Hardware supply-chain attacks are raising significant security threats to the boot process of multiprocessor systems. This paper identifies a new, prevalent hardware supply-chain attack surface that can bypass multiprocessor secure boot due to the absence of processor-authentication mechanisms. To defend against such attacks, we present PA-Boot, the first formally verified processor-authentication protocol for secure boot in multiprocessor systems. PA-Boot is proved functionally correct and is guaranteed to detect multiple adversarial behaviors, e.g., processor replacements, man-in-the-middle attacks, and tampering with certificates. The fine-grained formalization of PA-Boot and its fully mechanized security proofs are carried out in the Isabelle/HOL theorem prover with 306 lemmas/theorems and ~7,100 LoC. Experiments on a proof-of-concept implementation indicate that PA-Boot can effectively identify boot-process attacks with a considerably minor overhead and thereby improve the security of multiprocessor systems.