Algebraic Equivalence Classes in AES Key Space via Weyl Group Action on GF(2^8)

We establish a rigorous algebraic framework for analyzing the AES key space through group actions on GF(2^8). By constructing G = Z_2 x Z_85 x (Z_2)^2 of order 680, we prove GF(2^8) partitions into exactly 2 equivalence classes. This yields a theoretical compression of 112 bits for AES-128 (2^128 to 2^16) and 224 bits for AES-256 (2^256 to 2^32). The compression does not constitute a practical attack without an orbit-membership oracle -- blocked by AES Wide Trail Strategy. Key contributions: (1) First Z_2 x Z_85 x (Z_2)^2 orbit decomposition on GF(2^8). (2) GF(2^8) partitions into exactly 2 non-trivial orbits under G. (3) Tight characterization of gap between compression and practical key recovery. (4) Generator g_85=0x07 links Lo-Shu cardinal encoding to finite field cryptography. Previous work: ZMLA AES-128 CPA (DOI:10.5281/zenodo.20262553).