simultaneously. For the above setting, the bases are sinusoids and spikes, and mutual incoherence is measured in terms of the largest inner product between different basis elements. The uncertainty principle holds for a variety of interesting basis pairs, not just sinusoids and spikes. The results have idealized applications to band-limited approximation with gross errors, to error-correcting encryption, and to separation of uncoordinated sources. Related phenomena hold for functions of a real variable, with basis pairs such as sinusoids and wavelets, and for functions of two variables, with basis pairs such as wavelets and ridgelets. In these settings, if a function f is representable by a sufficiently sparse superposition of terms taken from both bases, then there is only one such sparse representation; it may be obtained by minimum l sup 1 norm atomic decomposition. The condition "sufficiently sparse" becomes a multiscale condition; for example, that the number of wavelets at level j plus the number of sinusoids in the jth dyadic frequency band are together less than a constant times 2 sup j 2 . Supporting massive device transmission is challenging in machine-to-machine (M2M) communications. Particularly, in event-driven M2M communications, a large number of devices become activated within a short period of time, which in turn causes high radio congestions and severe access delay. To address this issue, we propose a Fast Adaptive S-ALOHA (FASA) scheme for random access control of M2M communication systems with bursty traffic. Instead of the observation in a single slot, the statistics of consecutive idle and collision slots are used in FASA to accelerate the tracking process of network status that is critical for optimizing S-ALOHA systems. With a design based on drift analysis, the estimate of the number of the active devices under FASA converges fast to the true value. Furthermore, by examining the T-slot drifts, we prove that the proposed FASA scheme is stable as long as the average arrival rate is smaller than e-1, in the sense that the Markov chain derived from the scheme is geometrically ergodic. Simulation results demonstrate that under highly bursty traffic, the proposed FASA scheme outperforms traditional additive schemes such as PB-ALOHA and achieves near-optimal performance in reducing access delays. Moreover, compared to multiplicative schemes, FASA shows its robustness under heavy traffic load in addition to better delay performance. The concept of partial synchrony in a distributed system is introduced. Partial synchrony lies between the cases of a synchronous system and an asynchronous system. In a synchronous system, there is a known fixed upper bound Δ on the time required for a message to be sent from one processor to another and a known fixed upper bound P on the relative speeds of different processors. In an asynchronous system no fixed upper bounds Δ and P exist. In one version of partial synchrony, fixed bounds Δ and P exist, but they are not known a priori. The problem is to design protocols that work correctly in the partially synchronous system regardless of the actual values of the bounds Δ and P. In another version of partial synchrony, the bounds are known, but are only guaranteed to hold starting at some unknown time T , and protocols must be designed to work correctly regardless of when time T occurs. Fault-tolerant consensus protocols are given for various cases of partial synchrony and various fault models. Lower bounds that show in most cases that our protocols are optimal with respect to the number of faults tolerated are also given. Our consensus protocols for partially synchronous processors use new protocols for fault-tolerant “distributed clocks” that allow partially synchronous processors to reach some approximately common notion of time. Modern shared-memory multiprocessors use complex memory system implementations that include a variety of non-trivial and interacting optimizations. More time is spent in verifying the correctness of such implementations than in designing the system. In particular, large-scale Distributed Shared Memory (DSM) systems usually rely on a directory cache-coherence protocol to provide the illusion of a sequentially consistent shar ed address space. Verifying that such a distributed protocol satisfies sequential consistency is a difficult task. Current formal protocol verification techniques [18] complement simulation, but ar e some what nonintuitive to system designers and verifiers, and they do not scale well to practical systems. In this paper, we examine a new reasoning technique that is precise and (we find) intuitive. Our technique is based on Lamport’ s logical clocks, which were originally used in distributed systems. We make modest extensions to Lamport’ s logical clocking scheme to assign timestamps to r elevant protocol events to construct a total ordering of such events. Such total orderings can be used to verify that the requirements of a particular memory consistency model have been satisfied. We apply Lamport clocks to prove that a non-trivial directory protocol implements sequential consistency. T o do this, we describe an SGI Origin 2000-like protocol [12] in detail, provide a timestamping scheme that totally orders all protocol events, and then prove sequential consistency (i.e., a load always returns the value of the “last” stor e to the same address in timestamp order). In this paper, we study the wireless synchronization problem which requires devices activated at different times on a congested single-hop radio network to synchronize their round numbering. We assume a collection of n synchronous devices with access to a shared band of the radio spectrum, divided into F narrowband frequencies. We assume that the communication medium suffers from unpredictable, perhaps even malicious interference, which we model by an adversary that can disrupt up to t frequencies per round. Devices begin executing in different rounds and the exact number of participants is not known in advance. We first prove a lower bound, demonstrating that at least Ω(log2n (F-t)loglogn + Ft F-t logn) rounds are needed to synchronize. We then describe two algorithms. The first algorithm almost matches the lower bound, yielding a running time of O(F F - t log2n + Ft F - t logn) rounds. The second algorithm is adaptive, terminating in O(t′ log3n) rounds in good executions, that is, when the devices begin executing at the same time, and there are never more than t′ frequencies disrupted in any given round, for some t′ Deep autoregressive sequence-to-sequence models have demonstrated impressive performance across a wide variety of tasks in recent years. While several common architecture classes including recurrent, convolutional, and self-attention networks make different trade-offs between the amount of computation needed per layer and the length of the critical path at training time, inference for novel inputs still remains an inherently sequential process. We propose a novel blockwise parallel decoding scheme that takes advantage of the fact that some architectures can score sequences in sublinear time. By generating predictions for multiple time steps at once then backing off to the longest prefix validated by the scoring model, we can substantially improve the speed of greedy decoding without compromising performance. When tested on state-of-the-art self-attention models for machine translation and image super-resolution, our approach achieves iteration reductions of up to 2x over a baseline greedy decoder with no loss in quality. Relaxing the acceptance criterion and fine tuning model parameters allows for reductions of up to 7x in exchange for a slight decrease in performance. Our fastest models achieve a 4x speedup in wall-clock time. The convergence and precision of synchronization algorithms based on the theory of pulse-coupled oscillators is evaluated on programmable radios. Measurements in different wireless topologies show that such algorithms reach precisions in the low microsecond range. Based on the observation that phase rate deviation among radios is a limiting factor for the achievable precision, we propose a distributed algorithm for automatic phase rate equalization and show by experiments that an improved precision below one microsecond is possible in the given setups. It is also experimentally demonstrated that the stochastic nature of coupling is a key ingredient for convergence to synchrony. The proposed scheme can be applied in wireless systems for distributed synchronization of transmission slots, or sleep cycles.