In cryptography

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, signcryption is a public-key primitive that simultaneously performs the functions of both digital signature

Digital signature

A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. A valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit...

 and encryption

Encryption

In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

.

Encryption and digital signature are two fundamental cryptographic tools that can guarantee the confidentiality

Confidentiality

Confidentiality is an ethical principle associated with several professions . In ethics, and in law and alternative forms of legal resolution such as mediation, some types of communication between a person and one of these professionals are "privileged" and may not be discussed or divulged to...

, integrity

Integrity

Integrity is a concept of consistency of actions, values, methods, measures, principles, expectations, and outcomes. In ethics, integrity is regarded as the honesty and truthfulness or accuracy of one's actions...

, and non-repudiation

Non-repudiation

Non-repudiation refers to a state of affairs where the purported maker of a statement will not be able to successfully challenge the validity of the statement or contract. The term is often seen in a legal setting wherein the authenticity of a signature is being challenged...

. Until the previous decade, they have been viewed as important but distinct building blocks of various cryptographic systems. In public key schemes, a traditional method is to digitally sign a message then followed by an encryption (signature-then-encryption) that can have two problems: Low efficiency and high cost of such summation, and the case that any arbitrary scheme cannot guarantee the security. Signcryption is a relatively new cryptographic technique that is supposed to fulfill the functionalities of digital signature and encryption in a single logical step and can effectively decrease the computational costs and communication overheads in comparison with the traditional signature-then-encryption schemes.

Signcryption provides the properties of both digital signatures and encryption schemes in a way that is more efficient than signing and encrypting separately. This means that at least some aspect of its efficiency (for example the computation time) is better than any hybrid of digital signature and encryption schemes, under a particular model of security. Note that sometimes hybrid encryption can be employed instead of simple encryption, and a single session-key reused for several encryptions to achieve better overall efficiency across many signature-encryptions than a signcryption scheme but the session-key reuse causes the system to loose security under even the relatively weak CPA model. This is the reason why a random session key is used for each message in a hybrid encryption scheme but for a given level of security (i.e., a given model, say CPA), a signcryption scheme should be more efficient than any simple signature-hybrid encryption combination.

The first signcryption scheme was introduced by Yuliang Zheng

Yuliang Zheng

Yuliang Zheng is a Professor at the University of North Carolina at Charlotte. He is best known for inventing the Signcryption cryptographic primitive that combines the digital signature and encryption operations into one single step...

 in 1997 . Zheng also proposed an elliptic curve

Elliptic curve

In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...

-based signcryption scheme that saves 58% of computational and 40% of communication costs when it is compared with the traditional elliptic curve-based signature-then-encryption schemes . There are also many other signcryption schemes that are proposed throughout the years, each of them having its own problems and limitations, while they are offering different level of security services and computational costs.

A signcryption scheme typically consists of three algorithms: Key Generation (Gen), Signcryption (SC), and Unsigncryption (USC). Gen generates a pair of keys for any user, SC is generally a probabilistic algorithm, and USC is most likely to be deterministic. Any signcryption scheme should have the following properties :

1. Correctness: Any signcryption scheme should be correctly verifiable.
2. Efficiency: The computational costs and communication overheads of a signcryption scheme should be smaller than those of the best known signature-then-encryption schemes with the same provided functionalities.
3. Security: A signcryption scheme should simultaneously fulfill the security attributes of an encryption scheme and those of a digital signature. Such additional properties mainly include: Confidentiality, Unforgeability, Integrity, and Non-repudiation. Some signcryption schemes provide further attributes such as Public verifiability and Forward secrecy of message confidentiality while the others do not provide them. Such properties are the attributes that are required in many applications while the others may not require them. Hereunder, the above-mentioned attributes are briefly described.

• Confidentiality: It should be computationally infeasible for an adaptive attacker to gain any partial information on the contents of a signcrypted text, without knowledge of the sender's or designated recipient's private key.
• Unforgeability: It should be computationally infeasible for an adaptive attacker to masquerade an honest sender in creating an authentic signcrypted text that can be accepted by the unsigncryption algorithm.
• Non-repudiation: The recipient should have the ability to prove to a third party (e.g. a judge) that the sender has sent the signcrypted text. This ensures that the sender cannot deny his previously signcrypted texts.
• Integrity: The recipient should be able to verify that the received message is the original one that was sent by the sender.
• Public verifiability: Any third party without any need for the private key of sender or recipient can verify that the signcrypted text is the valid signcryption of its corresponding message.
• Forward secrecy of message confidentiality: If the long-term private key of the sender is compromised, no one should be able to extract the plaintext of previously signcrypted texts. In a regular signcryption scheme, when the long-term private key is compromised, all the previously issued signatures will not be trustworthy any more. Since the threat of key exposure is becoming more acute as the cryptographic computations are performed more frequently on poorly protected devices such as mobile phones, the forward secrecy seems an essential attribute in such systems.

Applications

Signcryption is seen to have several applications including the following:

• Secure and authentic email
  Email
  Electronic mail, commonly known as email or e-mail, is a method of exchanging digital messages from an author to one or more recipients. Modern email operates across the Internet or other computer networks. Some early email systems required that the author and the recipient both be online at the...
  
  , (e.g. SMEmail).
• E-commerce and M-commerce applications that often require confidentiality
  Confidentiality
  Confidentiality is an ethical principle associated with several professions . In ethics, and in law and alternative forms of legal resolution such as mediation, some types of communication between a person and one of these professionals are "privileged" and may not be discussed or divulged to...
  
  , authenticity
  Authentication
  Authentication is the act of confirming the truth of an attribute of a datum or entity...
  
  , and perhaps non-repudiation
  Non-repudiation
  Non-repudiation refers to a state of affairs where the purported maker of a statement will not be able to successfully challenge the validity of the statement or contract. The term is often seen in a legal setting wherein the authenticity of a signature is being challenged...
  
  (e.g. SSMS).