Searchable encryption (SE) technology allows users to use keywords to retrieve encrypted data and ensure that useful plaintext information of encrypted data will not be disclosed. For a secure SE scheme, if it is able to meet the multi-trapdoor privacy (MTP), the security will be improved compare with the traditional SE scheme. However, there are few searchable encryption schemes that can meet the requirement of MTP. In addition, many existing schemes ignore the need of multi keyword search, and both sides of communication use the same cryptosystem and cryptographic parameters, which leads to the problem of low search efficiency and practicability. Therefore, we propose a heterogeneous SE scheme that supports multi-keyword search, provides MTP and allows both sides of communication to be worked in different cryptosystems with different cryptographic parameters. With the use of the random oracle model (ROM), we demonstrate the security of the proposed scheme, and we show the excellent performance of the proposed scheme at the end of the article.