Abstract

In this paper, we discuss the strong attack model security for public key encryption scheme and dig-ital 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 findan essential mechanism of secure schemes under strong attack model. So, we prove several impos-sibility results underSCCAmodel. For the purpose, we classify two types of public key encryptionschemes: First model isP=(Gen;Enc;Dec)which we call the setup-free model, second model isP=(Setup;Gen;Enc;Dec)which we call the setup model. We prove that it is impossible to reduceindistinguishability under strong chosen ciphertext attack (IND-SCCA) security to any other weakersecurity notion under black-box analysis in the standard model. Second, when a public key encryp-tion scheme is modeled asP=(Setup;Gen;Enc;Dec), we show that it is impossible that the securityofSCCAis proven if the reduction is setup-preserving black-box reductions which we define in thispaper. From the similar discussion, we prove impossibilities for digital signature schemes. Finally,we discuss the essential mechanism to constructIND-SCCAsecure public key encryption scheme inthe standard model.