Elements of information theory
Elements of information theory
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Handbook of Applied Cryptography
Handbook of Applied Cryptography
New Iterative Geometric Methods for Robust Perceptual Image Hashing
DRM '01 Revised Papers from the ACM CCS-8 Workshop on Security and Privacy in Digital Rights Management
Robust Hash Functions for Digital Watermarking
ITCC '00 Proceedings of the The International Conference on Information Technology: Coding and Computing (ITCC'00)
Fragility analysis of adaptive quantization-based image hashing
IEEE Transactions on Information Forensics and Security
Unicity Distance of Robust Image Hashing
IEEE Transactions on Information Forensics and Security - Part 1
Robust and Secure Image Hashing via Non-Negative Matrix Factorizations
IEEE Transactions on Information Forensics and Security - Part 1
Robust and secure image hashing
IEEE Transactions on Information Forensics and Security
Perceptual Image Hashing Via Feature Points: Performance Evaluation and Tradeoffs
IEEE Transactions on Image Processing
Random Gray code and its performance analysis for image hashing
Signal Processing
Robust image hash in Radon transform domain for authentication
Image Communication
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How to measure the security of image hashing is still an open issue in the field of image authentication. Some works have been conducted on the security measure of image hashing. One of the most important works is the randomness measure proposed by Swaminathan et al., which uses differential entropy as a metric to evaluate the security of randomized image features and has been applied mainly in the security analysis of the feature extraction stage of image hashing. It is meaningful to measure the randomness of the image features over the secret-key set for the security of image hashing because the image features extracted by image hashing should be generated randomly and difficult to guess. However, as is well known, differential entropy is not invariant to scaling; thus it might not be enough to evaluate the security of randomized image features. In this paper, we show the fact that if the image features of an image hash function are scaled by a constant that is large than one, then the tradeoff between the robustness and the fragility of the image hash function will not change at all, but the security indicated by the randomness measure will increase. The above-mentioned fact seems to contradict the following. First, the security of image hashing, which conflicts with robustness and fragility, cannot increase freely. Secondly, a deterministic operation, such as deterministic scaling, does not change the security of image hashing in terms of the difficulty of guessing the secret key or randomized image features. Therefore, the randomness measure should be modified to be invariant to scaling at least.