Cryptanalysis of Reversible Data Hiding in Encrypted Images by Block Permutation and Co-Modulation

Reversible data hiding in encrypted images (RDH-EI) technology is commonly used in cloud storage images for privacy protection. Most existing RDH-EI techniques reported in the literature applied block permutation and co-modulation (BPCM) encryption to generate encrypted images. This work analyses the security of the RDH-EI algorithm based on BPCM encryption under known plaintext attacks (KPAs). Different from the existing KPAs, this paper considers that attackers can perform KPAs based on marked encrypted images and shows that BPCM encryption has the risk of information leakage. To find the constant features of a block before and after co-modulation, the first-pixel difference block (FDB) of a block is first defined. Then, a pseudo cypher difference image of the cyphertext image is constructed to eliminate the changed FDBs so that the differences in the cyphertext FDBs are the same as the FDBs in the corresponding plaintext difference image. Finally, we design an FDB-based block permutation key estimation method according to the plaintext difference image and pseudocyphertext difference image. The influence of block size on key estimation accuracy and the time complexity of the proposed KPA algorithm are analysed and discussed. Experimental results show that the correct rate of key estimation is positively correlated with the block size and the number of plain-cyphertext pairs. The average correct rate of key estimation reaches 63% when the block size is greater than 3×3.