ID-based encryption

ID-based encryption, or identity-based encryption (IBE), is an important primitive of ID-based cryptography. As such it is a type of public-key encryption 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). This can use the text-value of the name or domain name as a key or the physical IP address it translates to.

ID-based encryption was proposed by Adi Shamir in 1984.[1] He was however only able to give an instantiation of identity-based signatures. Identity-based encryption remained an open problem for many years. The pairing-based Boneh–Franklin scheme[2] and Cocks's encryption scheme[3] based on quadratic residues both solved the IBE problem in 2001.

Usage

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 (referred to as master key). Given the master public key, any party can compute a public key corresponding to the identity ID by combining the master public key with the identity value. To obtain a corresponding private key, the party authorized to use the identity ID contacts the PKG, which uses the master private key to generate the private key for identity ID.

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 infeasible 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,[4] secure key issuing cryptography[5] and certificateless cryptography.[6]

The steps involved are depicted in this diagram:

ID Based Encryption: Offline and Online Steps

Protocol framework

Dan Boneh and Matthew K. Franklin defined a set of four algorithms that form a complete IBE system:

  1. A set \textstyle \mathcal{P} of system parameters, including the message space and ciphertext space \textstyle \mathcal{M} and \textstyle \mathcal{C},
  2. a master key \textstyle K_m.

Correctness constraint

In order for the whole system to work, one has to postulate that:

 \forall m \in \mathcal{M}, ID \in \left\{0,1\right\}^*: Decrypt\left(Extract\left(\mathcal{P}, K_m, ID\right), \mathcal{P}, Encrypt\left(\mathcal{P}, m, ID \right) \right) = m

Encryption schemes

The most efficient identity-based encryption schemes are currently based on bilinear pairings on elliptic curves, such as the Weil or 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 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 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

All these algorithms have security proofs.

Advantages

One of the 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 a method of key revocation). The majority of derivatives of this system which have key revocation lose this advantage.

Moreover, as public keys are derived from identifiers, IBE eliminates the need for a public key distribution infrastructure. The authenticity of the public keys is guaranteed implicitly as long as the transport of the private keys to the corresponding user is kept secure (Authenticity, Integrity, Confidentiality).

Apart from these aspects, IBE offers interesting features emanating from the possibility to encode additional information into the identifier. For instance, a sender might specify an expiration date for a message. He appends this timestamp to the actual recipient's identity (possibly using some binary format like X.509). When the receiver contacts the PKG to retrieve the private key for this public key, the PKG can evaluate the identifier and decline the extraction if the expiration date has passed. Generally, embedding data in the ID corresponds to opening an additional channel between sender and PKG with authenticity guaranteed through the dependency of the private key on the identifier.

Drawbacks

See also

References

  1. Adi Shamir, Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, 7:47--53, 1984
  2. Dan Boneh, Matthew K. Franklin, Identity-Based Encryption from the Weil Pairing Advances in Cryptology - Proceedings of CRYPTO 2001 (2001)
  3. Clifford Cocks, An Identity Based Encryption Scheme Based on Quadratic Residues, Proceedings of the 8th IMA International Conference on Cryptography and Coding, 2001
  4. Craig Gentry Certificate-Based Encryption and the Certificate Revocation Problem Advances in Cryptology - Proceedings of EUROCRYPT 2003 (2003)
  5. Lee, Byoungcheon; Dawson, Ed; Kim, Kwangjo; Yang, Jeongmo; Yoo, Seungjae (2004). Secure Key Issuing in ID-based Cryptography. ACS Conferences in Research and Practice in Information Technology - Proceedings of the Second Australian Information Security Workshop-AISW 2004. CiteSeerX: 10.1.1.6.337.
  6. SS Al-Riyami, KG Paterson Certificateless Public Key Cryptography Advances in Cryptology - Proceedings of ASIACRYPT 2003 (2003)
  7. Sakai, Ryuichi; Kasahara, Masao (2003). "ID Based cryptosystems with pairing on elliptic curve". Cryptography ePrint Archive. 2003/054.
  8. Boneh, Dan; Boyen, X (2004). "Efficient selective-ID secure identity based encryption without random oracles". LNCS. Advances in Cryptography - EUROCRYPT 2004 (Springer-Verlag) 3027: 223–238. doi:10.1007/978-3-540-24676-3_14.

External links