Method of Applying (t,n)-Threshold Scheme in Steganography Anton N. Mironenko, Mikhail D. Velichko Computer Sciences Faculty Dostoevsky Omsk State University Omsk, Russia MironenkoAN@omsu.ru; mihailvelichko23@gmail.com Abstract—This work is devoted to the development of the rows and columns. It is shown that this steganography system method of information concealment, in the raster image using retains its resistance to passive stegoanalytic attacks with block steganography together with cryptography the solving the overlapping up to 24x24 pixels and at this overlap value is problem of recovering a message if the image which contains more stable than the standard and improved steganography hidden data is damaged. It proposes a method of implementing method based on direct spreading of the spectrum. the steganography for insert data on digital image not in its entirety, but previously using (t, n)-threshold scheme and In the article [8] the author proposes a new steganography inserting each of the parts received independently. The software method based on the compression standard according to the was developed for approbation of the proposed method. A series Joint Photographic Expert Group and an Entropy Thresholding of experiments confirming the possibility of applying the technique. The algorithm uses a pair of keys: public and proposed method was carried out. Text information is inserted private, to generate a pseudo-random sequence that indicates into the raster image. Further, the image was subjected to where the secret information will be embedded. The insertion modification, simulates container damage when it was takes eventually place at the first seven AC coefficients in the transmitted through the communication channel or as a result of transformed DCT domain. Before the insertion of the message intentional actions of an intruder. As a result of the experiments, the image undergoes several transformations. After the it can be said about the possibility of applying the proposed insertion the inverse transformations are applied in reverse method. order to the original transformations. The insertion itself takes Keywords— cryptography; secret sharing; stegnographic inser; only place if an entropy threshold of the corresponding block is raster image; data concealing; increased reliability; LSB . satisfied and if the pseudorandom number indicates to do so. In steganography, the following problems can be I. INTRODUCTION distinguished: The issue of maintaining and ensuring the confidentiality of 1. detection of a steganography inserts (stegoanalysis); information is relevant. The software, allowing transferring data securely, is encrypted. If an open channel is used, a man in 2. reliability of information concealment during its the middle (MITM) attack is possible, and the attacker, if not transmission. able to decrypt the data, may violate their integrity. The The first problem is solved in [9]. solution to this problem can be the use of steganography, i.e. concealment of the fact of the transfer of classified The solution of the second problem is proposed in [10], in information. A lot of scientific works are devoted to this topic, this work studying focuses on integrating schemes like OFDM, for example [1-4]. CDMA and MC-CDMA with steganography and image encryption techniques to develop wireless systems with inbuilt The article [5] discusses the main trends in steganography. information security feature. The [6] paper introduces work on developing secure data In the article [11] the authors consider the method of communication system. It includes the usage of two unifying cryptography and steganography. Encryption is algorithms RSA and AES used for achieving cryptography performed on images with subsequent embedding of secret data along with LSB for achieving steganography both on Android platform. The joining of these three algorithms This work is also devoted to the problem of increasing the helps in building a secured communication system on reliability of information hiding when it is transmitted, i.e. the ‘Android’ platform which is capable of withstanding task of restoring information in case the image which contains multiple threats. hidden data is damaged (image-container). In [7] proposed steganography system of information Consider the possibility of combining the steganography protection on the basis of the proposed original algorithm for method and the (t, n)-threshold scheme. The analysis of embedding information with overlapping blocks of images in existing steganography algorithms and threshold schemes is carried out. 93 II. STATEMENT OF THE PROBLEM AND ITS SOLUTION secret data into some vectors with the length of m*n. For each We will analyze the existing methods of steganography and block, one Hamiltonian path is first found such that the LSB of find which one is most suitable. pixels of the block along this path have the maximum similarity to the corresponding vector of data. Then this part of Next, we will consider algorithms for embedding data is embedded into the first LSB of pixels of the block along information in the part of the original image. The advantage of the best path using the modified LSB matching and the code of these algorithms is that for implementation, you do not need to this path is embedded into the second LSB of the pixels using a perform complex linear transformations of the image. novel method such that the minimum MSE value between the Information will be introduced by manipulating the brightness block of the cover image and the block of the stego-image is or the color components of the image. achieved. 1. Kutter’s algorithm. After analyzing known methods of data concealment in raster images to achieve the goal and studying works [17-18], it In this algorithm, the information will be embedded in the was decided to use the LSB method, which was suitable for blue channel because the changes in this color are less visible describing the problem, since it splits the image into parts and to the human eye. A pseudo-random position is selected in the then records the information in them. image into which the information will be inserted and further into the blue channel. This information is introduced by We analyze the existing threshold schemes. modifying the brightness. 1. Shamir’s secret sharing scheme [19]. In work [12], the possibility of using the steganographic method Kutter-Jordan-Bossen allowing hiding the information Briefly, this algorithm can be described as follows. Let a of the video sequence is considered. In addition, the criterion finite field G be given. We fix n different non-zero non-secret for selecting a container image is proposed in the work. elements of this field. Each of these elements is assigned to a certain member of the group. Next, an arbitrary set of t 2. Langelaar’s algorithm. elements of the field G from which the polynomial f (x) is composed over the G field of degree t-1, 1