Study On Certificateless Signcryption

Certi?cateless public key cryptography (CL-PKC), which was introduced by Al-Riyami and Paterson in ASIACRYPT 2003, is receiving signi?cant attention becauseit is a new paradigm that overcomes the problem of certi?cate management in thetraditional PKC and solves the inherent key escrow problem su?ered by identity-basedpublic key cryptography (ID-PKC). Certi?cateless signcryption (CLSC) is one of themost important security primitives in CL-PKC that simultaneously ful?lls both thefunctions of digital signature and public key encryption in a logically single step, andwith a cost signi?cantly lower than that required by the traditional signature followedby encryption.In this dissertation, we study the construction of the certi?cateless signcryptionscheme. The results obtained are outlined as followed:(1) We proposed an e?cient certi?cateless signcryption scheme, which requires only twopairing operations in the signcrypt and unsigncrypt phases, and is more e?cientthan all the existing CLSC schemes based on bilinear pairings. We ?rstly givethe formal de?nition of CLSC and its security model, and then we describe thescheme. Finally, we prove its security in the random oracle model. Speci?cally, weprove its con?dentiality under the q-BDHI Assumption and CDH Assumption and itsUnforgeability under the q-SDH Assumption and DL Assumption.(2) Motivated by Baek et al.'s pairing-free certi?cateless encryption schemes, We pro-posed a pairing-free CLSC scheme, which is more e?cient than all the previousconstruction. We prove its security in the random oracle model. Speci?cally, weprove its con?dentiality under the hardness of Gap Di?e-Hellman Problem and itsUnforgeability under the hardness of Gap Discrte Logarithm Problem. As far as weknow,this is the ?rst CLSC scheme that does not depend on the bilinear pairings.