New Public Key Cryptosystemsbased on the Dependent {

Since the Diie-Hellman paper, asymmetric encryption has been a very important topic, and furthermore ever well studied. However, between the eeciency of RSA and the security of some less eecient schemes, no trade-oo has ever been provided. In this paper, we propose better than a trade-oo: indeed, we rst present a new problem, derived from the RSA assumption, the \Dependent{RSA Problem". A careful study of its diiculty is performed and some variants are proposed, namely the \Decisional Dependent{RSA Problem". They are next used to provide new encryption schemes which are both secure and eecient. More precisely, the main scheme is proven semantically 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 eecient as the original RSA encryption scheme and reach semantic security.