International Journal of Engineering Practical Research IJEPR Volume 1, Issue 1, August 2012 PP. 21-25 IJEPR Volume 1, Issue 1 August 2012 PP. 21-25 © Science and Engineering Publishing Company - 21 - Use of Complex Discrete Signals for Steganographic Information Security Alexandr Kuznetsov, Alexey Smirnov Kozhedub Air Force University, Kharkov, Ukraine Department of Software, Kirovohrad National Technical University, Kirovohrad, Ukraine kuznetsov_alex@rambler.ru, assa_s@mail.ru (Abstract) The steganographic methods of information embedding in stable images for the secure transfer of information are investigated. The method of steganographic security based on the use of complex discrete signals and technology of direct expansion of spectrum is examined, its efficiency is probed from point of the provided security, carrier capacity and amount of introduced distortions in a container-image. Keywords: Container-image; Steganography; Noise-immunity; Erroneous Extraction. 1. RAISING THE PROBLEM IN A GENERAL VIEW AND ANALYSIS OF LITERATURE Steganographic systems are an important direction in the development of modern facilities of information security. They secure from the opponent not only informative content of transferred information but the fact of passing the messages itself [1, 2]. Steganographic method based on the developed mathematical apparatus of discrete signals theory and noise-immune communication [3 - 21]. This research studies the steganographic method of information protection in stable images [2, 10-11, 20], based on the use of complex discrete signals and technology of direct expansion of a spectrum, estimation of its efficiency from the point of provided security, carrier capacity and amount of the insertion distortions in a container-image. 2. DIRECT EXPANSION OF SPECTRUM (DIRECT SEQUENCE) IN A COMMUNICATION THEORY The methods of discrete signals theory, cross-correlation and spectral analysis are utilized [3 – 5, 21] for the construction of modern noise-immune digital communication networks. Broadband systems with complex discrete signals and direct expansion of spectrum [3, 4] are considered to be the most perspective from the point of the effective use of frequency-time and energy resources of communication channels. We will consider an informative signal, which is a set of separate values taken at certain moments of time, as a discrete signal. We will further consider a complex discrete signal as a binary pseudorandom sequence (BPRS) ( ) 1 1 0 ,..., , − = Φ n i i i i ϕ ϕ ϕ of length of n from set { } 1 1 0 ,..., , − Φ Φ Φ = Φ M with power of M = Φ . The elements of binary BPRS take one of the following values:    − + = 1 1 z i ϕ , 1 ,..., 0 − = n z (1) For the construction of noise-immune broadband connection the concept of correlation of discrete signals to statistical relationship of two or a few BPRS is utilized. The mathematical measure of correlation (conformity) of two discrete signals Φ ∈ Φ Φ j i , is the coefficient of correlation ) , ( j i Φ Φ ρ [3, 4]: ( ) ∑ − = Φ Φ = Φ Φ 1 0 1 , n z z j z i j i n ρ (2) Two signals j i Φ Φ , are orthogonal, if coefficient of correlation 0 ) , ( = Φ Φ j i ρ . If 0 ) , ( ≈ Φ Φ j i ρ , we will name signals i Φ and j Φ quasi-orthogonal[5, 7]. In a modern digital communication theory the large assemblies of weak-correlated discrete signals are utilized for the construction of the wide-band noise-immune systems of data communication. Transferred messages in such channels acquire the appearance of noise-like sequences, and due to high power of assemblies of discrete signals and direct expansion of frequency spectrum, high authentication, noise-immunity and secrecy of the digital connection channels are provided [3 – 5]. For communication of data in a broadband communication network, informative signal: ()    − + = 1 1 t x , is modulated by means of multiplying by an extending code signal () Φ ∈ Φ = i t g – pseudorandom sequence of the assemblies of discrete signals which were considered earlier. As code signal due to its statistical properties is similar to noise, therefore the extended signal: () () () t e t y t y + = ' (3) is poorly distinguished from noises in a communication channel, which allows to carry out a hidden transmission.