We study how to make any deterministic encryption scheme probabilistic and secure against adaptively chosen cipher text attacks. A new trans positional padding encryption scheme is proposed, with which we construct a universal scheme, namely, a trans positional padding encryption scheme, which has three novel attributes: 1) it can pad a given plain text into several different values once the randomness is chosen while the previous padding schemes only pad a given plain text into a fixed value; 2) it introduces the randomness into a cipher text without employing hash function or random oracle, and; 3) it enables the encrypted message to contain more useful information that may exceed the upper limit of plain text space.Then, we give this encryption scheme an instantiation of RSA, which is proven to be indistinguishable under adaptively chosen cipher text attacks without random oracle that assumes a variant of the standard RSA problem. The variant problem is a novel arithmetic problem, and it is weaker than the standard RSA problem
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