  Concerns for the privacy of communication is widely discussed in research and
overall society. For the public financial infrastructure of blockchains, this
discussion encompasses the privacy of transaction data and its broadcasting
throughout the network. To tackle this problem, we transform a discrete-time
protocol for contact networks over infinite trees into a computer network
protocol for peer-to-peer networks. Peer-to-peer networks are modeled as
organically growing graphs. We show that the distribution of shortest paths in
such a network can be modeled using a normal distribution
$\mathcal{N}(\mu,\sigma^2).$ We determine statistical estimators for
$\mu,\sigma$ via multivariate models. The model behaves logarithmic over the
number of nodes n and proportional to an inverse exponential over the number of
added edges k. These results facilitate the computation of optimal forwarding
probabilities during the dissemination phase for optimal privacy in a limited
information environment.
