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Steganography - A review Lidan Miao 11/03/03

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Outline History Motivation Application System model Steganographic methods Steganalysis Evaluation and benchmarking Adaptive stegangraphy

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History Prisoner’s Problem － Simmons, 1984 From “Techniques for Steganography and Digital Watermarking.” S. Katzenbeisser and F. A. P. Petitcolas

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Motivation Multimedia data Rapid growth of Internet Publishing and broadcasting industry Government’s restriction

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Application Copyright protection Authentication Access control Covert communication

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Terminology Cryptography Scramble message to make it meaningless. Classic steganography Hide the existence of communication. Watermarking Robust data hiding, all the instances are marked in the same way. Fingerprinting All the instances are marked in different way to trace unlawful provision.

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System model

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System requirement Imperceptibility Modification is invisible (HVS). Undetectability Statistical model is consistent. Capacity How many bits can be embedded in a given medium.

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Steganographic techniques LSB Insertion Spread Spectrum Transform domain Other techniques Odd-even embedding Geometric transform Image mosaic

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Common idea Partition image into blocks and embed certain mount of message in each block. Important issues: (1) Features are different in each block (2) Size of block (3) Capacity in each block (4) Distribution of message

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A1: Image segmentation The algorithm divides a binary image into noise like region and signal region. If a region is too simple to hide information, a conjugate operation is introduce, which can convert a simple pattern into a complex pattern without lose any shape information.

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A1: Image segmentation-cont’ Complexity measure m: the size of blocks

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A1: Image segmentation-cont’ Conjugate operation Original Result Object Background Checkboard

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A2: ME steganography The algorithm takes advantage of local characteristics of a cover-image to embed maximal amount of message in the cover and maintain the imperceptible alteration.

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A2: ME steganography-cont’s To replace the least k-LSBs, the maximum error is. Adjust the k+1 bit, and check its embedding error. The maximum-error can be restricted to. Origin Embedded k=2

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A3: Convert UEC to EEC The distribution of embeddable pixels vary from block to block. Shuffling is applied, which redistribute the values between all subsets to produce at least one bit in each region is embeddable. Embedding is performed in the shuffling domain and inverse shuffling is performed to get a marked image.

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A4: Weighted matrix Embed r bits of data into image block by changing at most 2 bits. The goal is to modify into to ensure the following invariant : is the secret message. W is the weighted matrix, k is the secret key.

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A4: Weighted matrix-cont’ Secret data : , and r=3 SUM1 = 24 (mod 8) = 0 SUM2 = 36 (mod 8) = 4

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A4: Weighted matrix-cont’ This algorithm can hide as many as bits of data in the image by changing at most 2 bits in the image block. This scheme can provide higher security, embed more data, and maintain higher quality of the host image.

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A5: Image Mosaic The sender and the receiver share the same image database. Each tile image corresponds to an integer. Embedding algorithm chose different tile image according to secret message. The Receiver extract message from tile images.

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A5: Image Mosaic-cont’

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A6: Histogram preserve This algorithm based on histogram preserving data mappings (HPDM). Cachin defined a system is perfectly secure when the statistics of the stego-image and the cover image are identical, i.e., the relative entropy between the cover and stego is zero. Based on this definition, Eggers proposed his algorithm that preserves the histogram of the cover image.

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Steganalysis The art of detecting and decoding hidden message within a given object. A steganographic system is considered broken if an attacker can guess whether or not a given image contains secret message with a success rate better than random guessing.

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Steganalysis Visual attack (color images) The idea is to remove all parts of the image covering the message. Statistical attack Embedding process change the statistical characteristics of images.

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Visual attack (EzStego )

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Visual attack(S-Tools)

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Visual attack(Steganos)

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A1: PoVs analysis(LSB) Those pixels only differ in LSB are called pairs of values (PoVs). (for example: 2 and 3) LSB embedding causes the frequency of individual elements of a PoV to flatten out with respect to one another. LSB embedding can only be reliably detected when the message length becomes comparable with the number of pixels in the image.

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A2: Hypothesis testing (LSB) The image is partitioned into 3 subsets. The pixel value in stego-image is expressed: The goal is to find if the first two subsets are non- empty. Formulated as the following multiple hypothesis testing problem:

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A3: RS steganalysis (LSB) LSB flipping: Shifted LSB flipping: No flipping: Discrimination function f :

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RS steganalysis-cont’ Three types of pixel groups: R, S, and U M : an n-tuple mask with values –1, 0, 1.

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RS steganalysis-cont’ Before embedding After embedding The difference between and increase, while the difference between and goes to zero when 50% pixels are embedded.

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RS steganalysis-cont’ Step1: Calculate the number of R, S. Step2: Flip LSB of all pixels and repeat step1. Step3: Randomly flip LSB and get the mean. Step4: Fit line and quadratic function and estimate p.

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A4: Sample pair analysis Sample pair: (u, u+n) or (u+n, u), which means the two values differ by n. The algorithm can estimate the length of hidden messages with high precision. The image is partitioned into 4 subsets, and LSB embedding affects the transmission between these subsets.

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Sample pair analysis-cont’ The finite-state machine is closer, but the subsets are not under LSB embedding.

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A5: Universal blind analysis This algorithm is based on high statistical model. Extract feature vectors based on multiple-scale decomposition. (1) Coefficients statistics (2) Error statistics Classify cover image from stego-image by means of their feature vectors.

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Comparison Those methods targeted to a specific steganographic method, such as RS steganalysis, will most likely give more accurate and reliable results than any universal blind steganalytic method. However, universal blind approaches are very important because of their flexibility and ability to be quickly adjusted to new or completely unknown steganalytic methods.

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Evaluation and benchmarking This is an important and often neglected issue. Some author proposed fair evaluation methods for image watermarking systems. Three points need to be commented. (1) Visual quality metrics (2) Statistic test (3) Capacity comparison

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Some thoughts on adaptive steganography Adaptively chose embedding regions. Adaptively determine embedding capacity. Process stego-image to mask hidden message and avoid detection.

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