Reversible Steganography and Authentication via Transform Encoding [1st ed.] 9789811543968, 9789811543975

Table of contents :
Front Matter ....Pages i-xvii
Introduction (Jyotsna Kumar Mandal)....Pages 1-18
State of the Art in Transform Encoding for Reversible Steganography and Authentication (Jyotsna Kumar Mandal)....Pages 19-26
Reversible Encoding in Spatial and Spectral Domain (Jyotsna Kumar Mandal)....Pages 27-62
Discrete Fourier Transform-Based Steganography (Jyotsna Kumar Mandal)....Pages 63-98
Discrete Cosine Transformation-Based Reversible Encoding (Jyotsna Kumar Mandal)....Pages 99-128
Wavelet-Based Reversible Transform Encoding (Jyotsna Kumar Mandal)....Pages 129-155
Z-Transform-Based Reversible Encoding (Jyotsna Kumar Mandal)....Pages 157-195
Reversible Transform Encoding via Discrete Binomial Transformation (Jyotsna Kumar Mandal)....Pages 197-211
Reversible Transform Encoding Using Grouplet Transformation (Jyotsna Kumar Mandal)....Pages 213-278
Nonlinear Dynamics in Transform Encoding-Based Authentication (Jyotsna Kumar Mandal)....Pages 279-298
Metrics of Evaluation for Steganography and Authentication (Jyotsna Kumar Mandal)....Pages 299-310
Analysis and Comparisons of Performances on Different Transform Encoding Techniques (Jyotsna Kumar Mandal)....Pages 311-313
Conclusions (Jyotsna Kumar Mandal)....Pages 315-315
Future Directions (Jyotsna Kumar Mandal)....Pages 317-317
Back Matter ....Pages 319-325

Citation preview

Studies in Computational Intelligence 901

Jyotsna Kumar Mandal

Reversible Steganography and Authentication via Transform Encoding

Studies in Computational Intelligence Volume 901

Series Editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Computational Intelligence” (SCI) publishes new developments and advances in the various areas of computational intelligence—quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution, which enable both wide and rapid dissemination of research output. The books of this series are submitted to indexing to Web of Science, EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink.

More information about this series at http://www.springer.com/series/7092

Jyotsna Kumar Mandal

Reversible Steganography and Authentication via Transform Encoding

123

Jyotsna Kumar Mandal Department of Computer Science and Engineering University of Kalyani Kalyani, West Bengal, India

ISSN 1860-949X ISSN 1860-9503 (electronic) Studies in Computational Intelligence ISBN 978-981-15-4396-8 ISBN 978-981-15-4397-5 (eBook) https://doi.org/10.1007/978-981-15-4397-5 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Dedicated to My sweet daughter Pragati and beloved wife Shyamali

Preface

This book entitled Reversible Steganography and Authentication via Transform Encoding contains fourteen chapters. Out of fourteen chapters, Chap. 1 contains the introductory remarks. This chapter reflects the aspects of introductory literature about cryptography, steganography, authentication and related issues in various domains. The genesis of steganography and authentication starting from the ancient era to the digital era is addressed in this chapter. State-of-the-art neural cryptography, tuning of neural machine, is also given in this chapter. In Chap. 2, the state-of-the-art literature survey in respect of reversible steganography and authentication has been outlined. The survey of the literature from 2005 to 2019 is incorporated. In Chap. 3, the details about steganography and authentication in different domains, e.g., spatial, spectral and composite domains, have been explained. The explanations are substantiated by examples in terms of fabrication and extraction in detail. Aspects of steganographic applications in spatial domain, spectral domain and also in composite domain have been discussed in detail. In Chap. 4, DFT-based reversible encoding with the formula for FDT and IDFT has been discussed. The problem of transformation for the whole image matrix is addressed. To reduce the computational complexity, the reduction in generalized equation of DFT and IDFT into 2  2 window-based computation has been done and the generalized equation is converted to a simpler form. The reversible encoding for application of steganography and authentication is also given. Detailed computational aspects of this reversible process are highlighted. Steganographic applications based on these reversible computations along with its process of authentication are given. In Chap. 5, DCT-based reversible computation and image matrix-based transform computation are incorporated. Sliding window using 2  2 size to compute reversible computation and reduction in generalized DCT equation into a simpler form based on small size windows is the main focus of this chapter. Steganographic applications for embedding and extraction in real components of transform coefficients using LSB and hash functions have been elaborated. The process of authentication and its applications in various real fields are also given. vii

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Preface

In Chap. 6, wavelet transformation is discussed in detail. This book has been emphasized on Haar wavelets for reversible computations. Reversible computations in smaller size windows are the prime focus of this chapter. The process of embedding and authentication is discussed in detail. Embedding and extraction of binary strings for authentication and invisible communication along with related applications of the same for various real-time applications are given. Z-transformation-based reversible encoding is done in Chap. 7. Detailed computation of Z-transform has been addressed in this chapter. Computational aspects of Z-transform with varying ROC have been taken care of in detail. Embedding of binary bits in real components in transform coefficients of Z-transform is the main focus area for embedding and authentication. Extraction of embedded bits from the embedded image is also elaborated in detail along with examples for reversibility to ensure authentication. This chapter also addresses the higher ROC of Z-transform with embedding and extraction to/from imaginary components of transformed coefficients using different values of r. Reversible transform encoding via discrete binomial transform has been embodied in Chap. 8. Here, the reversibility of computations has also been done taking 2  2 subimages. Detailed algorithmic approach with 1.5 bpB embedding payload has been given in detail with the implementation of results. Computation of Grouplet transformation for reversible computation based on its rotation and reflection properties has been done in Chap. 9. Various dihedral groups like D3, D4, D5 … D10 are used for computation of reversibility along with implementation in each case. Embedding and extraction of information into transform coefficients of various G-Lets based on its reflection and rotation properties are given in detail. Process of authentication based on various G-Let functions is given along with explicit examples. A complete algorithm for embedding and extraction with implementation results is given in this chapter. The utility of nonlinear dynamics in steganography and authentications is discussed in Chap. 10. Use of various logistic maps and computations of series of real values using various logistic maps and encoding it into binary sequence and embedding this binary sequence into various transform coefficients of different transformations is the primary goal of this chapter. Decoding of binary sequence at the receiving end using the logistic equation has been given. Some glimpse of testing of binary sequence for their randomness in terms of Monobit, Serial and Poker tests is given. Optimization of seeds for the generation of the better pseudorandom sequence using various evolutionary algorithms such as genetic algorithm has also been discussed. In Chap. 11, various matrices to evaluate the performances of various reversible transform techniques in terms of embedding, quality of embedding, image fidelity (IF), PSNR, SSIM, standard deviations (SD), etc. are discussed in detail. NIST test suit containing 15 tests are also discussed. In Chap. 12, implementation issues of all reversible transform encodings, embedding and extraction along with results are discussed in detail. Comparative study of various transformations in terms of reversible encoding and extraction is also given.

Preface

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An analysis in terms of performances with respect to embedding, extraction along with various quality factors is the main focus of this analysis. Concluding remarks on transform encoding along with their limitations, possibilities and concern are outlined in Chap. 13. Chapter 14 addresses the future scope of this study. I would like to express my sincere gratitude to the Department of Computer Science and Engineering and the University of Kalyani for encouraging me continuously to complete such massive work. I shall remain grateful to my scholars who encouraged me a lot and helped me in preparing this manuscript. Particularly Dr. Arindam Sarkar, Sujit Das, Dr. Amrita Khamrui, Khondeker Lutful Hassan, Dr. Parthajit Roy, Dr. Kousik Dasgupta, Rajeev Chatterjee, Sadhu Prasad Kar, Debarpita Santra, Dr. Somnath Mukhopadhyay, Dr. Rajdeep Chakraborty, Dr. Madhumita Sengupta, Dr. Uttam Mondal and Dr. Utpal Nandi. I would also like to express my sincere gratitude to Dr. Biswapati Jana of Vidyasagar University for his assistance. I am grateful to Mr. Ashes Saha, Senior Assistant of IQAC and other staff members of IQAC, University of Kalyani, for extending their help and cooperation in various stages of preparing the manuscript. My dearest daughter Pragati and my beloved wife Shyamali who never questioned me during my study through my life except extending their love and affection. This book is the outcome of the research of the last 15 years with all of my beloved scholars and students without whom I could not able to complete this book. My main source of inspiration of writing this book is Mr. Aninda Bose of Springer who encouraged me to write such a book three years back. Thanks to Aninda Bose for his constant encouragement so that I could complete this book. I am always blessed by my teacher Prof. Atal Choudhuri, Vice Chancellor, BSSUT, Odisha, India. My sincere regards to him. I always received enormous encouragement from Dr. Aloke K. Gupta and Mrs. Chayya Gupta during the preparation of this book. Their positive suggestions always inspired me a lot. This book is basically for the undergraduate and postgraduate students and for the research scholars who will be inspired from this literature for their work and research in the field of invisible communication. Practicing engineers will also find this book helpful for them. Hope this book will serve as very good material in the domain of security and authentication through invisible communication. Kalyani, India February 2020

Jyotsna Kumar Mandal

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2

State of the Art in Transform Encoding for Reversible Steganography and Authentication . . . . . . . . . . . . . . . . . . . . . . . . .

