The analysis on the well-known optimal asymmetric encryption and its improved schemes reveal some drawbacks. For one, these schemes use plaintext padding mechanism and hash functions to hide the statistic property of plaintext, and the property of Hash function makes it difficult to prove that these schemes or their variants are secure in the standard model. Many research works show that, assuming that RSA problem and their variants are difficult, it is difficult to prove the RSA-OAEP schemes or their improvements secure against adaptive chosen cipher-text attack in the standard model. In addition, because these schemes encrypt randomized message using padding mechanism, the randomized message is k-bit longer than the plain-text. This increases the computational complexity of these schemes. To address the problem, this paper proposes an RSA-type encryption scheme based pairing functions. This scheme has the following advantages. First, the scheme does not use hash function to hide the statistical property of plain-text, which makes it possible to prove its security in the standard model. In this scheme, the randomized message can be shorter than the plain-text. Second, it is proved in the standard model that the scheme is secure against adaptive chosen cipher-text attacks. Third, when used in sign-encryption, it is not necessary for the users to negotiate the order of signature modulus or the encryption modulus.