5.2.1. Network Latency

Figure 4 presents the network latency for EconLedger with respect to completing an entire epoch round of PoENF consensus protocol given the number of validators varying from 5 to 20. For each test point, we let all validators perform tasks simultaneously and waited until the bundle of tasks is finished. The latency includes the round trip time (RTT) and service processing time on the remote host. Broadcasting an ENF *tx* needs O(*K*) communication complexity and *K* × O(1) computation complexity for verification. Thus, the total complexity is O(*K*) such that latency of ENF collection T*ec* is linearly scale to committee size *K*. Chain finality requires all validators to broadcast their vote among committee members so that it has the same complexity as ENF collection. Thus, the delay of chain finality T*c f* is almost linear scale to *K*.

The green line in Figure 4 shows the latency of block proposal T*bp*, which indicates how long a proposed block could be accepted by all validators in the PoENF committee. The communication complexity of block proposal is O(*K*), which is similar to ENF collection and chain finality. However, during block generation and verification processes, PoENF algorithm requires a validator using Equation (1) to compute ENF scores based on collected proofs from others, and it has computation complexity of <sup>O</sup>(*K*2*d*). As a result, the total complexity of block proposal is O(*K*2*d* + *<sup>K</sup>*). In general, ENF samples size *d* is a small value such as 60, and it has less effect on computation cost than *K* does. Thus, T*bp* is almost linearly scaled relative to <sup>O</sup>(*K*<sup>2</sup>). The total latency shows that EconLedger takes about 2 s to finish an epoch cycle of PoENF committee consensus (T*ec* + T*bp* + T*c f*) given the committee size *K* = 20.

**Figure 4.** Latency for an epoch cycle of PoENF consensus with different committee size.