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3

Reversible Encoding in Spatial and Spectral Domain . . . . 3.1 Characteristics of Steganography . . . . . . . . . . . . . . . . 3.1.1 Perceptual Invisibility . . . . . . . . . . . . . . . . . 3.1.2 Embedding/Payload Capacity . . . . . . . . . . . 3.1.3 Undetectability . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Robustness Against Attacks . . . . . . . . . . . . 3.2 Types of Steganography . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Text Steganography . . . . . . . . . . . . . . . . . . 3.2.2 Image Steganography . . . . . . . . . . . . . . . . . 3.2.3 Audio Steganography . . . . . . . . . . . . . . . . . 3.2.4 Audio Authentication in Transform Domain . 3.2.5 Video Steganography . . . . . . . . . . . . . . . . . 3.2.6 Network Steganography . . . . . . . . . . . . . . . 3.3 Domain-Based Classification of Steganography . . . . . . 3.3.1 Steganography in Spatial Domain . . . . . . . . 3.3.2 Steganography in Frequency Domain . . . . . .

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4

Discrete Fourier Transform-Based Steganography . . . . . . . . . 4.1 One-Dimensional Fourier Transform (1D DFT) . . . . . . . . 4.1.1 Example of 1D Fourier Transform . . . . . . . . . . . 4.2 Two-Dimensional Fourier Transform (2D DFT) . . . . . . . . 4.2.1 Reversibility Computations of DFT . . . . . . . . . . 4.3 Discrete Fourier Transformation for Image Steganography 4.3.1 Algorithm: Embedding . . . . . . . . . . . . . . . . . . . 4.3.2 Algorithm: Decoding . . . . . . . . . . . . . . . . . . . .

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Discrete Cosine Transformation-Based Reversible Encoding 5.1 Embedding Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Properties of DCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Decorrelation . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Energy Compaction . . . . . . . . . . . . . . . . . . . . 5.3.3 Separability . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Computation of 2D DCT and IDCT with Examples . . . . 5.5 Computation of Three-Dimensional (3D) DCT and IDCT with Examples for 3D Images . . . . . . . . . . . . . . . . . . . . 5.5.1 Forward DCT Computations . . . . . . . . . . . . . . 5.5.2 Inverse DCT Computation . . . . . . . . . . . . . . . 5.5.3 Embedding and Extraction . . . . . . . . . . . . . . . 5.5.4 Embedding Algorithm . . . . . . . . . . . . . . . . . . . 5.6 Implementation of Steganographic Scheme Based on 2D DCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Encoding and Embedding Algorithm . . . . . . . . 5.6.2 Extraction and Decoding Algorithm . . . . . . . . . 5.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Applications of DCT . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LSB Encoding for Invisible Communication and Image Authentication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 LSB Encoding with Example . . . . . . . . . . . . 4.4.2 Extraction and Authentication . . . . . . . . . . . . 4.4.3 Results, Comparisons and Analysis . . . . . . . . Applications of DFT . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Transform Encoding . . . . . . . . . . . . . . . . . . . 4.5.2 Data Compression . . . . . . . . . . . . . . . . . . . . 4.5.3 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . 4.5.4 Telemedicine . . . . . . . . . . . . . . . . . . . . . . . .

Wavelet-Based Reversible Transform Encoding . . . . . . . . . 6.1 Haar Wavelet Transformation . . . . . . . . . . . . . . . . . . . 6.1.1 Information Flow Analysis of Original Image for Authentication Process . . . . . . . . . . . . . . 6.1.2 Multilevel Wavelet Transformation . . . . . . . . 6.1.3 Inverse Wavelet Transformation . . . . . . . . . . 6.1.4 Wavelet Transform of a Discrete Signal . . . . . 6.1.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.6 Transform Computation of Haar Wavelet . . . . 6.1.7 Inverse Transform Computation . . . . . . . . . .

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Z-Transform-Based Reversible Encoding . . . . . . . . . . . . . . . . . . 7.1 Z-Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Z-Transform Pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Forward Z-Transform . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Examples of ROC . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Inverse Z-Transform . . . . . . . . . . . . . . . . . . . . . . . 7.4 Generalized One Dimensional (1D) Z-Transform . . . . . . . . . 7.4.1 Forward Transform Equation . . . . . . . . . . . . . . . . . 7.4.2 Inverse Transform Equation . . . . . . . . . . . . . . . . . 7.4.3 Example of Reversible Computations . . . . . . . . . . 7.5 Generalized Two-Dimensional (2D) Z-Transform . . . . . . . . . 7.5.1 2D Forward Transform . . . . . . . . . . . . . . . . . . . . . 7.5.2 2D Inverse Transform . . . . . . . . . . . . . . . . . . . . . . 7.5.3 Examples of 2D Transform Computations in Z-Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Reversible Computation for Different Values of r in Z-Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.1 Computation of Z-Transform for r = 1 . . . . . . . . . . 7.6.2 Computation of Z-Transform for r = 2 . . . . . . . . . . 7.6.3 Computation of Z-Transform for r = 3 . . . . . . . . . . 7.6.4 Computation of Z-Transform for r = 4 . . . . . . . . . . 7.6.5 Computation of Z-Transform for r = 5 . . . . . . . . . . 7.7 Steganographic Algorithm in Z-transform Domain . . . . . . . . 7.7.1 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Embedding into the Imaginary Coefficients of the Z-Domain . 7.8.1 Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9 Algorithm for Embedding and Authentication with 1.25 bpB Payload with Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9.1 Insertion Technique for 1.25 bpB . . . . . . . . . . . . . 7.9.2 Extraction Technique . . . . . . . . . . . . . . . . . . . . . . 7.9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.3

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Two-Dimensional (2D) Haar Wavelet Transform . . . . . . . . 6.2.1 Forward Transform . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Inverse Transform . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Embedding Technique . . . . . . . . . . . . . . . . . . . . GA-Based Color Image Authentication Using Haar Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 The Technique . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

