Identity-based encryption: Difference between revisions

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'''ID-based cryptography''' (or '''identity -based cryptography''' or '''identity -based encryption''') is a [[key authentication]] system in which the [[public key]] of a user is some unique information about the identity of the user (e.g. a user's email address). The first identity-based cryptosystem was a signature scheme developed by [[Adi Shamir]] in 1984, which allowed users to verify digital signatures using only public information such as the user's identity. Modern schemes include [[Dan Boneh|Boneh]]/[[Matthew K. Franklin|Franklin]]'s [[bilinear pairing|pairing]]-based encryption scheme, and [[Cocks's IBE scheme|Cocks's]] encryption scheme based on [[quadratic residue]]s.

Identity-based systems allow any party to generate a public key from a known identity value such as an ASCII string. A trusted third party, called the [[Private Key Generator]] (PKG), generates the corresponding private keys. To operate, the PKG first publishes a "master" public key, and retains the corresponding master private key. Given the master public key, any party can compute a public key corresponding to the identity ''I'' by combining the master public key with the identity value. To obtain a corresponding private key, the party authorized to use the identity ''I'' contacts the PKG, which uses the master private key to generate the private key for identity ''I''.

This system works by having a trusted third party who has a secret which can be combined with a user's identity information to produce the user's secret key. The third party also produces some public information which is derived from

its secret.

As a result, parties may encrypt messages (or verify signatures) with no prior distribution of keys between individual participants. This is extremely useful in cases where pre-distribution of authenticated keys is inconvenient or infeasable due to technical restraints. However, to decrypt or sign messages, the authorized user must obtain the appropriate private key from the PKG. A caveat of this approach is that the PKG must be highly trusted, as it is capable of generating any user's private key and may therefore decrypt (or sign) messages without authorization. Because any user's private key can be generated through the use of the third party's secret, this system has inherent [[key escrow]]. A number of variant systems have been proposed which remove the escrow including [[certificate-based encryption]], [[secure key issuing cryptography]] and [[certificateless cryptography]].

To decrypt or sign a message the user uses their private key as with normal public key cryptography, but to verify the signature or encrypt a message only the identity information and the third party's public information is needed.

The most efficient identity-based encryption schemes are currently based on [[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]]-like approach. Though the Boneh-Franklin scheme is [[provably security|provably secure]], the security proof rests on relatively new assumptions about the hardness of problems in certain elliptic curve groups. Only limited work has been done in terms of formally analyzing these cryptosystems, some of which have been recently broken (said in 2004).

Originally when this system was developed in 1984 by [[Adi Shamir]] it could only be used for keys for digital signatures, but in 2001 the method was extended by [[Dan Boneh]] and [[Matthew K. Franklin]] to encryption/decryption through the use of [[Weil pairing]]s.

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]].

Only limited work has been done in terms of formally analysing ID based cryptosystems, some of which have been recently broken (said in 2004).

One of this system'sthe major advantages of any identity-based encryption scheme is that if there are only a finite number of users, after all users have been issued with keys the third party's secret can be destroyed. This can take place because this system assumes that, once issued, keys are always valid (as this basic system lacks an method of [[key revocation]]). The majority of derivatives of this system which have key revocation lose this advantage.

Because any user's private key can be generated through the use of the third party's secret, this system has inherent [[key escrow]]. A number of variant systems have been proposed which remove the escrow including [[certificate-based encryption]], [[secure key issuing cryptography]] and [[certificateless cryptography]].

One of this system's major advantages is that if there are only a finite number of users, after all users have been issued with keys the third party's secret can be destroyed. This can take place because this system assumes that, once issued, keys are always valid (as this basic system lacks an method of [[key revocation]]). The majority of derivatives of this system which have key revocation lose this advantage.

==References==

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*Yevgeniy Dodis, Jonathan Katz, Shouhuai Xu, Moti Yung, Strong Key-Insulated Signature Schemes (2002).

*[[Dan Boneh]], Matthew K. Franklin, Identity-Based Encryption from the Weil Pairing. ''Advances in Cryptology - Proceedings of CRYPTO 2001'' (2001).

*[[Clifford Cocks]], An Identity Based Encryption Scheme Based on Quadratic Residues, ''Proceedings of the 8th IMA International Conference on Cryptography and Coding'', 2001.

==External links==