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To protect the contents of images in the mobile internet era during image storage and transmission, image encryption has achieved a tremendous success during the last decades. Currently, little attention has been paid to non-RGB color spaces such as HSV, YUV and L*a*b* color spaces in the color image encryption community. In this paper we use high level encryption schemes in more informative channels and low level encryption schemes in less informative channels. This paper is the first time to encrypt color image in CIE L*a*b* color space. First we convert RGB to L*a*b* color space. The 2D Arnold’s cat map followed by the 3D Lu chaotic map are conducted in the L* channel. The less complicated DNA coding and 1D logistic map based encryption scheme is leveraged in the a* and b* channels, which contain less information than that in the L* channel. The experimental results reveal that our method achieves similar results with the method that conducts the same scheme in each channel of the RGB color space, while consuming less time. In addition, our method can resistant several attacks such as brute-force attack, statistic attack, correlation attack.