Reversible Transform Encoding via Discrete Binomial Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Forward Binomial Transform Equation . . . . . . . . . . . 8.2 Inverse Transform Equation . . . . . . . . . . . . . . . . . . . 8.3 Example of Forward Transform Computations . . . . . 8.4 Example of Inverse Transform Computations . . . . . . 8.5 Algorithm for Embedding and Authentication . . . . . . 8.5.1 Transformation . . . . . . . . . . . . . . . . . . . . . 8.5.2 Embedding . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.1 Embedding . . . . . . . . . . . . . . . . . . . . . . . . 8.6.2 Extraction . . . . . . . . . . . . . . . . . . . . . . . . 8.7 Implementation of an Algorithm for Embedding and Extraction with Payload of 1.5 bpB . . . . . . . . . . . . . 8.7.1 Algorithm 1 for Embedding . . . . . . . . . . . 8.7.2 Algorithm 2 for Extraction . . . . . . . . . . . . 8.7.3 Simulations and Results . . . . . . . . . . . . . . 8.8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reversible Transform Encoding Using Grouplet Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Dihedral Group . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Construction of G-Let (Forward and Inverse Transformations) . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 The Group D3 . . . . . . . . . . . . . . . . . . 9.2.2 The Group D4 . . . . . . . . . . . . . . . . . . 9.2.3 The Group D5 . . . . . . . . . . . . . . . . . . 9.2.4 The Group D6 . . . . . . . . . . . . . . . . . . 9.2.5 The Group D7 . . . . . . . . . . . . . . . . . . 9.2.6 The Group D8 . . . . . . . . . . . . . . . . . . 9.2.7 The Group D9 . . . . . . . . . . . . . . . . . . 9.2.8 The Group D10 . . . . . . . . . . . . . . . . . . 9.3 Implementation of an Algorithm for Embedding and Extraction with Payload of 0.5 bpB . . . . . . . 9.3.1 Embedding . . . . . . . . . . . . . . . . . . . . . 9.3.2 Decoding . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Adjustment . . . . . . . . . . . . . . . . . . . . 9.3.4 Algorithm for Embedding . . . . . . . . . . 9.3.5 Algorithm for Decoding . . . . . . . . . . . 9.3.6 G-Let Construction . . . . . . . . . . . . . . . 9.3.7 Stego Image Generation . . . . . . . . . . . 9.4 Applications of G-Let . . . . . . . . . . . . . . . . . . . .

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Contents

10 Nonlinear Dynamics in Transform Encoding-Based Authentication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Discrete Chaotic Equations . . . . . . . . . . . . . . . . . . . . . . . 10.2 Characteristics of Chaotic Systems . . . . . . . . . . . . . . . . . . 10.3 PN Sequence from Chaos . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Monobit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Serial Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Poker Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Chaotic Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.1 Skew Tent Map . . . . . . . . . . . . . . . . . . . . . . . . 10.7.2 Crossed Couple Map . . . . . . . . . . . . . . . . . . . . 10.7.3 Arnold’s Cat Map . . . . . . . . . . . . . . . . . . . . . . . 10.8 Image Encryption and Data Hiding Using Chaotic System 10.8.1 Embedding Algorithm . . . . . . . . . . . . . . . . . . . . 10.8.2 Decryption Algorithm . . . . . . . . . . . . . . . . . . . . 10.8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.9 GA Anchored Chaos for Seed Generation . . . . . . . . . . . . 10.9.1 Real-Valued Genetic Algorithm (RGA) . . . . . . . 11 Metrics of Evaluation for Steganography and Authentication . 11.1 Mean Squared Error (MSE) . . . . . . . . . . . . . . . . . . . . . . . 11.2 Peak Signal-to-Noise Ratio (PSNR) . . . . . . . . . . . . . . . . . 11.3 Image Fidelity (IF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Universal Quality Index (UQI) . . . . . . . . . . . . . . . . . . . . 11.5 Structural Similarity Index Measurement (SSIM) . . . . . . . 11.6 Histogram Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7 Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.8 Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.9 NIST Statistical Test and Analysis . . . . . . . . . . . . . . . . . . 11.9.1 Frequency (Monobits) Test . . . . . . . . . . . . . . . . 11.9.2 Test for Frequency Within a Block . . . . . . . . . . 11.9.3 Runs Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.9.4 Longest Run of Ones in a Block . . . . . . . . . . . . 11.9.5 Binary Matrix Rank Test . . . . . . . . . . . . . . . . . 11.9.6 Discrete Fourier Transform Test . . . . . . . . . . . . 11.9.7 Non-overlapping (Aperiodic) Template Matching Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.9.8 Overlapping (Periodic) Template Matching Test . 11.9.9 Maurer’s “Universal Statistical” Test . . . . . . . . . 11.9.10 Linear Complexity Test . . . . . . . . . . . . . . . . . . 11.9.11 Serial Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.9.12 Approximate Entropy Test . . . . . . . . . . . . . . . .

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11.9.13 Cumulative Sums Test . . . . . . . . . . . . . . . . . . . . . . . 310 11.9.14 Random Excursions Test . . . . . . . . . . . . . . . . . . . . . . 310 11.9.15 Random Excursions Variant Test . . . . . . . . . . . . . . . . 310 12 Analysis and Comparisons of Performances on Different Transform Encoding Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 311 13 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 14 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Bibilography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

About the Author

Jyotsna Kumar Mandal received his M.Tech. in Computer Science from the University of Calcutta in 1987, and his Ph.D. (Engineering) in Computer Science and Engineering from Jadavpur University in 2000. He is a Professor of Computer Science & Engineering, and was Dean of the Faculty of Engineering, Technology & Management at Kalyani University from 2008–2012. He has also served as the Director of IQAC at Kalyani University; Chairman of CIRM; a Professor of Computer Applications at Kalyani Government Engineering College; Associate Professor and Lecturer of Computer Science at North Bengal University; and a Lecturer at NERIST, Itanagar India. He has 33 years of teaching and research experience in the field of coding theory, data and network security and authentication, remote sensing & GIS-based applications, data compression, error correction, visual cryptography and steganography. He is Guest Editor of Springer’s MST Journal (SCI indexed). He has published more than 400 research articles in national and international journals. He has also published 7 books, organized 34 international conferences. In addition, he has served as a Corresponding Editor and Volume Editor for leading international publishing houses. He received the SikshaRatna Award for outstanding teaching from the Government of West Bengal, India in 2018; Vidyasagar Award from the International Society for Science Technology and Management at the Fifth International Conference on Computing, Communication and Sensor Networks 2016; Chapter Patron Award, CSI Kolkata Chapter at the CSI Annual Convention in 2014; Bharat Jyoti Award for meritorious services, outstanding performance and remarkable role in the field of Computer Science & Engineering in 2012 from International Friendship Society (IIFS), New Delhi; and the A. M. Bose Memorial Silver Medal and Kali Prasanna Dasgupta Memorial Silver Medal from Jadavpur University India.

xvii

Chapter 1

Introduction

Communication is an integral part of our daily life. Most of the citizens have a handheld device with some applications for communicating with others may be with family members or friends or officially to others. The most common technique of communicating over distance is through electrical signal, either over physical wire or through free space using radio waves. The communication is a hopped based process using a mesh network. This leads to the birth of a problem of eves dropping the signal/communicated information. Hence, it is required to have a layer of safety, while we are communicating the information. As a result, security in communication becomes an integral part of communication. The need of information security within/among group/society/party is now the need of each moment. The measures for security have undergone major procedural upgradations and enhancement in the last few decades. All data processing-based communicating equipment needs to be a safeguard from malfunctions due to spyware and similar un-wanting activities. The security of information used to be provided primarily by carnal and organizational means. The need of mechanized utensils for defending information stored in the computer and during communication became evident. With the amazing progress of expertise and technology, availability of services and amenities, the interest and need of individuals to connect computing devices to form networks is increasing enormously. During the process of transmission, message can be seized by somebody which may cause delinquent. Overall following physiognomies connected with such data broadcast. • Enormous volume of information is fingered/transported. • The safekeeping of information communicated from foundation to end point through communiqué links via different nodes is the most significant staple to be concerned. • Validation of quantifiable by the receiver is a chief possible delinquent. • Inter-device and inter-process communication must be authenticated prior to use the communicated materials.

