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The Federal Communications Commission (FCC) has released the 3.5 GHz (3550-3700 MHz) band, termed Citizens Broadband Radio Service (CBRS), for shared broadband use between incumbent federal and secondary users through dynamic and opportunistic spectrum access. FCC requires that this band be operated and managed through the use of spectrum access systems (<inline-formula> <tex-math notation="LaTeX">$\mathit {SAS}$ </tex-math></inline-formula>s), which are to be deployed specifically for this purpose. The challenge is that <inline-formula> <tex-math notation="LaTeX">$\mathit {SAS}$ </tex-math></inline-formula> requires that secondary users provide some of their private operational data, such as their physical location, identity and spectrum usage, in order for them to acquire spectrum availability information. In this paper, we propose a privacy-preserving <inline-formula> <tex-math notation="LaTeX">$\mathit {SAS}$ </tex-math></inline-formula> framework, <inline-formula> <tex-math notation="LaTeX">$\mathit {TrustSAS}$ </tex-math></inline-formula>, that synergizes state-of-the-art cryptographic mechanisms with blockchain technology to enable anonymous access to <inline-formula> <tex-math notation="LaTeX">$\mathit {SAS}$ </tex-math></inline-formula> by protecting users&#x2019; privacy while still complying with FCC&#x2019;s regulatory design requirements and rules. We evaluate the performance of <inline-formula> <tex-math notation="LaTeX">$\mathit {TrustSAS}$ </tex-math></inline-formula> through theoretic analysis, computer simulation and testbed experimentation, and show that it can offer high security guarantees, making it suitable for <inline-formula> <tex-math notation="LaTeX">$\mathit {SAS}$ </tex-math></inline-formula> environments without needing to compromise private information of its secondary users.