New public key cryptosystems based on the dependent-RSA problems

Abstract

Since the Diffie-Hellman paper, asymmetric encryption has been a very important topic, and furthermore ever well studied. How- ever, between the efficiency of RSA and the security of some less efficient schemes, no trade-of has ever been provided. In this paper, we propose better than a trade-off: indeed, we first present a new problem, derived from the RSA assumption, the “Dependent-RSA Problem". A careful study of its dificulty is performed and some variants are proposed, namely the “Decisional Dependent-RSA Prob- lem". They are next used to provide new encryption schemes which are both secure and efficient. More precisely, the main scheme is proven semanti- cally secure in the standard model. Then, two variants are derived with improved security properties, namely against adaptive chosen-ciphertext attacks, in the random oracle model. Furthermore, all those schemes are more or less as efficient as the original RSA encryption scheme and reach semantic security.