Two Lower Bounds In Asynchronous Distributed Computation

We introduce new techniques for deriving lower bounds on the message complexity in asynchronous distributed computation. These techniques combine the choice of specific patterns of communication delays and crossing sequence arguments with consideration of the speed of propagation of messages, together with careful counting of messages in different parts of the network. They enable us to prove the following results, settling two open problems: An Ω(n log* n) lower bound for the number of messages sent by an asynchronous algorithm for computing any nonconstant function on a bidirectional ring of n anonymous processors. An Ω(n log n) lower bound for the average number of messages sent by any maximum finding algorithm on a ring of n processors, in case n is known

Model Checking of Robot Gathering

Recent advances in distributed computing highlight models and algorithms for autonomous mo- bile robots that self-organize and cooperate together in order to solve a global objective. As results, a large number of algorithms have been proposed. These algorithms are given together with proofs to assess their correctness. However, those proofs are informal, which are error prone. This paper presents our study on formal verification of mobile robot algorithms. We first propose a formal model for mobile robot algorithms on anonymous ring shape network under multiplicity and asynchrony assumptions. We specify this formal model in Maude, a specification and pro- gramming language based on rewriting logic. We then use its model checker to formally verify an algorithm for robot gathering problem on ring enjoys some desired properties. As the result of the model checking, counterexamples have been found. We detect the sources of some unforeseen design errors. We, furthermore, give our interpretations of these errors

Identity-based edge computing anonymous authentication protocol

With the development of sensor technology and wireless communication technology, edge computing has a wider range of applications. The privacy protection of edge computing is of great significance. In the edge computing system, in order to ensure the credibility of the source of terminal data, mobile edge computing (MEC) needs to verify the signature of the terminal node on the data. During the signature process, the computing power of edge devices such as wireless terminals can easily become the bottleneck of system performance. Therefore, it is very necessary to improve efficiency through computational offloading. Therefore, this paper proposes an identity-based edge computing anonymous authentication protocol. The protocol realizes mutual authentication and obtains a shared key by encrypting the mutual information. The encryption algorithm is implemented through a thresholded identity-based proxy ring signature. When a large number of terminals offload computing, MEC can set the priority of offloading tasks according to the user’s identity and permissions, thereby improving offloading efficiency. Security analysis shows that the scheme can guarantee the anonymity and unforgeability of signatures. The probability of a malicious node forging a signature is equivalent to cracking the discrete logarithm puzzle. According to the efficiency analysis, in the case of MEC offloading, the computational complexity is significantly reduced, the computing power of edge devices is liberated, and the signature efficiency is improved

Leader Election in Anonymous Rings: Franklin Goes Probabilistic

We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size

Memory lower bounds for deterministic self-stabilization

In the context of self-stabilization, a \emph{silent} algorithm guarantees that the register of every node does not change once the algorithm has stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent algorithm must use a memory of $\Omega(\log n)$ bits per register in $n$-node networks. Similarly, Korman et al. [Dist. Comp. '07] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning trees (MST), every silent algorithm must use a memory of $\Omega(\log^2n)$ bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity. In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for general algorithms, also established at the end of the 90's, is due to Beauquier et al.~[PODC '99] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing a tight lower bound of $\Theta(\log \Delta+\log \log n)$ bits per register for self-stabilizing algorithms solving $(\Delta+1)$-coloring or constructing a spanning tree in networks of maximum degree~$\Delta$. The lower bound $\Omega(\log \log n)$ bits per register also holds for leader election