Random Gray code and its performance analysis for image hashing

The discrete-binary conversion stage, which plays the role of converting quantized hash vectors into binary hash strings by encoding, is one of the most important parts of authentication-oriented image hashing. However, very few works have been done on the discrete-binary conversion stage. In this paper, based on Gray code, we propose a key-dependent code called random Gray (RGray) code for image hashing, which, according to our theoretical analysis and experimental results, is likely to increase the security of image hashing to some extent and meanwhile maintains the performance of Gray code in terms of the tradeoff between robustness and fragility. We also apply a measure called distance distortion, which was proposed by Rothlauf (2002) [1] for evolutionary search, to investigate the influence of the discrete-binary conversion stage on the performance of image hashing. Based on distance distortion, we present a theoretical comparison of the encodings applied in the discrete-binary conversion stage of image hashing, including RGray encoding. And our experimental results validate the practical applicability of distance distortion on the performance evaluation of the discrete-binary conversion stage.