BonehFranklin

BonehFranklin refers to the Boneh–Franklin identity-based encryption (IBE) scheme, a foundational construction in public-key cryptography introduced by Dan Boneh and Matthew Franklin in 2001. The scheme enables encryption using a recipient’s identity as the public key, removing the need for a separate certificate-based key distribution system. It is built on bilinear pairings on elliptic curves, which provide a mathematical bridge between identity-derived data and the private keys issued by a trusted authority.

In Boneh–Franklin IBE, a trusted Private Key Generator (PKG) produces system parameters and a master secret. The PKG publishes a master public key and keeps the master secret. To obtain a private key, a user with identity ID computes a point Q_id = H1(ID) on an elliptic-curve group, and the PKG issues the private key d_id = s·Q_id, where s is the master secret and H1 maps identities to curve points. To encrypt a message for ID, a sender computes Q_id = H1(ID), selects a random r, and forms a ciphertext component using a pairing-based term derived from e(Q_id, P_pub)^r, along with the message encrypted under a symmetric key. To decrypt, the recipient uses d_id to derive the same pairing value e(Q_id, P_pub)^r and recovers the symmetric key to decrypt the message.

Security relies on the hardness of bilinear Diffie-Hellman problems and is proven (in the random oracle model) under standard assumptions for IND-CCA-like security in the identity-based setting. The PKG model provides convenience and certificate-free public keys but introduces key escrow, since the PKG can derive any private key. Boneh–Franklin stimulated extensive research in pairing-based cryptography and various practical IBE variants and extensions.