MERA-Crystal: A Post-Quantum Key Encapsulation Mechanism from Crystal Boundary Security with Non-Abelian Gauge Groups

We propose MERA-Crystal, a post-quantum key encapsulation mechanism whose security derives from the gauge groups of the Standard Model of particle physics. Unlike existing post-quantum schemes (Kyber, McEliece) whose hardness rests on unproven assumptions about arbitrary mathematical structures, MERA-Crystal locates its security at the boundaries between crystal sectors of the finite spectral algebra A_F = C + M_2(C) + M_3(C), using the non-abelian gauge groups SU(n). The scheme has three independent security layers: (1) SVP on the gauge algebra lattice, (2) the non-abelian hidden subgroup problem on simple groups SU(n), which no efficient quantum algorithm can solve because simple groups have no normal subgroups for Shor-type attacks to exploit, and (3) combinatorial path selection through crystal boundaries. The v2 implementation achieves 100% decryption correctness across all four security configurations (NIST Levels 1, 3, 5, and full spectral tower D=42), exceeding NIST security targets by large margins. To the authors' knowledge, MERA-Crystal is the first cryptographic scheme whose hardness is derived from the architecture of physical reality rather than from an arbitrary mathematical structure observed to be hard. Code and analysis are provided for peer review. Copyright © 2026 Daland Montgomery. All Rights Reserved. Creative Commons Attribution Non Commercial No Derivatives 4.0 International For a private, proprietary license, contact: quidbit@icloud.com Software Implementation: The formulas and constants derived in this work are implemented in the CrystalAgent engine, available under the AGPL-3.0 license at: https://github.com/CrystalToe/CrystalAgent.