Oblivious transfer is a fundamental tool in modern cryptography. In the past few years, many studies concentrate on oblivious transfer variants with more powerful functions. In this paper, the authors propose several variants of oblivious transfer in cut-and-choose scenario, providing multiple ways of transferring data in an oblivious manner. In addition, based on homomorphic encryption, the authors construct instantiations of these primitives, which can be proven secure in malicious model under ideal/real simulation paradigm and achieve the highest security level in the real world.