Tight bounds for shared memory systems accessed by Byzantine processes

Abstract

We provide efficient constructions and tight bounds for shared memory systems accessed by n processes, up to t of which may exhibit Byzantine failures, in a model previously explored by Malkhi et al. [21]. We show that sticky bits are universal in the Byzantine failure model for n ≥ 3t + 1, an improvement over the previous result requiring n ≥ (2t +1)(t +1). Our result follows from a new strong A preliminary version of the results presented in this paper appeared in [23]. consensus construction that uses sticky bits and tolerates t Byzantine failures among n processes for any n ≥ 3t + 1, the best possible bound on n for strong consensus. We also present tight bounds on the efficiency of implementations of strong consensus objects from sticky bits and similar primitive objects.

Sharing Memory between Byzantine Processes Using Policy-Enforced Tuple Spaces

“…The paper provides algorithms for consensus and a universal construction that are much simpler than previous ones based on sticky bits and ACLs [1,16]. They are also more efficient in terms of number of bits and objects needed to solve a certain problem.…”

“…Previous works on objects shared by Byzantine processes consider that the access to operations in these objects is protected by ACLs [1,3,16]. In that model, each operation provided by an object is associated to a list of processes that have access to that operation.…”

“…Despite the large amount of Byzantine fault-tolerant algorithms for message-passing systems designed through the years [4,8,9,10,11,17], only recently algorithms for the coordination of processes subject to Byzantine failures using shared memory have appeared [1,3,16]. The motivation for this line of research is the current availability of several solutions for the emulation of dependable shared memory objects on message-passing distributed systems subject to Byzantine failures [7,8,9,10,17].…”

“…They have shown that simple objects like registers and sticky bits [20] when combined with access control lists (ACLs) are enough to implement consensus [16], that the optimal resilience for strong consensus is n ! 3t + 1 in this model [1,16] (t is an upper bound on the number of faulty processes and n the total number of processes), and that sticky bits with ACLs are universal, i.e., they can be used to implement any shared memory object [16], to state only some of those contributions. Despite the undeniable importance of these theoretical results, on the practical side these works also show the limitations of combining simple objects like sticky bits with ACLs: the amount of objects required and the amount of operations requested in these objects is enormous, making the developed algorithms impractical for real systems.…”

Byzantine consensus in asynchronous message-passing systems: a survey

“…An alternative system model would be shared-memory (Attie, 2002;Friedman et al, 2002;Malkhi et al, 2003;Alon et al, 2005;Bessani et al, 2009), but in the system architecture we are considering the shared memory itself has to be implemented using message-passing algorithms. For shared memory, consensus has been shown to be universal, i.e., to be enough to implement any shared memory object, both with crash (Herlihy, 1991) and Byzantine faults (Malkhi et al, 2003).…”