© Springer Nature Singapore Pte Ltd. 2020 J. K. Mandal, Reversible Steganography and Authentication via Transform Encoding, Studies in Computational Intelligence 901, https://doi.org/10.1007/978-981-15-4397-5_1

1

2

1 Introduction

• Any short of applications like telemedicine is an important aspect of medical practice owners where verification is the obligation for therapeutic records of a patient for appropriate diagnosis. Communication can be captured by somebody during the course of the broadcast which may cause unruly. Hence, data and information security and message confidentiality have become a dominant obligation for such arrangements. Security is a vital issue for many domains. The aspect of security is mainly safeguarding the assets in any form. The digital era has urged the research fraternity to think about security from different dimensions. The digital assets cover a wide range of varieties to name a few digital checks, digital signature, etc. To be more precise, the information is conveyed with added security to make sure the indented receiver gets the intended information intact. The integrity of the data is preserved by different security techniques which have been used over the decades. The security approach can be broadly categorized into two main types—cryptography and Steganography. In cryptography the information is scrambled into unintelligent form, and this is visible to anyone. Unlike cryptography, the information is concealed into another media in case of Steganography and the hidden information is visible publicly without perceptibility. Encrypting an ensemble proceeding to its broadcast is the method of data encryption. The equivalent data decryption procedure is castoff to decipher the converted memo. Steganography is the fine art and discipline of hiding posts into shelter media in such a way that except the sender and envisioned beneficiary realize the existence of the memo. This is a form of safekeeping attained through anonymity. The advantage of steganography over cryptography is that posts do not entice consideration to general entities. Encrypted ensembles may generate doubt, and hence, intuition may be generated to reveal the source. So cryptography only shields the contents of a memo, but steganography ensures to guard both posts and communicating parties both as no noticeable changes are visible in the cover during transmission. Steganography embraces the camouflage of evidence within source/cover. In modern steganography, automated transportations associate steganographic coding into the shell of a transport layer into the form of various files and associated formats. Mass media documentations are the model for steganographic transmission as dimensionally they are large. Standard steganographic methods typically accompanying with keys associated with technique to obscure input material in a perceptible means into the image. Nowadays steganographic systems are planned in connotation with chaos-based systems where random binary sequences are produced using logistic maps. The process integrates an extra layer of security into the cover media embedded with an extremely subtle confused arrangement to improve safety without affecting the visible properties much. Construction of a sheltered information walloping technique in cardinal pictures is the prime process in various applications. The image steganographic techniques use the image as asylum media for implanting clandestine memo in connotation with

1 Introduction

3

chaotic sequences. The urgent obligation for a steganographic procedure is invisibility while taking full advantage of the cargo during implanting. Logistic chaotic maps are used to scramble the secret followed by embedding into the career picture utilizing implanting methods; as a result, the surreptitious information bit is not entrenched straight into the career picture as in normal steganography. Steganographic systems relating to equally spatial and spectral province entrenching linked with confused order are dealt recently. In the spectral domain, pictures are converted to frequency coefficient using DCT, DFT, DWT, wavelet, Z and Legender, etc., and posts are rooted in bit level or in block level. Association of logistic maps offers a further safety in averting arrangements from moderating. Statistical and parametric examination is made to ensure heftiness and haphazardness with decent trustworthiness. The ultimate objective of cryptography and steganography is to allow the broadcast of a memo from one foundation point to the corresponding terminus point over a broadcast media in such a means that the memo during its communication is very hard to capture by somebody. In cryptography, the source ensemble is called plaintext. The veiled memo that is to be conveyed is denoted as ciphertext. The process of translating from the plaintext to the ciphertext is known as enciphering or encryption. Re-establishing the plaintext from the ciphertext is dubbed as deciphering or decryption. The focused area of learning relating to numerous arrangements used for enciphering is identified as cryptography. The system is branded as a cryptographic system or cryptosystem or cipher. Methods are cast-off for decoding a memo without any information of enciphering facts which institute the zone of cryptanalysis. The zones of cryptography and cryptanalysis collectively called cryptology. Cryptosystem £ can be defined as a set of (, , ¥, E, ), where the given circumstances are to be fulfilled: 1. 2. 3. 4. 5. 6.

 is a finite set of plaintexts.  is a finite set of ciphertexts. ¥ is the Key of finite length may be single or set of keys (K). E is encrypted stream.  is a decrypted stream which will be identical to . For each ¥ m K, encryption is done using some specific rule and  K m E = F(, ¥) and a conforming decoding rule K m  = F(, ¥). Each  K :  →  and K :  →  are functions such that K = (E K ():  → ) =  which is identical to source plaintexts.

There are six prime characteristics in the process of cryptosystem. This conforms that if a plaintext x is encoded by means of eK , and the subsequent ciphertext is next decrypted via d K , then the unique plaintext x fallouts during decryption. In general, two cryptographic processes are 1. Symmetric cryptosystem (secret-key cryptography) 2. Asymmetric cryptosystem (public-key cryptography). In symmetric cryptosystem, the key is sovereign to the plaintext. This procedure will harvest a dissimilar yield liable on the precise key being cast-off at the spell.

4

1 Introduction

Fig. 1.1 Example of symmetric cryptosystem

1101 – Input Stream 1011 – 1st Iteration 1110 – 2nd Iteration 1001 – 3rd Iteration 1101 – 4th Iteration

1011 – Input Stream 1110 – 1st Iteration 1001 – 2nd Iteration 1101 – 3rd Iteration 1011 – 4th Iteration

0010 – Input Stream 0011 – 1st Iteration 0010 – 2nd Iteration 0011 – 3rd Iteration 0010 – 4th Iteration

1111 – Input Stream 1000 – 1st Iteration 1100 – 2nd Iteration 1010 – 3rd Iteration 1111 – 4th Iteration

The precise replacement and renovation achieved by the process be contingent on the key. Most of the symmetric key cryptosystem reproduce the plaintext during the process of encryption in a cyclic manner. That means same procedure anchored with encryption and decryption That means the number of iterations in a cycle of the encryption process is fixed and depends on the block length of the input stream. So, if the total number of iterations in a symmetric encryption is k and the input is encrypted using p iteration then the encrypted stream can be decrypted using (k-p) iteration. Consider an example. Consider an encryption technique which will take binary stream as input and the symmetric encryption is done using following rules during the process of encryption which is iterative symmetric one. 1. LSB is kept as it is. 2. Exclusive OR operation is done between two consecutive bits pairwise from left to right (LSB towards MSB). 3. The process is iterated p times (p < k where k is the number of iterations to regenerate the source stream that is the length of the cycle). The decryption is done using the same algorithm 1. Encrypted stream is taken as input. 2. LSB is kept as it is. 3. Exclusive OR operation is done between two consecutive bits pairwise from left to right (LSB towards MSB). 4. The process is iterated (k-p) times where k is the number of iterations to regenerate the source stream. Consider four 4-bit streams as, 1011, 1101, 0010 and 1111. All four input streams will be regenerated in four iterations. So, k is 4. Consider the value of p(iteration) for four-bit stream is 1, 2 and 3, respectively, as given in Fig. 1.1. So, the encrypted stream for the input stream 1101 will be 1011, 1110 and 1001, respectively. This four-bit stream will be regenerated after 4th iteration. So, the value of k is 4, and the value of (k-p) for each case will be 3, 2

1 Introduction

5

and 1, respectively. So, it is seen from all four examples that the process is forming a cycle in all cases and the same technique is repeated in the forward direction for decryption also. No separate algorithm is used for decryption. Here, block size and number of iterations constitute the keys. These symmetric encryptions are very much useful to incorporate security in wireless sensor networks where low power-based computations are very much required. In asymmetric encryption, two keys are used out of which one is acting as a private key and the other is public key at both ends. The system is to generate the pair of keys prior to transmission. Also, the key exchange is another major step prior to commencing the transmission using schemes like Diffie–Hellman key exchange process. The computation complexity of this computation process is much more than a symmetric encryption process. Also, this key exchange process suffers from the man-in-the-middle attack. Nowadays neural cryptography is being used to avoid this key exchange process. Neural tuning at both ends of the network eliminates the key exchange process. The tree parity engine is an unusual type of multilayer feed-forward neural network. This system comprises one output neuron, K hidden neurons and K * N input neurons where N is the number inputs. Inputs are binary and expressed as given in Eq. 1.1. X i j = {−1, +1}

(1.1)

The weights for input and hidden neurons get values from Eq. 1.2 Wi j ∈ {−L , . . . , 0, . . . , +L}

(1.2)

Output of hidden neuron is computed as sum multiplications of input neurons and weights by means of calculation (1.3). ⎛ σi = sgn⎝

N 

⎞ Wi j X i j ⎠

(1.3)

j=1

Signum is an unpretentious function, which returns −1, 0 or 1 and is shown in Eq. 1.4. ⎧ ⎨ −1 if x < 0 sgn = 0 if x = 0 ⎩ 1 if x > 0

(1.4)

If scalar product = 0, the output of the hidden neuron is plotted to −1 to guarantee the binary output. The output of the system is calculated as the multiplication of all values produced by hidden elements based on 1.5.

