An Extension of the RSA Trapdoor in a KEM/DEM Framework

A trapdoor based on an extension of the RSA trapdoor is proposed. The same function as in the RSA cryptosystem is used, i.e. xemodn, but there is no restriction for the exponent to be prime relatively to the order of the group while the function remains a permutation on a subgroup of Z_n ^*. For the case when the exponent is not prime to the order of the group the resulting cryptosystem has its security equivalent to solving the integer factorization problem. This trapdoor is further used in a KEM/DEM (key encapsulation mechanisms /data encryption mechanisms) framework in order to obtain more efficient encryption and to achieve resistance against active adversaries. The resulting hybrid encryption scheme is provable secure against adaptive chosen ciphertext adversaries in the random oracle model.