HD{RSA: Hybrid Dependent RSA a New Public-Key Encryption Scheme

This paper describes a new hybrid RSA-based public-key encryption scheme, the HD-RSA. It relies on the recently proposed Dependent{RSA problem, which can be proven as di cult as the original RSA problem, in some circumstances. The basic scheme, using the \one-time pad" symmetric encryption, provides a both very e cient scheme and secure relative to the sole Dependent{RSA problem. A more general proposal, by integrating symmetric encryption schemes, allows much higher rates under a very weak assumption about the symmetric scheme used. The general scheme is rst presented together with a careful study of its security relative to the Dependent{RSA problem. Then, the hardness of this new problem is discussed, namely by proving its equivalence with RSA, for well-chosen exponents. Therefore, it results that this new encryption scheme is semantically secure against any kind of attacks, namely non-adaptive and even adaptive chosen-ciphertext ones. Moreover, with a similar security as OAEP{RSA (PKCS #1 v2.0), this scheme can reach higher speed rates. Furthermore, if one compares it with the DHAES or EPOC (two other IEEE P1363a candidates for encryption), e ciency gets many times better.