6

1 Introduction

Fig. 1.2 Tree parity machine

τ=

K

σi

(1.5)

i=1

Output for the system is binary (Fig. 1.2). Each party (S (sender) and R (receiver)) uses an individual tree parity engine with an identical structure. Synchronization of the machineries is attained using succeeding stages. 1. Random weights are initialized. 2. Subsequent steps are repeated to achieve complete synchronization. a. b. c. d.

Produce random input vectors X. Values of hidden neurons are calculated. Calculate values of output neuron. Compare output at both ends. I. If outputs are nonidentical: Go to step 2.a. II. If outputs at both ends are alike, apply some learning rules to the weights to update vectors.

Ensuring certain iterations, two tree parity machines will be identical in terms of weights and others if we continue in this process. On complete synchronization (the weights wij of both tree parity machines are identical), weights of S and R may be considered as keys. The process is designated as bidirectional culture. Hebbian’s rules may be used for the harmonization as given in Eq. 1.6 (Figs. 1.3 and 1.4).  wi+ = wi + σi xi (σi τ ) τ S τ R

(1.6)

1 Introduction

7 ∑

σ1 X1

W1,j

∑

Output layer

σ2

τS

Π

Input layer σ3 X2

∑

W2,j

σ4 ∑

Hidden layer Fig. 1.3 Tree parity machine S

∑

σ1 X1

W1,j

∑

σ2

Output layer Π

Input layer

τR

σ3

X2

∑

W2,j

σ4 ∑

Hidden layer Fig. 1.4 Tree parity machine R

Consider an example to illustrate the scheme of synchronization. It is assumed that 1. K-Number of hidden Neurons, K = 4 2. N-Number of Input Neurons, N = 2 3. L-Maximum value of weights {−3,…, +3}. Consider the execution in the first iteration. Pass 1: Initialize random weight values within the range{−3, +3}. Input vector is selected randomly for X i , within {−1, 1}. Input vector is the same for both S and R, but weight vectors are different for both the apparatuses. Here, for S, Random weight vectors W 1,j(j=1,2,3,4) are (from top to down edges) are 3, 1, 0, −1

8

1 Introduction

Random weight vectors W 2,j(j=1,2,3,4) are (from top to down edges) are 2, −1, −2, 0. The values of σ i(i=1,2,3,4) are computed using Eq. (1.3) Output of first hidden neuron, σ1 = sgn(x1 ∗ W1,1 + x2 ∗ w2,1 ) = (1) ∗ (3) + (−1) ∗ (2) = sgn(1) = 1  For second hidden neuron, σ2 = sgn x1 ∗ W1,2 + x2 ∗ w2,2 = (1) ∗ (1) + (−1) ∗ (−1) = sgn(2) = 2  For third hidden neuron, σ3 = sgn x1 ∗ W1,3 + x2 ∗ w2,3 = (1) ∗ (0) + (−1) ∗ (−2)sgn(2) = 2  For fourth hidden neuron, σ4 = sgn x1 ∗ W1,4 + x2 ∗ w2,4 = (1)∗(−1)+(−1)∗ (0) = sgn(−1) = −1. The hidden neurons in the output layer are mapped with sgn (signum function) using Eq. (1.4) to ensure a binary output. Hence, these are computed as follows. For the first hidden neuron (top to bottom of the network), as the scalar product is 1 [i.e., >0 as per Eq. (1.4)], the output of a hidden neuron is plotted to 1. For the second hidden neuron (top to bottom of the network), as the scalar product is 2 [i.e., >0 as per Eq. (1.4)], the output of the hidden neuron is charted to 1. For the third hidden neuron (top to bottom of the network), as the scalar product is 1 [i.e., >0 as per Eq. (1.4)], the output of the hidden neuron is charted to 1. For the fourth hidden neuron (top to bottom of the network), as the scalar product is −1 [i.e., Fit (C2)] iv. If the winner of this comparison is C1 then C2 is replaced with C1. a. Else there is no change. The whole operation is iterated 200 times. Then, the final mating pool is obtained. The chromosomes of the final mating pool go through a randomness testing, i.e., to check the randomness of the 128-bit stream or key that can be generated from these chromosomes. There are three test cases. If the chromosome passes through all these three test cases, then we can guarantee that the output key will be random. In this case, Monobit, Serial and Poker tests are used. For a 128-bit key, the chi-square values must be less than or equal to 3.8415, 5.9915 and 14.0671 for Monobit, Serial and Poker tests, respectively. Taking five chromosomes’ initial encoding, final pool and outputs containing optimized system parameters are given in Figs. 10.11, 10.12 and 10.13, respectively.

Fig. 10.11 Outputs of initial encoding process for genetic algorithm based system parameter optimization

Xn

Fig. 10.12 Final mating pool

Xn

R

R

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10 Nonlinear Dynamics in Transform Encoding-Based Authentication

Fig. 10.13 GA anchored results on Monobit, Serial and Poker testing for obtaining optimized system parameter

Monobit

Serial

Poker

Chapter 11

Metrics of Evaluation for Steganography and Authentication

In this chapter, various metrics for evaluations are discussed in details in terms of security applications and authentication. On the basis of the results of computation, the evaluation of the techniques may be ensured. The measurements are the mean square error, peak signal-to-noise ratio, image fidelity, universal quality index and structural similarity index measurement described in the following sections. A separate section is given where visual parameters to identify the quality of authentication techniques based on embedding have been explained. Histogram is used to analyze the performances using the histogram of original and embedded image which on analysis visually prove the quality of embedding techniques.

11.1 Mean Squared Error (MSE) In statistics, the mean squared error (MSE) of an estimator is one of the many ways to quantify the difference between values implied by an estimator and the true values of the quantity being estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or quadratic loss. MSE measures the average of the squares of the “errors.” The error is the amount by which the value implied by the estimator differs from the quantity to be estimated. The difference occurs because of randomness or because the estimator does not account for information that could produce a more accurate estimate. Mean squared errors are computed for estimating the amount of error integration. In statistics, the mean squared error or MSE of an estimator is one of the many ways to quantify the difference between an estimator and the true value of the quantity being estimated. The MSE represents the cumulative squared error between the embedded and the original image, the lower the value of MSE, the lower the error. The equation for computing error rate in terms of MSE is given in Eq. 11.1. © Springer Nature Singapore Pte Ltd. 2020 J. K. Mandal, Reversible Steganography and Authentication via Transform Encoding, Studies in Computational Intelligence 901, https://doi.org/10.1007/978-981-15-4397-5_11

299

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11 Metrics of Evaluation for Steganography and Authentication

MSE =

M−1 N −1 1  [X (i, j) − Y (i, j)]2 M N i=0 j=0

(11.1)

Here, M and N are the total number of rows and columns, respectively, and MN is the product of number of rows and columns, with X ij the true value that is original image pixel intensity, and Y ij is the estimator that is the embedded image pixel intensity after embedding.

11.2 Peak Signal-to-Noise Ratio (PSNR) The phrase peak signal-to-noise ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel scale. The PSNR is most commonly used as a measure of the quality of reconstruction of lossy compression codecs (e.g., for image compression). The signal, in this case, is the original data, and the noise is the error introduced by compression. When comparing compression codecs, it is used as an approximation to human perception of reconstruction quality; therefore in some cases, one reconstruction may appear to be closer to the original than another, even though it has a lower PSNR (a higher PSNR would normally indicate that the reconstruction is of higher quality). One has to be extremely careful with the range of validity of this metric; it is only conclusively valid when it is used to compare results between original value and perturbed value. The peak signal-to-noise ratio, abbreviated as PSNR, is the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. PSNR is usually expressed in terms of the logarithmic decibel scale. The computation of PSNR in dB below 30 dB is known to be highly contaminated. Higher the PSNR value indicates superior the quality of the image as compared to the original image. The formula for computing PSNR is given in Eq. 11.2.  PSNR = 10. log10

(Imax )2 MSE

 (11.2)

Here, the value of I max is the maximum value of pixel intensity allowed in an image, in both the grayscale and color images, the I max value is 255 because of eight-bit representation, and MSE is computed through Eq. 11.1.

