My research is a consolidation of work done with respect to several public key cryptographic primitives. More specifically, my research is on provably secure public key cryptosystems. The nature of work done varies from designing new cryptographic primitives according to the sheer needs of practical security and considering new types of attacks, modeling them mathematically and providing counter measures for improving the security of systems to withstand the new type of attacks, cryptanalysis of existing schemes, fixing the flaw in the existing schemes and eefficiency improvement. Specifically, my research can be split into three main parts. Research on Encryption, Digital Signature and Signcryption schemes and their variants.