Rebuttal: On the Security of Reversible Data Hiding in Encrypted Images by MSB Prediction

Abstract

Prior to the publication of our article in 2018, to our knowledge, there were no methods of achieving a favourable trade-off between the payload in bits-per-pixel (bpp) and the quality of the reconstructed image in terms of PSNR or SSIM. Indeed, a high payload value would lead to a degradation of the reconstructed image’s quality. Moreover, it should also be noted that almost all of the other state-of-the-art methods at the time, were based on Least Significant Bit (LSB) substitution and made little use of the redundancy between pixels in the clear domain to realize the data embedding of a secret message. In our proposed work <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> , we have taken the opposing view by developing a Most Significant Bits (MSB) prediction-based reversible data hiding in encrypted images (RDHEI) method. In the EPE-HCRDH approach, the original image is encrypted without modification and information about the location of all pixels which cannot be correctly predicted is embedded by MSB substitution. In order to localize the prediction errors, flags of consecutive bits equal to 1 are used. With this information, the data hider can detect all the bits which can be marked and substitute them with bits of a secret message. In this case, the payload is slightly lower than 1 bpp, but perfect reversibility is achieved. So, the proposed EPE-HCRDH approach provides a high payload with a little complexity. But as highlighted by Dragoi and Coltuc <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , the fact of using flags, so that the data hider can embed a secret message introduces security flaws in the method. Despite this, the method has attracted the attention of many researchers, with 100 citations (according to Google Scholar on November 9, 2020) in several peer-reviewed journals of excellent reputation (IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> , IEEE TRANSACTIONS ON MULTIMEDIA <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> – <xref ref-type="bibr" rid="ref5" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <xref ref-type="bibr" rid="ref6" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <xref ref-type="bibr" rid="ref7" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[7]</xref> , IEEE ACCESS <xref ref-type="bibr" rid="ref8" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[8]</xref> , IEEE TRANSACTIONS ON SIGNAL PROCESSING, and IEEE TRANSACTION ON DEPENDABLE AND SECURE COMPUTING <xref ref-type="bibr" rid="ref9" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[9]</xref> . Today, we can say that high capacity RDHEI has become a hot topic.