FEASIBLE REGION OF RTCT VERIFICATION PARAMETERS IN DECENTRALIZED OVERLAY NETWORKS

Abstract

This paper constructs the feasible region of verification parameters based on Random Time Challenge Tokens (RTCT) in decentralized overlay networks as the intersection of an upper bound on the false-miss rate of honest nodes and a lower bound on the cost of sustaining a set of fake identities. The false-miss law is derived from the distribution of the puzzle-solving time and therefore depends on the challenge difficulty; the minimum response window must be computed for the slowest tolerated node, otherwise the false-miss rate in a heterogeneous population is underestimated by a factor of 5.8. The capacity an adversary needs to service k identities is obtained from a loss-system staffing problem with the Erlang formula, insensitive to the distribution of the solving time; its dependence on k has two regimes. It is proved that, when the CPU duty cycle of an honest node is bounded and resource prices are linear, the adversary’s per-identity computing cost has an asymptotic ceiling independent of both the difficulty and the challenge intensity; with public energy and compute-rental prices it is about 6·10⁻⁴ EUR per identity per day, an order of magnitude below the cost of network presence. The deterrent effect of RTCT therefore rests on the enforced recurrence of entry costs rather than on computing cost: the number of identities that can be held without servicing is proportional to the ratio of the eviction time to the sum of the eviction time and the recovery time of the scarce entry resource. For a strictly increasing security index with a positive marginal effect at the load bound, the optimum is a corner solution on the honest-side constraints, and the Lagrange multiplier of the load constraint is the shadow price of security. The results were verified by Monte Carlo simulation.