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, Bᴀsᴀʟᴛ, 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 Bᴀsᴀʟᴛ 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 Bᴀsᴀʟᴛ are equitably distributed amongst nodes, allowing for a system which is both open and where no single entity can gain excessive power.