ID-based cryptography

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ID-based cryptography (or Identity-Based Encryption (IBE) or identity-based cryptography) is a type of public-key cryptography 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[1], which allowed users to verify digital signatures using only public information such as the user's identifier. Modern schemes include Boneh/Franklin's pairing-based encryption scheme[2], and Cocks's encryption scheme[3] based on quadratic residues.

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[edit] 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, secure key issuing cryptography and certificateless cryptography.[citation needed]

[edit] Protocol Framework

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

  • Setup: This algorithm is run by the PKG one time for creating the whole IBE environment. The master key is kept secret and used to derive users' private keys, while the system parameters are made public. It accepts a security parameter \textstyle k (i.e. binary length of key material) and outputs:
  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.
  • Extract: This algorithm is run by the PKG when a user requests his private key. Note that the verification of the authenticity of the requestor and the secure transport of \textstyle d are problems with which IBE protocols do not try to deal. It takes as input \textstyle \mathcal{P}, \textstyle K_m and an identifier \textstyle ID \in \left\{0,1\right\}^* and returns the private key \textstyle d for user \textstyle ID.
  • Encrypt: Takes \textstyle \mathcal{P}, a message \textstyle m \in \mathcal{M} and \textstyle ID \in \left\{0,1\right\}^* and outputs the encryption \textstyle c \in \mathcal{C}.
  • Decrypt: Accepts \textstyle d, \textstyle \mathcal{P} and \textstyle c \in \mathcal{C} and returns \textstyle m \in \mathcal{M}.

[edit] 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

[edit] 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.

[edit] 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 data 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.

[edit] Problems

For large networks like the internet, the centralistic approach of IBE can be problematic. A major drawback is the implicit key escrow which does not exist with the current PKI system where private keys are usually generated on the user's computer. A number of variant systems have been proposed which remove the escrow including certificate-based encryption, secret sharing, secure key issuing cryptography and certificateless cryptography.

Besides, the problem of authentic key distribution is shifted: A secure channel between a user and the PKG is required for transmitting the private key on joining the system. Here, a SSL-like connection could be a feasible solution for large-scale system. This in turn requires the distribution of the PKG's authentic root public key, an old, still not completely resolved issue with public key cryptography.

[edit] See also

  • Trend Micro, owners of Identum's ID-based cryptography technology

[edit] 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

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