Identity-based encryption

Last updated February 18, 2024

Identity-based encryption (IBE), is an important primitive of identity-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 means that a sender who has access to the public parameters of the system can encrypt a message using e.g. the text-value of the receiver's name or email address as a key. The receiver obtains its decryption key from a central authority, which needs to be trusted as it generates secret keys for every user.

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 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:

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:

A set $\textstyle {\mathcal {P}}$ of system parameters, including the message space and ciphertext space $\textstyle {\mathcal {M}}$ and $\textstyle {\mathcal {C}}$ ,
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 $\textstyle m\in {\mathcal {M}}$ .

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\}^{*}:\mathrm {Decrypt} \left(\mathrm {Extract} \left({\mathcal {P}},K_{m},ID\right),{\mathcal {P}},\mathrm {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

Boneh–Franklin (BF-IBE).
Sakai–Kasahara (SK-IBE).^[7]
Boneh–Boyen (BB-IBE).^[8]

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

If a Private Key Generator (PKG) is compromised, all messages protected over the entire lifetime of the public–private key pair used by that server are also compromised. This makes the PKG a high-value target to adversaries. To limit the exposure due to a compromised server, the master private-public key pair could be updated with a new independent key pair. However, this introduces a key-management problem where all users must have the most recent public key for the server.
Because the Private Key Generator (PKG) generates private keys for users, it may decrypt and/or sign any message without authorization. This implies that IBS systems cannot be used for non-repudiation. This may not be an issue for organizations that host their own PKG and are willing to trust their system administrators and do not require non-repudiation.
The issue of implicit key escrow does not exist with the current PKI system, wherein private keys are usually generated on the user's computer. Depending on the context key escrow can be seen as a positive feature (e.g., within Enterprises). 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.
A secure channel between a user and the Private Key Generator (PKG) is required for transmitting the private key on joining the system. Here, a SSL-like connection is a common solution for a large-scale system. It is important to observe that users that hold accounts with the PKG must be able to authenticate themselves. In principle, this may be achieved through username, password or through public key pairs managed on smart cards.
IBE solutions may rely on cryptographic techniques that are insecure against code breaking quantum computer attacks (see Shor's algorithm).

Related Research Articles

In cryptography, a cipher is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.

<span class="mw-page-title-main">Public-key cryptography</span> Cryptographic system with public and private keys

Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security.

RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ), the British signals intelligence agency, by the English mathematician Clifford Cocks. That system was declassified in 1997.

A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key's security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange.

In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1985. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption.

Certificate-based encryption is a system in which a certificate authority uses ID-based cryptography to produce a certificate. This system gives the users both implicit and explicit certification, the certificate can be used as a conventional certificate, but also implicitly for the purpose of encryption.

Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanical and electromechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption; and the subsequent introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper.

Key exchange is a method in cryptography by which cryptographic keys are exchanged between two parties, allowing use of a cryptographic algorithm.

Ciphertext indistinguishability is a property of many encryption schemes. Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish pairs of ciphertexts based on the message they encrypt. The property of indistinguishability under chosen plaintext attack is considered a basic requirement for most provably secure public key cryptosystems, though some schemes also provide indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack. Indistinguishability under chosen plaintext attack is equivalent to the property of semantic security, and many cryptographic proofs use these definitions interchangeably.

A deterministic encryption scheme is a cryptosystem which always produces the same ciphertext for a given plaintext and key, even over separate executions of the encryption algorithm. Examples of deterministic encryption algorithms include RSA cryptosystem, and many block ciphers when used in ECB mode or with a constant initialization vector.

Homomorphic encryption is a form of encryption that allows computations to be performed on encrypted data without first having to decrypt it. The resulting computations are left in an encrypted form which, when decrypted, result in an output that is identical to that produced had the operations been performed on the unencrypted data. Homomorphic encryption can be used for privacy-preserving outsourced storage and computation. This allows data to be encrypted and out-sourced to commercial cloud environments for processing, all while encrypted.

The Boneh–Franklin scheme is an identity-based encryption system proposed by Dan Boneh and Matthew K. Franklin in 2001. This article refers to the protocol version called BasicIdent. It is an application of pairings over elliptic curves and finite fields.

Cocks IBE scheme is an identity based encryption system proposed by Clifford Cocks in 2001. The security of the scheme is based on the hardness of the quadratic residuosity problem.

Identity-based cryptography is a type of public-key cryptography in which a publicly known string representing an individual or organization is used as a public key. The public string could include an email address, domain name, or a physical IP address.

Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe or quantum-resistant, is the development of cryptographic algorithms that are thought to be secure against a cryptanalytic attack by a quantum computer. The problem with popular algorithms currently used in the market is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete logarithm problem. All of these problems could be easily solved on a sufficiently powerful quantum computer running Shor's algorithm or even faster and less demanding alternatives.

A key-recovery attack is an adversary's attempt to recover the cryptographic key of an encryption scheme. Normally this means that the attacker has a pair, or more than one pair, of plaintext message and the corresponding ciphertext. Historically, cryptanalysis of block ciphers has focused on key-recovery, but security against these sorts of attacks is a very weak guarantee since it may not be necessary to recover the key to obtain partial information about the message or decrypt message entirely. Modern cryptography uses more robust notions of security. Recently, indistinguishability under adaptive chosen-ciphertext attack has become the "golden standard" of security. The most obvious key-recovery attack is the exhaustive key-search attack. But modern ciphers often have a key space of size $or greater, making such attacks infeasible with current technology.$

Attribute-based encryption is a generalisation of public-key encryption which enables fine grained access control of encrypted data using authorisation policies. The secret key of a user and the ciphertext are dependent upon attributes. In such a system, the decryption of a ciphertext is possible only if the set of attributes of the user key matches the attributes of the ciphertext.

<span class="mw-page-title-main">Functional encryption</span>

Functional encryption (FE) is a generalization of public-key encryption in which possessing a secret key allows one to learn a function of what the ciphertext is encrypting.

The Sakai–Kasahara scheme, also known as the Sakai–Kasahara key encryption algorithm (SAKKE), is an identity-based encryption (IBE) system proposed by Ryuichi Sakai and Masao Kasahara in 2003. Alongside the Boneh–Franklin scheme, this is one of a small number of commercially implemented identity-based encryption schemes. It is an application of pairings over elliptic curves and finite fields. A security proof for the algorithm was produced in 2005 by Chen and Cheng. SAKKE is described in Internet Engineering Task Force (IETF) RFC 6508.

Identity-based conditional proxy re-encryption (IBCPRE) is a type of proxy re-encryption (PRE) scheme in the identity-based public key cryptographic setting. An IBCPRE scheme is a natural extension of proxy re-encryption on two aspects. The first aspect is to extend the proxy re-encryption notion to the identity-based public key cryptographic setting. The second aspect is to extend the feature set of proxy re-encryption to support conditional proxy re-encryption. By conditional proxy re-encryption, a proxy can use an IBCPRE scheme to re-encrypt a ciphertext but the ciphertext would only be well-formed for decryption if a condition applied onto the ciphertext together with the re-encryption key is satisfied. This allows fine-grained proxy re-encryption and can be useful for applications such as secure sharing over encrypted cloud data storage.

References

↑ Shamir, Adi (1984). "Identity-Based Cryptosystems and Signature Schemes". In Blakley, G. R.; Chaum, David (eds.). Advances in Cryptology, Proceedings of CRYPTO '84, Santa Barbara, California, USA, August 19–22, 1984, Proceedings. Lecture Notes in Computer Science. Vol. 196. Springer. pp. 47–53. doi: 10.1007/3-540-39568-7_5 .
↑ Boneh, Dan; Franklin, Matthew (2003). "Identity-based encryption from the Weil pairing". SIAM Journal on Computing . 32 (3): 586–615. doi:10.1137/S0097539701398521. MR 2001745.
↑ Cocks, Clifford C. (2001). "An identity based encryption scheme based on quadratic residues". In Honary, Bahram (ed.). Cryptography and Coding, 8th IMA International Conference, Cirencester, UK, December 17–19, 2001, Proceedings. Lecture Notes in Computer Science. Vol. 2260. Springer. pp. 360–363. doi:10.1007/3-540-45325-3_32.
↑ Gentry, Craig (2003). "Certificate-based encryption and the certificate revocation problem". In Biham, Eli (ed.). Advances in Cryptology – EUROCRYPT 2003, International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4–8, 2003, Proceedings. Lecture Notes in Computer Science. Vol. 2656. Springer. pp. 272–293. doi: 10.1007/3-540-39200-9_17 .
↑ Lee, Byoungcheon; Boyd, Colin; Dawson, Ed; Kim, Kwangjo; Yang, Jeongmo; Yoo, Seungjae (2004). "Secure key issuing in ID-based cryptography". In Hogan, James M.; Montague, Paul; Purvis, Martin K.; Steketee, Chris (eds.). ACSW Frontiers 2004, 2004 ACSW Workshops – the Australasian Information Security Workshop (AISW2004), the Australasian Workshop on Data Mining and Web Intelligence (DMWI2004), and the Australasian Workshop on Software Internationalisation (AWSI2004), Dunedin, New Zealand, January 2004. CRPIT. Vol. 32. Australian Computer Society. pp. 69–74.
↑ Al-Riyami, Sattam S.; Paterson, Kenneth G. (2003). "Certificateless public key cryptography". In Laih, Chi-Sung (ed.). Advances in Cryptology – ASIACRYPT 2003, 9th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, November 30 – December 4, 2003, Proceedings. Lecture Notes in Computer Science. Vol. 2894. Springer. pp. 452–473. doi: 10.1007/978-3-540-40061-5_29 .
↑ Sakai, Ryuichi; Kasahara, Masao (2003). "ID Based cryptosystems with pairing on elliptic curve". Cryptography ePrint Archive.
↑ Boneh, Dan; Boyen, Xavier (2004). "Efficient selective-ID secure identity based encryption without random oracles". In Cachin, Christian; Camenisch, Jan (eds.). Advances in Cryptology – EUROCRYPT 2004, International Conference on the Theory and Applications of Cryptographic Techniques, Interlaken, Switzerland, May 2–6, 2004, Proceedings. Lecture Notes in Computer Science. Vol. 3027. Springer. pp. 223–238. doi: 10.1007/978-3-540-24676-3_14 .

