International Journal Of Computational Engineering Research (<strong>ijcer</strong>online.com) Vol. 2 Issue. 8[22] Lu G. M., Wang K. Q. and Zhang, D., ―Wavelet based independent component analysis for palmprint identification‖,Proceedings of 2004 International Conference on Machine Learning and Cybernetics, Vol 6, 26-29 August 2004,Shanghai, China, Pages 3547-3550.[23] Rafael D. M., Travieso, C. M., Alonso, J. B. and Ferrer, M. A., ―Biometric system based in the feature of hand palm‖,38th Annual 2004 International Carnahan Conference on Security Technology, 11-14 October 2004, Albuquerque,New Mexico, United States of America, Pages 136-139.[24] Struc V and N. Pavesic, ―Phase Congruency features for palmprint verification‖, IET Signal Processing, Vol. 3, Issue4, 2008, Pages 258-268.[25] Tantachun, S., Pintavirooj, C., Lertprasart P. and Bunluechokchai S., ―Biometrics with Eigen -Hand‖, 1st IEEEConference on Industrial Electronics and Applications 2006, 23 – 26 May 2006, Singapore, Pages 1-4.[26] Tao J. W., Jiang W., Gao Z., Chen S. and Wang C., ―Palmprint Recognition Based on 2-Dimension PCA‖, FirstInternational Conference on Innovative Computing, Information and Control 2006, ICICIC ‗06, Vol 1, 30-01 August2006, Beijing, China, Pages 326-330.[27] Wang M. and Ruan Q. Q., ―Palmprint Recognition Based on Two-Dimensional Methods‖, The 8th InternationalConference on Signal Processing, Vol 4, 16-20 November 2006, Guilin, China.[28] Wei X. