Editing Identity-based encryption (section)

== Encryption schemes ==
The most efficient identity-based encryption schemes are currently based on [[Pairing|bilinear pairings]] on [[elliptic curves]], such as the [[weil pairing|Weil]] or [[Tate pairing|Tate]] pairings.  The first of these schemes was developed by [[Dan Boneh]] and [[Matthew K. Franklin]] (2001), and performs [[probabilistic encryption]] of arbitrary ciphertexts using an [[ElGamal encryption|Elgamal]]-like approach.  Though the [[BonehFranklinScheme|Boneh-Franklin scheme]] is [[Provable security|provably secure]], the security proof rests on relatively new assumptions about the hardness of problems in certain elliptic curve groups.

Another approach to identity-based encryption was proposed by [[Clifford Cocks]] in 2001.  The [[Cocks IBE scheme]] is based on well-studied assumptions (the [[quadratic residuosity problem|quadratic residuosity assumption]]) but encrypts messages one bit at a time with a high degree of [[ciphertext expansion]].  Thus it is highly inefficient and impractical for sending all but the shortest messages, such as a session key for use with a [[symmetric cipher]].

A third approach to IBE is through the use of lattices.

=== Identity-based encryption algorithms ===
The following lists practical identity-based encryption algorithms
* [[Boneh–Franklin scheme|Boneh–Franklin]] (BF-IBE).
* [[Sakai–Kasahara scheme|Sakai–Kasahara]] (SK-IBE).<ref>{{cite web|last1=Sakai|first1=Ryuichi|last2=Kasahara|first2=Masao|title=ID Based cryptosystems with pairing on elliptic curve|work=Cryptography ePrint Archive|year=2003|volume=2003/054|url=https://eprint.iacr.org/2003/054}}</ref>
* Boneh–Boyen (BB-IBE).<ref>{{cite conference
 | last1 = Boneh | first1 = Dan | author1-link = Dan Boneh
 | last2 = Boyen | first2 = Xavier
 | editor1-last = Cachin | editor1-first = Christian
 | editor2-last = Camenisch | editor2-first = Jan
 | contribution = Efficient selective-ID secure identity based encryption without random oracles
 | contribution-url = https://eprint.iacr.org/2004/172
 | doi = 10.1007/978-3-540-24676-3_14
 | pages = 223–238
 | publisher = Springer
 | series = Lecture Notes in Computer Science
 | title = Advances in Cryptology – EUROCRYPT 2004, International Conference on the Theory and Applications of Cryptographic Techniques, Interlaken, Switzerland, May 2–6, 2004, Proceedings
 | volume = 3027
 | year = 2004| doi-access = free
 }}</ref>
All these algorithms have [[Provable security|security proofs]].