On the security of an RSA based encryption scheme

In [21] some simple modifications of the RSA, respectively Dickson/LUC, cryptosystems have been presented which are practical and provably as secure in difficulty as factorizing their modulus. Similar to Rabin's provable secure cryptosystem, these schemes are vulnerable to chosen ciphertext attacks. We are going to provide a method for immunizing the RSA based system against adaptive chosen ciphertext attacks and simultaneously provide information authentication capability. By means of probabilistic encoding, the scheme achieves semantic security and plaintext awareness in the standard (i.e. non random oracle) model under the assumption of a collision-resistant hash function and the factorization intractability of the receiver's modulus.