Signcryption as a cryptographic primitive that offers both confidentiality and authentication simultaneously. Generally, in signcryption schemes, the message is hidden and thus the validity of the signcryption can be verified only after the unsigncryption process. Thus, a third party will not be able to verify whether the signcryption is valid or not. Signcryption schemes that allow any one to verify the validity of signcryption without the knowledge of the message are called public verifiable signcryption schemes. Third party verifiable signcryption schemes allow the receiver of a signcryption, to convince a third party that the signcryption is valid, by providing some additional information along with the signcryption. This information can be anything other than the receiver’s private key and the verification may or may not require the exposure of the corresponding message.
This paper shows the security weaknesses in two such existing schemes namely  and . The scheme in  is Public Key Infrastructure (PKI) based scheme and the scheme in  is an identity based scheme. More specifically,  is based on elliptic curve digital signature algorithm (ECDSA). We also, provide a new identity based signcryption scheme that provides both public verifiability and third party verification. We formally prove the security of the newly proposed scheme in the random oracle model.