Byzantine-Resistant Total Ordering Algorithms

AbstractMulticast group communication protocols are used extensively in fault-tolerant distributed systems. For many such protocols, the acknowledgments for individual messages define a causal order on messages. Maintaining the consistency of information, replicated on several processors to protect it against faults, is greatly simplified by a total order on messages. We present algorithms that incrementally convert a causal order on messages into a total order and that tolerate both crash and Byzantine process faults. Varying compromises between latency to message ordering and resilience to faults yield four distinct algorithms. All of these algorithms use a multistage voting strategy to achieve agreement on the total order and exploit the random structure of the causal order to ensure probabilistic termination

Self-Healing Computation

In the problem of reliable multiparty computation (RC), there are $n$ parties, each with an individual input, and the parties want to jointly compute a function $f$ over $n$ inputs. The problem is complicated by the fact that an omniscient adversary controls a hidden fraction of the parties. We describe a self-healing algorithm for this problem. In particular, for a fixed function $f$, with $n$ parties and $m$ gates, we describe how to perform RC repeatedly as the inputs to $f$ change. Our algorithm maintains the following properties, even when an adversary controls up to $t \leq (\frac{1}{4} - \epsilon) n$ parties, for any constant $\epsilon >0$. First, our algorithm performs each reliable computation with the following amortized resource costs: $O(m + n \log n)$ messages, $O(m + n \log n)$ computational operations, and $O(\ell)$ latency, where $\ell$ is the depth of the circuit that computes $f$. Second, the expected total number of corruptions is $O(t (\log^{*} m)^2)$, after which the adversarially controlled parties are effectively quarantined so that they cause no more corruptions.Comment: 17 pages and 1 figure. It is submitted to SSS'1