Authenticated Byzantine Generals in Dual Failure Model

Abstract

Pease et al. introduced the problem of Byzantine Generals (BGP) to study the effects of Byzantine faults in distributed protocols for reliable broadcast. It is well known that BGP among n players tolerating up to t faults is (efficiently) possible if and only if n > 3t. To overcome this severe limitation, Pease et al. introduced a variant of BGP, Authenticated Byzantine General (ABG). Here players are supplemented with digital signatures (or similar tools) to thwart the challenge posed by Byzantine faults. Subsequently, they proved that with the use of authentication, fault tolerance of protocols for reliable broadcast can be amazingly increased to n > t (which is a huge improvement over the n > 3t).Byzantine faults are the most generic form of faults. In a network not all faults are always malicious. Some faulty nodes may only leak their data while others are malicious. Motivated from this, we study the problem of ABG in (t b ,t p )-mixed adversary model where the adversary can corrupt up to any t b players actively and control up to any other t p players passively. We prove that in such a setting, ABG over a completely connected synchronous network of n nodes tolerating a (t b ,t p )-adversary is possible if and only if n > 2t b +min(t b , t p ) when t p > 0. Interestingly, our results can also be seen as an attempt to unify the extant literature on BGP and ABG.

Distributed Computing

“…By invoking Lemma 1, Lemma 6 and Lemma 7 and the result of Gupta et al [GGBS10], we establish the theorem. By invoking Lemma 1, Lemma 6 and Lemma 7 and the result of Gupta et al [GGBS10], we establish the theorem.…”

“…To understand the utility, potential and limitations of using authentication in distributed protocols for agreement, Gupta et al [GGBS10] studied ABA in new light. They generalize the existing models and thus, attempt to give a unified theory of agreements over the authenticated and non-authenticated domains.…”

“…Gupta et al [GGBS10] consider the problem of Authenticated Byzantine Agreement(ABA) under a mixed adversary model. They give completeness theorems for ABA protocols over a complete network.…”

Player-Centric Byzantine Agreement

“…We point out that, in that model, adding passive corruption makes no difference for Consensus [5]. Feasibility of BA with active and passive corruption (and a trusted PKI) was previously studied in [21] for Consensus, and in [20] for Consensus and Broadcast. In both works, a threshold adversary is considered; the corresponding bound for Consensus is 2t a + min{t a , t p } < n. In such a threshold world, constructing BA protocols for the corresponding bound turns out to be less involved than in the general-adversary setting, as one can consider the cases t a ≤ t p and t a > t p separately, and construct one protocol for each.…”

“…The reason is that in such a model the signatures of passively corrupted players are not reliable, as the adversary knows the signing keys and can trivially fake them. In [21] it is shown that given a Public-Key Infrastructure (PKI), an adversary who can actively corrupt up to t a players and passively corrupt up to t p players can be tolerated for Consensus if and only if 2t a + min{t a , t p } < n.…”