The Barrett Algorithm Reimagined for Post-Quantum Signatures

This paper extends the Homomorphic Polynomial Public Key (HPPK) cryptosystem into a digital signature scheme resilient against quantum attacks. By innovating on Barrett reduction, the authors transform modular multiplications into verifiable divisions over prime fields, embedding signatures non-linearly into public polynomials. The result is the HPPK DS: a post-quantum signature protocol with exponential resistance to key recovery and forgery, illustrating both its functionality and security through a worked toy example.