11.3 Image Fidelity (IF)

301

11.3 Image Fidelity (IF) Image fidelity is a parametric computation to quantify the perfectness of human visual perception. The computation formula is given in Eq. 11.3.  IF = 1 −



2  2 X i j − Yi j / Xi j

M,N

 (11.3)

M,N

Here, M and N are the total number of rows and column, respectively, X ij is the original pixel intensity value of image, and Y ij is the pixel intensity value after embedding.

11.4 Universal Quality Index (UQI) UQI is a method to model any image distortion via a combination of three factors: loss of correlation, luminance distortion and contrast distortion (Wang 2002). The computation of UQI shows the best value as 1 if and only if both the X i and Y i are same. The formula is given in Eq. 11.4. UQI = 

x¯ y¯

4σx y   x¯ 2 + y¯ 2 σx2 + σ y2

(11.4)

where x¯ = N1 iN xi and y¯ = N1 iN yi , standard deviation is given in Eq. 11.5, and covariance is given in Eq. 11.6.

  σx =

1 N −1



N    2 (xi − μx ) , σ y = i=1



N  2 1 yi − μ y N − 1 i=1

  1  (xi − μx ) yi − μ y N − 1 i=1

(11.5)

N

σx y =

(11.6)

11.5 Structural Similarity Index Measurement (SSIM) Structural similarity can be obtained by comparing local patterns of pixel intensities that have been normalized for luminance and contrast. Calculation of SSIM depends on the separate calculation of luminance, contrast and structure.

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11 Metrics of Evaluation for Steganography and Authentication

Luminance measurement l(x, y), contrast measurement c(x, y) and structure measurement s(x, y) are separately given in Eqs. 11.7–11.9, respectively. l(x, y) =

2μx μ y + C1 μ2x + μ2y + C1

(11.7)

c(x, y) =

2σx σ y + C2 σx2 + σ y2 + C2

(11.8)

σx y + C 3 σx σ y + C 3

(11.9)

s(x, y) =

Here, C 1 , C 2 and C 3 are small constants used to avoid denominator becoming zero. Structural similarity index measurement in short SSIM is the multiplication of three components calculated through Eqs. 11.7, 11.8 and 11.9, and the SSIM formula is given in Eqs. 11.10 and 11.11 in combined form. SSIM(x, y) = [l(x, y)]α [c(x, y)]β [s(x, y)]γ

(11.10)

Parameters (α > 0, β > 0 and γ > 0) are used to adjust the relative importance of three parts.    2μx μ y + C1 2σx y + C2   SSIM(x, y) =  2 μx + μ2y + C1 σx2 + σ y2 + C2

(11.11)

where μx and μ y are the mean gray value of the image block x and y given in Eq. 11.12; σx and σ y are the variance of the image x and image y, respectively, given in Eq. 11.13; σx y is the covariance between the image x and image y given in Eq. 11.14. μx =

N N 1  1  xi , μ y = yi N i=1 N i=1

2 1  1  Yi − μ y (X i − μx )2 , σ y2 = N − 1 i=1 N − 1 i=1 N

σx2 =

(11.12)

N

  1  (X i − μx ) Yi − μ y N − 1 i=1

(11.13)

N

σx y =

(11.14)

Here, the value of C 1 , C 2 and C 3 with K 1 and K 2 are taken from Liu (2009) given in Eq. 11.15.

11.5 Structural Similarity Index Measurement (SSIM)

C1 = (K 1 L)2 , C2 = (K 2 L)2 and C3 = C2 /2

303

(11.15)

K 1 = 0.01, K 2 = 0.03

11.6 Histogram Analysis An image histogram is a type of histogram that acts as a graphical representation of the tonal distribution in a digital image. It plots the number of pixels for each tonal value. By looking at the histogram for a specific image, a viewer will be able to judge the entire tonal distribution at a glance. Image histograms are available on many modern digital cameras. Photographers can use them as an aid to show the dispersal of tones captured and whether image feature has been lost to blown-out highlights or blacked-out shadows. The horizontal axis of the graph represents the tonal variations, while the vertical axis represents the number of pixels in that particular tone. The left side of the horizontal axis represents the black and dark areas, the middle represents medium gray, and the right-hand side represents light and pure white areas. The vertical axis represents the size of the area that is captured in each one of these zones. Thus, the histogram for a very dark image will have the majority of its data points on the left side and center of the graph. Conversely, the histogram for a very bright image with few dark areas and/or shadows will have most of its data points on the right side and center of the graph. The histogram of an image is the 256 straight vertical lines representing pixel intensity values 0 to 255. The length of the vertical lines depends on the respective intensity values and its number of times appearance in the image. The base of the histogram shows the color shade from black to white indicating the position of pixel color. In case of color images, the three color components are separated before creating histogram. Three separated histograms in red, green and blue color represent the values of pixel from 0 to 255. Histogram of the original image and the embedded image is shown in Figs. 11.1 and 11.2, respectively, which can be compared with the histogram of embedded images after applying the proposed techniques of subsequent sections to verify the robustness of authentication techniques visually.

11.7 Standard Deviation Standard deviation (represented by the symbol sigma, σ ) shows how much variation or “dispersion” exists from the average (mean or expected value). A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values.

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Fig. 11.1 Histogram of original image

Fig. 11.2 Histogram of embedded image

Equation below gives the formula for computing the standard deviation.

 N 1  σ = (xi − μ)2 , N i=1 where μ is mean of all the pixel values, N is the number of pixels present in the image (row * column), and x i is the pixel value. Suppose the mean of all pixel value in the original image is 115 and the standard deviation is 86.465233 and mean of pixels in an embedded image is 115 and that of standard deviation is 86.659042. So, the difference in standard deviation of this implementation is 0.1938.

11.8 Noise Analysis Image noise is random (not present in the object imaged) variation of brightness or color information in images and is usually an aspect of electronic noise. It can be

11.8 Noise Analysis

305

produced by the sensor and circuitry of a scanner or digital camera. Image noise can also originate in film grain and in the unavoidable shot noise of an ideal photon detector. Image noise is an undesirable by-product of image capture that adds spurious and extraneous information.

11.9 NIST Statistical Test and Analysis National Institute of Standards and Technology (NIST) has suggested fifteen test metrics for accessing various approaches for analysis and authentication. These are based on the following needs and requirements. 1. Needs of Statistical Test • Selecting and testing random and pseudorandom number generators. The outputs of such generators may be used in many cryptographic and steganographic applications, such as the generation of key and input secret stream. • Generators suitable for use in steganographic and authentication applications may need to meet stronger requirements than for other applications. The outputs must be unpredictable in the absence of knowledge of the inputs. • These tests may be useful as a first step in determining whether or not a generator is suitable for steganographic and authentication application. 2. Randomness • A random bit generator using pseudo random equations having a near equal probability of ½ of producing a “0” or “1.” • Rudiments of the sequence are generated independently of each other, and the value of the next bit in the sequence should not be foretold, regardless of how many bits are generated. 3. Unpredictability • In the case of PRNGs, if the seed is unknown, the next output number in the sequence should be unpredictable in spite of any knowledge of previous random numbers in the sequence. This property is known as forward unpredictability. • It is not feasible to determine the seed from knowledge of any generated values. • No correlation between a seed and any value generated from that seed should be evident. • To ensure forward unpredictability, care must be taken in obtaining seeds. Also seed optimization is another potential area based on which generation of random numbers are generated.

