Using of Polar Codes in Steganography

In this paper, we propose a new steganographic scheme based on the polar codes. The scheme works according to two steps. The first offers a stego vector from given cover vector and message. The stego vector provided by the first method can be the optimal; in this case, the insertion is successful with a very low complexity. Otherwise, we formalize our problem in a linear program form with initial solution the stego vector given by the first method, to converge to the optimal solution. Our scheme works with the case of a constant profile as well with any profile; it is then adapted to the case of wet paper. Tests on multiple gray scale images showed its good performance in terms of minimizing the embedding impact. I. INTRODUCTION Steganography is a technique that allows hiding information in an unsuspected medium (image, sound or video) so that it was undetectable. To reach this objective it is indispensable to use a technique in order to reduce the distortion induced by the hiding of the secret message. The matrix embedding technique introduced by Crandall (1) has allowed the definition of steganographic schemes that minimize the embedding impact. The first implementation was created with the work of Westfeld (2) in which the Hamming codes were used. Afterwards, Bose-Chaudhuri- Hocquenghem (BCH) codes (3), (4), Reed-Solomon codes (RS) (5) and Syndrome-Trellis-Codes (STC) (6) are used in steganography. Combination of LSB, matrix embedding and wet paper techniques allowed building more effective and more reliable steganographic schemes. Our works is a contribution to schemes of minimizing embedding impact. We propose in this paper a new steganographic scheme based on the polar codes. The scheme is applied to the cases of constant profile and of wet paper. We will consider, thought all the paper, the cover vector v made up of the LSBs of the cover image, the stego vector y, the changes vector e (y=v+e), the secret message m and the parity check matrix H of the polar code used. This paper is organized as following. Section II describes matrix embedding and minimizing embedding impact. In Section III, we study the linear programming. The polar codes, used to implement our scheme, are presented in Section IV. In Section V, we propose the scheme. Section VI shows the results obtained when the scheme is applied on images. Section VII concludes the paper.