The emergence of chiplet-based heterogeneous integration is transforming the semiconductor, AI, and high-performance computing industries by enabling modular designs and improved scalability. However, assembling chiplets from multiple vendors after fabrication introduces a complex supply chain that raises serious security concerns, including counterfeiting, overproduction, and unauthorized access. Current solutions often depend on dedicated security chiplets or changes to the timing flow, which assume a trusted SiP integrator. This assumption can expose chiplet signatures to other vendors and create new attack surfaces. This work addresses those vulnerabilities using Multi-party Computation (MPC), which enables zero-trust authentication without disclosing sensitive information to any party. We present SAFE-SiP, a scalable authentication framework that garbles chiplet signatures and uses MPC for verifying integrity, effectively blocking unauthorized access and adversarial inference. SAFE-SiP removes the need for a dedicated security chiplet and ensures secure authentication, even in untrusted integration scenarios. We evaluated SAFE-SiP on five RISC-V-based System-in-Package (SiP) designs. Experimental results show that SAFE-SiP incurs minimal power overhead, an average area overhead of only 3.05%, and maintains a computational complexity of 2^192, offering a highly efficient and scalable security solution.