Abstract: In order to achieve both ciphertext image security and searchability, the thumbnail-preserving image encryption (TPE) scheme ensures that the thumbnails are consistent before and after image encryption. Currently the mainstream TPE schemes are constructed based on the rank-then-encipher framework, but the time complexity of most TPE schemes under this framework are high. In order to improve the efficiency of the TPE schemes, a low time complexity rank function is proposed. By analyzing the rank function theoretically, it is found that the efficiency of the rank function can be improved by reducing the length of the pixel group, the sum of pixels and the range of pixel values. The pixel group is first divided into two smaller groups of pixels using pixel aages. The execution efficiency of rank function is improved by reducing their pixel sum and pixel value range. We construct a low time complexity TPE scheme based on this rank function. The experimental results show that the proposed scheme is more advantageous in terms of the encryption time, provided that the scheme is capable of lossless decryption.