PDKE-G: A Bio-Inspired Contributory Group Authenticated Key Exchange Grounded in Per-Member AlphaFold2 Protein Geometry

Authenticated key exchange underpins secure communication, yet the structural complexity of biological macromolecules has rarely served as cryptographic material. The recently proposed Protein-Derived Key Exchange (PDKE) protocol binds AlphaFold2-predicted protein geometry to ephemeral elliptic-curve Diffie–Hellman for two parties. We introduce PDKE-G, a contributory group authenticated key exchange in which each member’s signing credential is derived from its protein geometry as a member-specific input: the long-term signing key is extracted with HKDF from the protein’s Cα–Cα distance matrix keyed by a per-member 128-bit secret seed, and a constant-round Burmester–Desmedt core wrapped by the Katz–Yung compiler with these protein-derived signatures yields a shared 256-bit session key with forward secrecy. We give a computational proof of security under Decisional Diffie–Hellman, KDF security of HKDF, pseudorandomness of the credential derivation, and strong unforgeability (SUF-CMA) of the signature, in the random-oracle model for the hash-to-curve and SHA-256 maps, and we verify the three- and four-party instantiations symbolically in ProVerif. Because every broadcast carries a per-member certified signature bound to the session context, PDKE-G prevents the honest-member insertion attack of the member-tampering setting within the scope of Corollary 1. An empirical study of 519 AlphaFold structures across seven organisms finds their canonical geometry descriptors all distinct, with a mean of 12.3 descriptive Shannon bits per residue pair. Because the selection space of known proteins is only about 227.7, identity is anchored by the certified public key and the secret seed, which supplies the credential’s brute-force security. The protocol completes in a constant number of rounds independent of group size, with a logical-broadcast message count that is linear in the number of members; over point-to-point links both PDKE-G and pairwise composition are Θ(n2) in raw transmissions, so the advantages are the constant round count and the single contributory group key.