This paper presents the encryption method followed by compression with image. It encrypts the image using the B-transform and then compresses by the DCT (Discrete Cosine Transform) based the standard image compression method (e.g. JPEG). The output of B-transform is the partially sorted string and the additional position information from the original permutation string. The additional position information generates the B-code. This code used by the encryption key whose space is 10 19500 enough

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... o avoid to brute-force attack. Also, when the compression ratio of the reconstructed image is same, the PSNR of our method is about 1.5 times better than the conventional scheme. So, the proposed algorithm provides the secure encryption and the improvement of compression efficiency.