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4. Random Number Generators (RNGs) • Random number generator equations uses a nonlinear equation for better generation with proper randomness. • Testing methodologies are used to test true randomness of the generated sequence. Name of such tests are Monobit test, Serial test and Poket test etc. In Chap. 10, these are discussed in details. 5. Pseudorandom Number Generators (PRNGs) Pseudorandom numbers generator equations are also used to generate random numbers. Single or multiple seeds are used to generate such number. The generated pseudo random sequence produced by random number generator is to be tested using various parametric tests to conform its true randomness. 6. Testing The testing of generated random numbers is performed using various parametric tests like Monobit test, Serial test, Pocket test, etc., to ensure true randomness of the generated sequence in terms of uniformity, scalability and consistencies. The uniformity means at any subsequence position true randomness must be observed. Scalability means that mined subsequence must be random. Consistency means that single seed will produce consistent stream of binary random numbers. 7. Random Number Generation Tests The NIST test suite consists of 15 tests. All tests are based on statistical measures. Any sequence generated from hardware or software generator is applicable for these fifteen tests. All of these measures are to ensure true randomness whether satisfied or not. A total of fifteen statistical tests recommended in the NIST test suite are discussed to evaluate randomness of the techniques proposed in different chapters. These tests focused on a variety of different types of non-randomness could exist in various techniques. Some tests are decomposable into a variety of subtests. The fifteen tests are outlined for the implementation of the techniques to test the satisfiability conditions. These are: 1. 2. 3. 4. 5. 6. 7. 8.

The frequency (Monobit) test The test for frequency within a block The runs test The longest run of ones in a block The binary matrix rank test The discrete Fourier transform test The non-overlapping template matching test The overlapping (periodic) template matching test

11.9 NIST Statistical Test and Analysis

9. 10. 11. 12. 13. 14. 15.

307

Maurer’s “Universal Statistical” test The linear complexity test The Serial test The approximate entropy test The cumulative sums (Cusums) test The random excursions test The random excursions variant test.

For analysis of the statistical test, a large number of samples of bit sequences are considered. For m, samples of bit sequences obtained from the key of a technique are tested by producing one P-value, and a statistical threshold value is defined using Eq. 11.16.  Threshold value = (1 − α) − 3

α × (1 − α) m

 (11.16)

In frequency (Monobits) test, frequency within a block test, runs test, longest run of ones in a block test, binary matrix rank test, discrete Fourier transom test, non-overlapping (aperiodic) template matching test, overlapping (periodic) template matching test, Maurer’s universal statistical test, linear complexity test, approximate entropy test, the value of significance level (α) = 0.01, the size of m is greater than inverse of α. If m = 300, the threshold value = 0.972766. This means that such a test is considered statistically successful, if at least 292 sequences out of the given 300 sequences do pass the test. For a Serial test and cumulative sums test producing n P-values, for the calculation of threshold value, one should consider (m × n) instead of m. With same values of α and m, the threshold value is 0.977814 and such a test is considered statistically successful if at least 294 sequences out of the given 300 sequences do pass the test. Random excursions test produces n P-values, and for the calculation of threshold value, one should consider (m × n) instead of m. With same values of α and m, the threshold value is 0.983907 and such a test is considered statistically successful if at least 296 sequences out of the given 300 sequences do pass the test. Random excursions variant test producing n P-values, for the calculation of threshold value, one should consider (m × n) instead of m. With same values of α and m, the threshold value is 0.985938 and such a test is considered statistically successful if at least 297 sequences out of the given 300 sequences do pass the test. A methodology has been stipulated in NIST document to calculate the P-value of P-values, where it is stated that P-values for a particular test can be considered uniformly distributed if its P-value of P-values ≥ 0.0001.

11.9.1 Frequency (Monobits) Test We have already discussed this test in Chap. 10. The objective of this test is to determine whether number of zeros and ones are proportionately equal or near equal within the whole generated binary stream.

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11 Metrics of Evaluation for Steganography and Authentication

11.9.2 Test for Frequency Within a Block In this test, the generated bit stream is divided into K non-overlapping blocks each of size l. If the proportion of 0 in each block of size l is approximately equal to 1/2, the block can be treated as random.

11.9.3 Runs Test The prime objective of this test is to determine the status of zeros and ones in a generated stream of bits of length l. The objective of this run test is to determine whether the number of runs of one or zero of variable length is as expected for a random stream.

11.9.4 Longest Run of Ones in a Block The length of longest run of 1s within a sequence should be consistent and should be at per what should be in a random sequence. This longest run of 1s in a block is to be tested whether the same satisfies the condition of a random sequence.

11.9.5 Binary Matrix Rank Test This test conforms the linear dependencies between fixed length substreams in the generated source binary sequence. There is a critical value for satisfying the condition above which the test is satisfied.

11.9.6 Discrete Fourier Transform Test The discrete Fourier transform test determines the periodic features of pattern in the original binary sequence generated through random number generator. There is a critical value for satisfying the threshold condition of this periodicity above which it passes otherwise failed.

11.9 NIST Statistical Test and Analysis

309

11.9.7 Non-overlapping (Aperiodic) Template Matching Test This test is to detect the existence of very large number nonperiodic patterns. During scanning the binary sequence, when this type of nonperiodic pattern is obtained the pointer of the window relocated to the immediately next bit after this nonperiodic pattern and search continues for rest of the string. In this case also a threshold is there below which the test fails.

11.9.8 Overlapping (Periodic) Template Matching Test In this test, predefined target substring of a finite (given) length from generated binary string is taken. The technique will find the number of such substring within the binary sequence. If the obtained number does not match with the expected number, the test fails. There is a predefined threshold above which the test is successful.

11.9.9 Maurer’s “Universal Statistical” Test This is a statistical test. This test conforms the possibility of compressing the sequence notably without loss of information. That means, whether lossless compression can be achieved from the generated binary sequence. The expected proportion to satisfy the test is to exceed a given threshold. If the computed value exceeds the expected threshold, then the test is successful.

11.9.10 Linear Complexity Test The linear complexity test is characterized by a long feedback register. A short feedback register does not conform the randomness of the binary sequence generated from the random number generator. On the other hand, if the characteristics of a long feedback register is found to be satisfied from the generated random binary sequence, then the randomness of the binary sequence is satisfied. Here, also a threshold value is used. If the computed value exceeds the threshold value, then the test is successful.

11.9.11 Serial Test Monobit test computes the number of occurrences of single bit substream within a generated random number sequence computed by random number generator, but

310

11 Metrics of Evaluation for Steganography and Authentication

serial test considers a substream of two bit overlapping substream (00,01,10,11,0,1). So, the computation is done on occurrences of 2k k-bit overlapping substreams. The expected proportion has a threshold. If computed value exceeds this threshold, then the test is successful. Serial test is discussed in Chap. 10 elaborately.

11.9.12 Approximate Entropy Test The approximate entropy test computes the occurrences of each and every overlapping k-bit pattern. The prime objective is to compare the occurrence of two consecutive blocks of length k and k + 1. There is an expected value as threshold. If computed value supersits the expected threshold, then the test is successful.

11.9.13 Cumulative Sums Test In this tests the cumulative sum of the partial sequence is computed. This cumulative sum is called as random walk. For a random sequence, the cumulative sum should be near equal to zero. If it is so, then this test is successful.

11.9.14 Random Excursions Test This test finds out whether deviation occurs to a particular state within a cycle from the expected value for a random walk. The cumulative sum of random walk is computed from partial sum. If the observed value of the sum exceeds the expected value, then the test is a success.

11.9.15 Random Excursions Variant Test This test computes the total number of times a particular state occurs and hence detects the perturbation of the number from the expected number in the random walk. A computation methodology is followed to compute partial sums of substreams of variable lengths. If deviation of observed value exceeds the expected value, the test is successful.

