OAEP and other similar schemes proven secure in Random- Oracle Model require one or more hash functions with output size larger than those of standard hash functions. In this paper, we show that by utilizing popular Sponge constructions in OAEP framework, we can eliminate the need of such hash functions.We provide a new scheme in OAEP framework based on Sponge construction and call our scheme Sponge based asymmetric encryption padding (SpAEP). SpAEP is based on 2 functions: Sponge and Sponge Wrap, and requires only standard output sizes proposed and standardized for Sponge functions. Our scheme is CCA2 secure for any trapdoor one-way permutation in the ideal permutation model for arbitrary length messages. Our scheme utilizes the versatile Sponge function to enhance the capability and efficiency of the OAEP framework. SpAEP with any trapdoor one-way permutation can also be used as a key encapsulation mechanism and a tag-based key encapsulation mechanism for hybrid encryption. Our scheme SpAEP utilizes the permutation model efficiently in the setting of public key encryption in a novel manner. © Springer International Publishing Switzerland 2015.