The A-Scheme Cryptographic Paradigm

Executive Summary. Modern distributed cryptography faces a fundamental trilemma across access control, broadcast distribution, and private database retrieval: (i)~classical Attribute-Based Encryption (ABE)~{GPSW06}, Broadcast Encryption (BE)~{fiat_naor, nnl_broadcast, urivskiy_cubes, bgw_broadcast, gentry_waters}, and Fully Homomorphic Encryption Private Information Retrieval (FHE-PIR)~{bgv_fhe, apple_pir} enforce brittle exact-match Boolean logic, failing completely under a single bit of attribute or query noise; (ii)~evaluating XOR or Hamming-distance predicates inside encrypted containers either incurs prohibitive FHE polynomial multiplication and bootstrapping overhead~{tfhe_orig, bgv_fhe} or suffers from destructive inter-bit arithmetic carries (1 + 1 = 2 ≠ 0) in lightweight additively homomorphic groups; and (iii)~standard protocols expose cleartext access policies, revocation directories, or algebraic curve invariants to Deep Packet Inspection (DPI). The A-Scheme research program~{chmora2026ascheme, chmora2026stealthabbe, chmora2026fuzzypir, chmora_urivskiy_patent} resolves this trilemma through a unified mathematical paradigm: Stealth Transport via Algebraic Coding (STAC)~{chmora2026stealthabbe, chmora2026isogenies, chmora2026jacobi}. Rather than evaluating deep Boolean circuits over ciphertexts or transmitting combinatorial subset headers, we embed vectors over F2ᵐⁿ into the exponent of additively homomorphic ElGamal ciphertexts via carry-free Base-3 packing~{chmora2026ascheme} and recast authorization, revocation quarantine, and fuzzy record linkage as a single-pass blind bounded-distance decoding problem over non-systematic Maximum Distance Separable (MDS) Reed–Solomon (RS) codes~{macwilliams_sloane}.