External links

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[iseca.org-1] Shamir, Adi (1984). "Identity-Based Cryptosystems and Signature Schemes". In Blakley, G. R.; Chaum, David (eds.). Advances in Cryptology, Proceedings of CRYPTO '84, Santa Barbara, California, USA, August 19–22, 1984, Proceedings. Lecture Notes in Computer Science. Vol. 196. Springer. pp. 47–53. doi: 10.1007/3-540-39568-7_5 .

[2] Boneh, Dan; Franklin, Matthew (2003). "Identity-based encryption from the Weil pairing". SIAM Journal on Computing . 32 (3): 586–615. doi:10.1137/S0097539701398521. MR 2001745.

[3] Cocks, Clifford C. (2001). "An identity based encryption scheme based on quadratic residues". In Honary, Bahram (ed.). Cryptography and Coding, 8th IMA International Conference, Cirencester, UK, December 17–19, 2001, Proceedings. Lecture Notes in Computer Science. Vol. 2260. Springer. pp. 360–363. doi:10.1007/3-540-45325-3_32.

[4] Gentry, Craig (2003). "Certificate-based encryption and the certificate revocation problem". In Biham, Eli (ed.). Advances in Cryptology – EUROCRYPT 2003, International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4–8, 2003, Proceedings. Lecture Notes in Computer Science. Vol. 2656. Springer. pp. 272–293. doi: 10.1007/3-540-39200-9_17 .

[5] Lee, Byoungcheon; Boyd, Colin; Dawson, Ed; Kim, Kwangjo; Yang, Jeongmo; Yoo, Seungjae (2004). "Secure key issuing in ID-based cryptography". In Hogan, James M.; Montague, Paul; Purvis, Martin K.; Steketee, Chris (eds.). ACSW Frontiers 2004, 2004 ACSW Workshops – the Australasian Information Security Workshop (AISW2004), the Australasian Workshop on Data Mining and Web Intelligence (DMWI2004), and the Australasian Workshop on Software Internationalisation (AWSI2004), Dunedin, New Zealand, January 2004. CRPIT. Vol. 32. Australian Computer Society. pp. 69–74.

[6] Al-Riyami, Sattam S.; Paterson, Kenneth G. (2003). "Certificateless public key cryptography". In Laih, Chi-Sung (ed.). Advances in Cryptology – ASIACRYPT 2003, 9th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, November 30 – December 4, 2003, Proceedings. Lecture Notes in Computer Science. Vol. 2894. Springer. pp. 452–473. doi: 10.1007/978-3-540-40061-5_29 .

[7] Sakai, Ryuichi; Kasahara, Masao (2003). "ID Based cryptosystems with pairing on elliptic curve". Cryptography ePrint Archive.

[8] Boneh, Dan; Boyen, Xavier (2004). "Efficient selective-ID secure identity based encryption without random oracles". In Cachin, Christian; Camenisch, Jan (eds.). Advances in Cryptology – EUROCRYPT 2004, International Conference on the Theory and Applications of Cryptographic Techniques, Interlaken, Switzerland, May 2–6, 2004, Proceedings. Lecture Notes in Computer Science. Vol. 3027. Springer. pp. 223–238. doi: 10.1007/978-3-540-24676-3_14 .

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]