The convertible authentication encryption (CAE) scheme, enables the signatory to send a secret message and its associated signature to a designated receiver. If some dispute happens, then the receiver has the ability to get ordinary signature by converting the ciphertext signature. The receiver can solely perform this signature conversion without any extra computational costs. The recipient of the signature can prove himself that he/she is the actual designated recipient. We incorporate self - certified public key (SCPK) systems into a CAE scheme to propose our CAE scheme with authentication and computationally indistinguishable. Our CAE scheme provide robust security and apply it to different online financial applications. The security analysis reflects that, our CAE scheme satisfies all the security requirements. Moreover, it does not require additional certificate verification because the public key authentication and signature verification can be done in single logical step. Finally, from the result of performance analysis shows, that the presented CAE scheme is cost efficient than the existing Wu et al.'s scheme.