Document Type : Research Article


Faculty of Computer Engineering, University of Isfahan, Isfahan, Iran


In the last two decades bilinear pairings have found many applications in cryptography. Meanwhile identity-based cryptosystems based on bilinear pairings have received particular attention. The IEEE, IETF, and ISO organizations have been working on standardization of pairing-based cryptographic schemes. The Boneh-Franklin identity-based encryption and Sakai-Kasahara identity-based signature are the most well-known identity-based schemes that have been standardized. So far, various schemes have been proposed to reduce the computational overhead of pairing operations. All these schemes are trying to outsource pairing operations in a secure manner. But besides pairing operations, there are other basic and costly operations in pairing-based cryptography and identity-based schemes, including scalar multiplication on elliptic curves. In this research, we outsource the Boneh-Franklin encryption in a more secure and efficient (in terms of computational and communication complexity) way than existing schemes. Also we outsource the BLMQ signature (based on Sakai-Kasahara) scheme for the first time. The proposed schemes are secure in the OMTUP model. Also, unlike previous schemes, we considered communication channels insecure. Moreover, compared with the trivial solution which outsources every single operation (such as pairing, scalar multiplication and modular exponentiation) as a separate subroutine, our schemes offer less complexity by seamlessly outsourcing the whole encryption scheme for the first time.