Trust Management (TM) systems for authentication are vital to the security of online interactions, which are ubiquitous in our everyday lives. Various systems, like the Web PKI (X.509) and PGP's Web of Trust are used to manage trust in this setting. In recent years, blockchain technology has been introduced as a panacea to our security problems, including that of authentication, without sufficient reasoning, as to its merits.In this work, we investigate the merits of using open distributed ledgers (ODLs), such as the one implemented by blockchain technology, for securing TM systems for authentication. We formally model such systems, and explore how blockchain can help mitigate attacks against them. After formal argumentation, we conclude that in the context of Trust Management for authentication, blockchain technology, and ODLs in general, can offer considerable advantages compared to previous approaches. Our analysis is, to the best of our knowledge, the first to formally model and argue about the security of TM systems for authentication, based on blockchain technology. To achieve this result, we first provide an abstract model for TM systems for authentication. Then, we show how this model can be conceptually encoded in a blockchain, by expressing it as a series of state transitions. As a next step, we examine five prevalent attacks on TM systems, and provide evidence that blockchain-based solutions can be beneficial to the security of such systems, by mitigating, or completely negating such attacks.