Stealth ABBE: Carry-Free Homomorphic Packing and Blind Reed–Solomon Decoding

Classical Broadcast Encryption (BE) and Attribute-Based Broadcast Encryption (ABBE) schemes suffer from three fundamental bottlenecks in zero-trust and censorship-prone environments: (i) severe header bloat scaling with the number of authorized or revoked subsets, (ii) the explicit transmission of plaintext revocation lists and access structures that leak recipient metadata to Deep Packet Inspection (DPI), and (iii) prohibitive re-keying overhead during dynamic group membership updates. 

In this paper, we generalize the A-scheme to establish a novel framework for Stealth Attribute-Based Broadcast Encryption (Stealth ABBE). Instead of encrypting session keys across combinatorial subset trees, explicit pairing-based access trees, or rigid binary-cube topologies, our architecture symmetrically encrypts the primary content payload and encodes the monolithic session key material into a single non-systematic Reed–Solomon (RS) codeword over $\mathbb{F}_q^n$, which is then encrypted block-by-block via the additively homomorphic (exponential) ElGamal cryptosystem over $\mathbb{G}_1 \times \mathbb{G}_1$. Because component-wise ElGamal ciphertext addition induces integer addition in the scalar ring $\mathbb{Z}_\ell$ rather than characteristic-2 XOR, we embed $\eta$-bit codeword blocks using carry-free Base-3 packing. Each broadcast participant possesses a dense attribute vector encapsulated within a local ElGamal-encrypted Access Code acting as an algebraic error-correcting key; upon homomorphic ElGamal ciphertext aggregation and bilinear pairing-based decryption into $\mathbb{G}_T$, only participants whose attribute intersection with the broadcast policy satisfies the $k$-out-of-$n$ blind decoding threshold can reconstruct the session key and decrypt the content. Combined with constant-time point-to-uniform steganographic mappings under the STAC (Stealth Transport via Algebraic Coding) paradigm, the broadcast stream is rendered statistically indistinguishable from uniform noise, completely eliminating visible headers and explicit revocation lists.