We propose two precise duality frameworks for investigating the algebraiccomplexity of AES over GF (2⁸). First, we conjecture that the AES operationalgebra admits a Koszul dual over GF (2) in which the S-box inversion becomesa linear operation. Second, we propose that the geometric Langlandscorrespondence over GF (2), mediated by the Fargues-Fontaine curve, providesa geometric proxy for AES key-recovery. We identify mathematical obstacles, propose a five-step research agenda, and situate the conjectures within theP vs NP problem. The author is an IT systems integration practitioner and submits thisconjecture as an open invitation to specialists in algebraic geometryand cryptography.
Xuan Viet Nhat Nguyen (Tue,) studied this question.