Formal Proofs for the Security of Signcryption

Signcryption is a public key or asymmetric cryptographic method that provides simultaneously both message confidentiality and unforgeability at a lower computational and communication overhead. In this paper, we propose a sound security model for signcryption that admits rigorous formal proofs for the confidentiality and unforgeablity of signcryption. A conclusion that comes out naturally from this work is that, as an asymmetric encryption scheme, signcryption is secure against adaptive chosen ciphertext attack in the random oracle model relative to, quite interestingly, the Gap Diffie-Hellman problem, and as a digital signature scheme, signcryption is existentially unforgeable against adaptive chosen message attack in the random oracle model relative to the discrete logarithm problem.