Study On Signcryption Schemes From Bilinear Pairings

Signcryption is a cryptographic primitive that performs digital signature and publickey encryption simultaneously, at lower computational costs and communication over-heads than the signature-then-encryption approach. Signcryption provides a good ap-proach to transmit messages when both confidentiality and authenticity are needed. Inthis dissertation, we study the construction of the signcryption and its provable security.It consists of the following four aspects.1. Three e?cient signcryption schemes are proposed, including of a certificate-basedsigncryption scheme, an identity-based signcryption scheme, and a self-certified sign-cryption scheme. For the certificate-based and identity-based signcryption schemes,we firstly give their formal models and then describe the proposed schemes. Finally,we prove their security in the random oracle model and analyze their performance.The analysis results show that our schemes excel the existing schemes in termsof the security and e?ciency. We present the first signcryption scheme based onthe self-certified public keys. The self-certified signcryption scheme does not needpublic key certificates and eliminates the key escrow problem of the identity-basedsigncryption schemes.2. We propose an identity-based threshold signcryption scheme and an identity-basedthreshold unsigncryption scheme by combining the signcryption with threshold tech-nique. For the proposed identity-based threshold signcryption scheme, we firstly givethe formal model and then describe the proposed scheme. Finally, we prove its se-curity in the random oracle model and analyze its performance. Our scheme turnsout to be more e?cient than the two previously proposed schemes. We presentthe first identity-based threshold unsigncryption scheme, which is the integration ofChow et al.'s identity-based signcryption scheme, Shamir's (t,n) threshold schemeand Baek and Zheng's zero knowledge proof scheme for the equality of two discretelogarithms based on the bilinear map.3. We propose a certificate-based multi-recipient signcryption scheme and an identity-based multi-recipient signcryption scheme. We firstly give their formal models andthen describe the proposed schemes. Finally, we prove their security in the randomoracle model and analyze their performance. The analysis results show that ourscheme have much less computational costs than re-signcrypting a message n timesusing a corresponding signcryption scheme. Therefore, our schemes are useful tobroadcast a message to multiple users in a secure and authenticated manner.