Single attack giving joint bounds on safety violation and queue service

Develop an adversarial strategy within the exponential delay model of Nakamoto consensus that simultaneously yields a rigorous upper bound on both (i) the transaction safety violation probability and (ii) the sustainable transaction rate (queue service), or else establish that no single attack can provide tight, unified upper bounds for both metrics.

Background

The paper derives an upper bound on safety violation probability using a rigged private attack and analyzes throughput via a batch-service queue model, also considering a queue-service attack that impairs sustainable transaction rate. These analyses use different adversarial strategies for the two metrics.

In the conclusion, the authors explicitly pose whether one can devise a single adversarial attack that controls both dimensions simultaneously, highlighting a gap between security and throughput analyses.