Direct Physical-Entropy CBD Polynomial Sampling for ML-KEM: Bypassing SHAKE-256 with Domain-Separated MESI-LCG Injection

The NIST FIPS 203 standard (ML-KEM / CRYSTALS-Kyber) requires sampling random polynomials from a centered binomial distribution (CBD, η=2) during key generation and encapsulation. In the reference implementation, these polynomials are derived by applying SHAKE-256 to a seed with domain separators, and then extracting CBD coefficients from the hash output, which introduces a significant computational cost.

In this work, a direct injection method is implemented that completely bypasses SHAKE-256, generating CBD polynomials directly from physical entropy using the MESI-LCG Engine v3.0 with 128-bit NEON vector operations. Domain separation, which ensures independence between contexts such as key generation and encapsulation, is achieved through a deterministic multi-constant XOR seed construction that reproduces the isolation provided by domain tags without relying on hash functions.

Empirical validation over a large set of coefficients confirms the expected distribution, with no values outside the valid range and verified independence across distinct usage contexts. The proposed approach also achieves substantially higher throughput than SHAKE-256-based implementations, delivering a significant improvement in polynomial generation performance on multicore systems.