Backoff algorithms are used in many distributed systems where multiple devices contend for a shared resource. For the classic balls-into-bins problem, the number of singletons—those bins with a single ball—is important to the analysis of several backoff algorithms; however, existing analyses employ advanced probabilistic tools. Here, we show that standard Chernoff bounds can be used instead, and the simplicity of this approach is illustrated by re-analyzing some well-known backoff algorithms.

A popular technique for tolerating malicious faults in open distributed systems is to establish small groups of participants, each of which has a non-faulty majority. These groups are used as building blocks to design attack-resistant algorithms. Despite over a decade of active research, current constructions require group sizes of O(log n), where n is the number of participants in the system. This group size is important since communication and state costs scale polynomially with this parameter. Given the stubbornness of this logarithmic barrier, a natural question is whether better bounds are possible. Here, we consider an attacker that controls a constant fraction of the total computational resources in the system. By leveraging proof-of-work (PoW), we demonstrate how to reduce the group size exponentially to O(log log n) while maintaining strong security guarantees. This reduction in group size yields a significant improvement in communication and state costs.