A Signcryption Scheme Based on Integer Factorization

Signcryption is a public-key cryptographic primitive introduced by Zheng, which achieves both message confidentiality and nonrepudiatable origin authenticity, at a lower computational and communication overhead cost than the conventional ‘sign-then-encrypt’ approach. We propose a new signcryption scheme which gives a partial solution to an open problem posed by Zheng, namely to find a signcryption scheme based on the integer factorization problem. In particular, we prove that our scheme is existentially unforgeable, in the random oracle model, subject to the assumption that factoring an RSA modulus N = pq (with p and q prime) is hard even when given the additional pair (g, S), where g ∈ ZZN is an asymmetric basis of large order less than a bound S/2 ¿ √N .