Efficient signcryption for heterogeneous systems

Privacy and authentication are the two main security goals in secure communications. To solve the secure communications problem between two heterogeneous systems, we propose two efficient signcryption schemes that can simultaneously achieve confidentiality, integrity, authentication, and nonrepudiation in a logical single step. The first scheme allows a sender in a public key infrastructure (PKI) to send a message to a receiver in an identity-based cryptosystem (IBC) and the second scheme allows a sender in the IBC system to send a message to a receiver in the PKI system. We prove that the first scheme has indistinguishability against adaptive chosen ciphertext attacks (IND-CCA2) under the $q$-bilinear Diffie-Hellman inversion problem ($q$-BDHIP) and existential unforgeability against adaptive chosen messages attacks (EUF-CMA) under the Diffie-Hellman inversion problem in the random oracle model. We also prove that the second scheme has the IND-CCA2 property under the BDHIP and EUF-CMA property under the $q$-strong Diffie-Hellman problem ($q$-SDHP) in the random oracle model.