Consensus in anonymous asynchronous systems with crash-recovery and omission failures

In anonymous distributed systems, processes are indistinguishable because they have no identity and execute the same algorithm. Currently, anonymous systems are receiving a lot of attention mainly because they preserve privacy, which is an important property when we want to avoid impersonation attacks. On the other hand, Consensus is a fundamental problem in distributed computing. It is well-known that Consensus cannot be deterministically solved in pure asynchronous anonymous systems if processes can crash (the so-called crash-stop failure model). This impossibility holds even if message losses never occur in transmission. Failure detectors are an elegant and powerful abstraction for achieving deterministic Consensus in asynchronous distributed systems. A failure detector is a distributed object that gives the processes information about crashed processes. Failure detectors have attracted so much attention in the crash-stop failure model because they provide a totally independent abstraction. Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document} is the weakest failure detector to solve Consensus in classic asynchronous systems when a majority of processes never crash, and AΩ′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\varOmega '$$\end{document} is its implementable version for anonymous systems. As far as we know, there is a lack of works in the literature which tackle Consensus in anonymous asynchronous systems where crashed process can recover (the so-called crash-recovery failure model) and also assuming errors in transmission operations (the so-called omission failure model). Extending failure models in the system allows us to design more realistic systems and solve more practical security problems (i.e., fair exchange and the secure multiparty computation). We present, in this paper, an algorithm to solve Consensus using AΩ′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\varOmega '$$\end{document} in anonymous asynchronous systems under the crash-recovery and omission failure models. Another important contribution of this paper is a communication-efficient and latency-efficient implementation of AΩ′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\varOmega '$$\end{document} for these new failure models.