Diophantine Key Derivation: A Constant-Time O(1) Alternative to HKDF in Hybrid PQC

This paper demonstrates that a closed form Diophantine derivation, MRS(19,9), can replace the iterative HKDF SHA256 expand step in hybrid post quantum key encapsulation, achieving a 5 to 6 times latency reduction (101 to 114 ns versus 570 to 680 ns) with no security regression under the public session id model. The production ready Rust implementation couples NIST Level 5 Kyber1024 with AES 256 GCM via constant time O(1) arithmetic, offering a pragmatic path to low latency PQC deployment.