On The Security of Block Permutation and Co-XOR in Reversible Data Hiding

Block permutation and Co-XOR (BPCX) image encryption is a commonly used encryption method for reversible data hiding in the encryption domain, which can effectively improve the embedded capacity and the ability resisting the existing attacks including ciphertext-only attack and known plaintext attack (KPA). This paper proposes a KPA based on bit-block inversion and mean equivalent division (MED) to estimate the block permutation key of BPCX image encryption. Firstly, we divide an image block into the bit-block and point out that the maximum of the numbers of 0 bit and 1 bit of a bit-block before and after the Co-XOR encryption remains unchanged. And then two inversion rules of bit-block are defined to construct pseudo plain-ciphertext images to eliminate the influence of pixel value changes caused by Co-XOR encryption. Finally, the MED based KPA is designed to estimate the block permutation key sequence according to the pseudo plain-ciphertext images. The relationship between the key estimation accuracy and the number of known plain-ciphertext pairs, block size, and pseudo ciphertext are discussed. Experimental results show that even in the minimum block size (2×2), the average estimated correct rate of the block permutation sequence exceeds 40%. The block permutation key estimation accuracy is more than 50% when the block size is greater than 3×3. Some improved encryption methods against the proposed KPA are also given.