Signcryption is a cryptographic primitive which simultaneously provides both confidentiality and authenticity in a single logical step. In a proxy signature scheme, an original signer delegates his signing power to a proxy agent, who signs a message on behalf of him. This paper introduces a new proxy signcryption scheme based on the Discrete Logarithm Problem (DLP) with a reduced computational complexity compared to other schemes in literature. In this proposed scheme, the receiver is the only one who can verify the origin of the ciphertext. Moreover, in this scheme, an authorized proxy signcrypter can create valid proxy signatures after verifying the identity of the original signcrypter. The proposed scheme achieves the various desirable security requirements. An elliptic curve based version of the proposed proxy signcryption scheme has been implemented using Mathematica for realistic (256-bit) parameters to emphasize the ease of its practical use.

Signcryption is a cryptographic primitive which simultaneously provides both confidentiality and authenticity in a single logical step. Signcryption based on elliptic curves provides the same level of security using smaller keys compared to schemes based on the discrete logarithm problem over finite fields. Identity-based cryptography serves as an efficient alternative to the traditional certificate-based cryptosystems. The idea of identity-based cryptography is to enable a user to use any arbitrary string that uniquely identifies him as his public key. In a proxy signcryption scheme, an original signer delegates his signing power to a proxy agent, who signcrypts a message on behalf of him. This paper introduces a new identity based proxy signcryption scheme without bilinear pairings. Its security is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP) with a reduced computational complexity compared to other schemes in literature. In this proposed scheme, the receiver is the only one who can verify the origin of the ciphertext. Moreover, in this scheme, an authorized proxy signcrypter can create valid proxy signatures after verifying the identity of the original signcrypter. The proposed scheme achieves the various desirable security requirements. General TermsCryptography, Security.

Electronic commerce, as exemplified by the popularity of the Internet, is becoming more important along with fast progress in communications and information technology. The SET (Secure Electronic Transaction) protocol is a scheme designed to ensure that merchants and cardholders can conduct business over a public network. Although the SET protocol has some disadvantages, but still it is the most commonly used protocol in the Internet shopping. Signcryption is a cryptographic primitive which simultaneously provides both confidentiality and authenticity in a single logical step. Signcryption based on elliptic curves provides the same level of security using smaller keys compared to schemes based on the discrete logarithm problem over finite fields. This paper examines the benefits of using signcryption rather than signaturethen-encryption in the SET protocol. Using identity-based signcryption in the SET protocol reduces the number of encryption and decryption operations. Moreover, signcryption is less time consuming than signature-then-encryption.

A key establishment protocol allows entities to establish a common secret key to ensure secure communications over an insecure public network. This paper proposes two new twoparty key agreement protocols. Both protocols do not involve bilinear pairings. The first protocol is a certificate-based key agreement protocol that is more efficient than [1] due to its dependence on the elliptic curve discrete logarithm problem and the second is an extension to a certificateless key agreement protocol. Both protocols depend on the use of an authentication message to check that the shared session key is equal for both entities before using it. This authentication message prevents the key off-set attack that is valid for the Haiyan-Sun protocol [2]. The security analysis of the second protocol is discussed. The proposed certificateless key agreement protocol is compared with other protocols in literature [2,3,4] and it requires minimal computational cost. Moreover, this protocol is implemented using the Mathematica (7) program.

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