Polynomial Liveness

Important properties of many protocols are liveness or availability, i.e., that something good happens now and then. In asynchronous scenarios, these properties depend on the scheduler, which is usually considered to be fair in this case. The standard definitions of fairness and liveness are based on infinite sequences. Unfortunately, this cannot be applied to most cryptographic protocols since one must restrict the adversary and the runs as a whole to length polynomial in the security parameter