Multivariate Public Key Cryptography (MPKC) is one of the main candidates for secure communication in a post-quantum era. Recently, Yasuda and Sakurai proposed in  a new multivariate encryption scheme called SRP, which is very efficient and resists all known attacks against multivariate schemes. However, the key sizes of the scheme are quite large. In this paper we propose a new strategy to reduce the key size of the SRP scheme, which enables us to reduce the size of the public key by up to 54%. Furthermore, we can use the additional structure in the public key polynomials to speed up the encryption process of the scheme by up to 50%. We show by experiments that our modifications do not weaken the security of the scheme.