Increasingly, information systems rely on computational, storage, and network resources deployed in third-party facilities such as cloud centers and edge nodes. Such an approach further exacerbates cybersecurity concerns constantly raised by numerous incidents of security and privacy attacks resulting in data leakage and identity theft, among others. These have, in turn, forced the creation of stricter security and privacy-related regulations and have eroded the trust in cyberspace. In particular, security-related services and infrastructures, such as Certificate Authorities (CAs) that provide digital certificate services and Third-Party Authorities (TPAs) that provide cryptographic key services, are critical components for establishing trust in crypto-based privacy-preserving applications and services. To address such trust issues, various transparency frameworks and approaches have been recently proposed in the literature. This paper proposes TAB framework that provides transparency and trustworthiness of third-party authority and third-party facilities using blockchain techniques for emerging crypto-based privacy-preserving applications. TAB employs the Ethereum blockchain as the underlying public ledger and also includes a novel smart contract to automate accountability with an incentive mechanism that motivates users to participate in auditing, and punishes unintentional or malicious behaviors. We implement TAB and show through experimental evaluation in the Ethereum official test network, Rinkeby, that the framework is efficient. We also formally show the security guarantee provided by TAB, and analyze the privacy guarantee and trustworthiness it provides.