The Public key encryption scheme with keyword search (PEKS), firstly put forward by Boneh et al., can achieve the keyword searching without revealing any information of the initial data. However, the original PEKS scheme was required to construct a secure channel, which was usually expensive. Aimed at resolving this problem, Baek et al. put forward an improved scheme, which tried to construct a Secure channel free PEKS (SCF-PEKS). Subsequently, several SCF-PEKS schemes were proposed, however most of them turned out only secure in the random oracle model, which possibly lead to the construction of insecure schemes. Therefore, Fang et al. put forward an enhanced SCF-PEKS construction, which was provably secure in the standard model, however this construction needed a strong and complicated assumption. Then Yang et al. put forward an SCF-PEKS construction under simple assumption, but their construction had a big reduction in efficiency. In this article, we propose an SCF-PEKS construction, which is provably secure under the same assumption as that of Yang et al.'s scheme, however, with better performance. Then we give its full security proof, along with the performance analysis. Finally, we improve the SCF-PEKS construction to resist Keyword guessing attack (KGA) and give its security demonstration.