Self-Stabilizing and Private Distributed Shared Atomic Memory in Seldomly Fair Message Passing Networks

Abstract

We study the problem of privately emulating shared memory in message-passing networks. The system includes clients that store and retrieve replicated information on N servers, out of which e are data-corrupting malicious. When a client accesses a data-corrupting malicious server, the data field of that server response might be different from the value it originally stored. However, all other control variables in the server reply and protocol actions are according to the server algorithm. For the coded atomic storage algorithms by Cadambe et al., we present an enhancement that ensures no information leakage and data-corrupting malicious fault-tolerance. We also consider recovery after the occurrence of transient faults that violate the assumptions according to which the system was designed to operate. After their last occurrence, transient faults leave the system in an arbitrary state (while the program code stays intact). We present a self-stabilizing algorithm, which recovers after the occurrence of transient faults. This addition to Cadambe et al. considers asynchronous settings as long as no transient faults occur. The recovery from transient faults that bring the system counters (close) to their maximal values may include the use of a global reset procedure, which requires the system run to be controlled by a fair scheduler. After the recovery period, the safety properties are provided for asynchronous system runs that are not necessarily controlled by fair schedulers. Since the recovery period is bounded and the occurrence of transient faults is extremely rare, we call this design criteria self-stabilization in the presence of seldom fairness. Our self-stabilizing algorithm uses a bounded amount of storage during asynchronous executions (that are not necessarily controlled by fair schedulers). To the best of our knowledge, we are the first to address privacy, data-corrupting malicious behavior, and self-stabilization in the context of emulating atomic shared memory in message-passing systems.

Self-stabilizing Uniform Reliable Broadcast

“…1.6 Self-stabilizing systems in the presence of seldom fairness Dolev, Petig, and Schiller [18] studied self-stabilizing systems that their scheduler is seldom fair. Specifically, after the occurrence of the last transient fault, fairness eventually holds, but only for the bounded period that is sufficient for enabling Convergence.…”

“…Non-self-stabilizing fault-tolerant TO-URB exists [31,23], but we are interested in self-stabilizing solutions. Seldom fairness was used for solving self-stabilizing FIFO-URB [25], binary and multivalued consensus [27,28], atomic shared memory emulation and their wait-free snapshots [18,21], as well as set-constraint broadcast [26], to name a few. This earlier literature assumes seldom fairness and shows how to transform a non-self-stabilizing algorithm into a self-stabilizing one.…”

Message Passing Applications: A Review

“…One player transfers a move (using a message) to another player; the second player matches the move to the copy of the "playing board", measures its options, and transfers his "countermove" to the first player. In this example, there is nothing the player has to do except choose his move or wait for the second player to send his move, so there is no need to be able to synchronously receive and process messages [26]. This is not usually the case.…”

“…There may be an entrance to work with, many players for remote syncing, graphical screens may be required to update, and complex internal modules to keep the route right. To save every item in the proxy operating in the ideal way, asynchronous message I / O may be necessary so message-passing scheme will support this method [26] [27].…”

“…Asynchronous and distributed message Passing has little burden correlated with it to be structured in an easier way just by a procedure call [26]. In conventional procedure call, arguments are typically passed to the recipient through one or more what are known as common purpose registers or may be passed as a list of parameters including the arguments addresses.…”