On the (Im)possibility Results for Strong Attack Models for Public Key Cryptsystems

In this paper, we discuss the strong attack model security for public key encryption scheme and digital signature scheme. Recently, Barbosa and Farshim introduced strong chosen ciphertext attack (SCCA) which is stronger than chosen ciphertext attack. The main motivation of this paper is to find an essential mechanism of secure schemes under strong attack model. So, we prove several impossibility results under SCCA model. For the purpose, we classify two types of public key encryption schemes: First model is Π = (Gen,Enc,Dec) which we call the setup-free model, second model is Π = (Setup,Gen,Enc,Dec) which we call the setup model. We prove that it is impossible to reduce indistinguishability under strong chosen ciphertext attack (IND-SCCA) security to any other weaker security notion under black-box analysis in the standard model. Second, when a public key encryption scheme is modeled as Π = (Setup,Gen,Enc,Dec), we show that it is impossible that the security of SCCA is proven if the reduction is setup-preserving black-box reductions which we define in this paper. From the similar discussion, we prove impossibilities for digital signature schemes. Finally, we discuss the essential mechanism to construct IND-SCCA secure public key encryption scheme in the standard model.