Recent works have proposed new Byzantine consensus algorithms for blockchains based on epidemics, a design which enables highly scalable performance at a low cost. These methods however critically depend on a secure random peer sampling service: a service that provides a stream of random network nodes where no attacking entity can become over-represented. To ensure this security property, current epidemic platforms use a Proof-of-Stake system to select peer samples. However such a system limits the openness of the system as only nodes with significant stake can participate in the consensus, leading to an oligopoly situation. Moreover, this design introduces a complex interdependency between the consensus algorithm and the cryptocurrency built upon it. In this paper, we propose a radically different security design for the peer sampling service, based on the distribution of IP addresses to prevent Sybil attacks. We propose a new algorithm, $\scriptstyle{BASALT}$, that implements our design using a stubborn chaotic search to counter attackers' attempts at becoming over-represented. We show in theory and using Monte Carlo simulations that $\scriptstyle{BASALT}$ provides samples which are extremely close to the optimal distribution even in adversarial scenarios such as tentative Eclipse attacks. Live experiments on a production cryptocurrency platform confirm that the samples obtained using $\scriptstyle{BASALT}$ are equitably distributed amongst nodes, allowing for a system which is both open and where no single entity can gain excessive power.