Chapter 12

Analysis and Comparisons of Performances on Different Transform Encoding Techniques

This book contains fourteen chapters. Chapter 1 of the book consists of introductory discussion on Cryptography and Steganography. State of the art regarding transform encoding for reversible steganography and authentication are discussed in Chap. 2. Brief historical background along with some literatures is surveyed in recent past up to 2019. Emphasis has been given on last few years’ literatures. Though the book is on transform domain-based steganography and authentication, still in Chap. 3, various spatial domain steganographic approaches are discussed. This chapter started with a brief history of ancient steganography in Greece era followed by characteristics of steganographic approaches in the spatial and spectral domain including audio and video steganography along with algorithm and implementation details. Audio steganography in transform domain has also been addressed in this chapter in details with algorithm and implementations. LSB and hash-based embedding and authentication including implementation aspects are embodied here with detailed results. Genetic algorithm-based color image authentication technique in spatial domain has been given in detail. Algorithm for insertion and extraction with detailed steps of genetic process are discussed in detail. Implementation of the technique on 20 benchmark images are given in detail with analysis of PSNR, MSE and IF. From the implementation, it is seen that 256 × 256 secret images are embedded into the 512 × 512 cover images with a payload of 4 bpB. The minimum PSNR achieved in this technique is 35 and that of maximum is 38, and minimum IF achieved is 0.9997 and maximum is 0.9998. Comparisons of the technique with the existing technique have also been discussed. The technique of algorithmic implementation has also been done. Some glimpse of dual image steganographic approaches along with one implementation is given in this chapter. The discrete Fourier transform-based Steganography is used for reversible computation, embedding and authentication in Chap. 4. The generation of DFT is complex one. Reversibility computation process is very complex because it generates imaginary components in addition to real components at the spectral domain which is very difficult to handle particularly in terms of embedding and adjustment. To avoid this complex computation, the images are subdivided into subblocks of m × n where © Springer Nature Singapore Pte Ltd. 2020 J. K. Mandal, Reversible Steganography and Authentication via Transform Encoding, Studies in Computational Intelligence 901, https://doi.org/10.1007/978-981-15-4397-5_12

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m and n may vary from 1 to 3. But, in this book, we have used 2 × 2 subimage block to transform, embed and to generate inverse transform for generating stego. image. During decoding and authentication, forward transform is done again at the destination and secret bits/images are extracted. The process is repeated in row major order for the entire image. This simplified computation generates only real frequency components. In DFT-based reversible computations, both for 1D and 2D, a 2 × 2 submatrix is taken for all cases. Detailed examples for reversible computation are given in deals with associated algorithms for embedding and decoding. Implementation results are also posted for 10 benchmark images with computations of MSE and PSNR for the payload of 0.75 bpB. Histogram analysis has also been done in this chapter. Various applications of DFT have been outlined at the end of this chapter. Discrete cosine transformation-based reversible encoding has been given in Chap. 5. In this chapter, 1D, 2D, 3D DCT and IDCT computations are incorporated to show the reversibility properties. Detailed embedding and extraction procedures are fabricated in details in this chapter. Detailed calculations are done using 2 × 2 subimage matrix in row major order. Numerical examples for reversible computations for 1D, 2D and 3D are done using linear array for one dimension, 2 x 2 sub images and 2 x 2 x 2 sub images for 2D and 3D respectively. Implementation of a complete steganographic scheme based on 2D DCT is given with embedding and encoding algorithms. Implementation on benchmark images with cover image of size 512 × 512 and secret image of 64 × 64 is given. Application of DCT is given at the end of this chapter. Wavelet-based reversible transform encoding is given in Chap. 6. Mallet-based two-dimensional wavelet transformation is used for the detailed formulations. Information flow analysis for authentication process along with multilevel wavelet transform computation for reversibility is done here. Detailed computations with examples are shown stepwise. 2D Haar wavelet transformation is also done here with an example. A technique for image authentication using Haar wavelet transform is done with 2 × 2 subimage blocks. The implementation is done on ten benchmark images. The MSE, IF and PSNR values are computed for all ten images for payload of 3 bpB. The process of optimization is done on embedded images using genetic algorithm. Application of wavelet transform in authentication process is given at end. Z-transform-based reversible encoding is done in Chap. 7. This chapter starts with the basics of Z-transformation and conversion of Laplace transform to Zdomain. 1D and 2D Z-transform pair have been formulated with 2 × 2 sizes of sub image matrix. Example of forward and reverse computations is done with numerical examples. Detailed reversibility computations are done with different values of region of convergence (ROC). Here, all reversible computations are done for onedimensional and two-dimensional Z-transform using r = 1, 2, 3, 4 and 5. Numerical computations are done for reversibility taking one-dimensional Z-transformations. Embedding and extraction process along with tuning in Z-transform domain is also given in details. Embedding, tuning and extraction process is in imaginary parts of Z-transform domain. Two bits are embedded in each of the conjugate pair of the imaginary components. The results of implementations are given for ten benchmark images in terms of PSNR, MSE and IF where achievement of PSNR is more than 40

12 Analysis and Comparisons of Performances …

313

and IF is more than 0.99990. The application of Z-transform-based embedding and authentication is also given at the end. Chapter 8 deals with reversible transform encoding via discrete binomial transformation. In this transformation, 2 × 2 subimages are taken for reversible computations. An algorithm has also been given for embedding and authentication. In this technique, the embedding density is 1.5 bpB. Sixteen benchmark images are taken to implement the algorithm. The PSNR for this embedding technique is achieved between 36.3163 to 42.0294 dB. Applications of this technique are also given at the end. Reversible transform encoding using Grouplet (G-Let) transform is given in Chap. 9. Starting from the principles of dihedral group and its symmetric properties, the reversible computations using reflection and rotation operations for various G-Let are given in this chapter extensively. The reversible computations using D3 to D10 are given extensively with numerical examples. Implementation of G-Let D3 to D10 on images are given extensively will all G-Let component computations in terms of reflection and rotation operations. Reversible computations for transform domain to pixel domain are also given extensively for all G-Let. A complete steganographic technique using G-Let D3 transform computation is given in this chapter. The embedding density of 0.5 bpB is achieved in this technique using G-Let D3 transform computations. Chapter 10 gives a comprehensive detail of nonlinear dynamics in transform encoding-based authentication. In this chapter, discrete chaotic equations and its characteristics are discussed. Generation of pseudorandom numbers for the discrete chaotic equation is also given here. Testability for randomness is also given here in terms of Monobit, Serial and Poker test. System for different chaotic maps is used with the generation of PN sequence and encryption of images. The analysis of sensitivity maps is also given with detailed implementations. A GA-based chaos for optimised system parameter generation is also given. In Chap. 11 various metrics of evaluating various techniques are given in details. Fifteen tests of NIST test suit is also discussed in this chapter.

Chapter 13

Conclusions

This book is on reversible Steganography and authentication via transform encoding. The prime focus of the book is to present a computability and reversibility of transform equation and to avoid imaginary components of the transform computations. Reversibility computations of transformation techniques are done here, namely DFT, DCT, wavelets, Z-transform, Binomial and Grouplet. The chaos-based authentication pseudorandom number sequence generations and image or message encryptions are also done. In general, the book focuses on the real part of the transform computations for embedding and extraction, but in cases of Z-transform, complex conjugate part is also used for embedding and authentication. In this book, transform computations of all the transformations are done using 2 × 2 subimage blocks. The process is repeated in row major order for entire image. All computations are primarily on images. Detailed algorithms for encryption and description in all techniques are given extensively. The technique of embedding for all transform-based Steganographic process is embodied in details for all transformations. Adjustment of pixel values after embedding is also done for all techniques. Numerical examples of reversible computations are given for all transform computations. In case of chaos-based authentication, the quality of generator is also tested using Monobit, Serial and Poker test. NIST recommended fifteen test cases are also outlined in Chap. 11 where discussions on all 15 tests are done. Various metrics of image processing systems are also given in the chapter in detail.

© Springer Nature Singapore Pte Ltd. 2020 J. K. Mandal, Reversible Steganography and Authentication via Transform Encoding, Studies in Computational Intelligence 901, https://doi.org/10.1007/978-981-15-4397-5_13

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Chapter 14

Future Directions

The consideration of the book is to give a comprehensive reversible computation, embedding, extraction and authentication of information based on transform domain computations. This book contains transform encoding-based image authentication systems in detail. Six transformation techniques are given here in terms of reversible computations, embedding, extractions and authentication along with testability metrics. For the entire computations of this book, we have subdivided the image matrix in 2 × 2. This book did not consider other subimage size like 1 × 1, 1 × 2, 3 × 3, 4 × 4, etc. Particularly, to avoid generation of imaginary components in transform domain for higher window size of subimages. Only in case of Z transformation, transformation computations, embedding, extraction are done in complex conjugate pair with a complete encoding scheme. The book did not consider Lendre transform, Hartley transform, Sine transform and other variations of wavelets transformations which are the future scope of this book.

© Springer Nature Singapore Pte Ltd. 2020 J. K. Mandal, Reversible Steganography and Authentication via Transform Encoding, Studies in Computational Intelligence 901, https://doi.org/10.1007/978-981-15-4397-5_14

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