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 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. 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. 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. 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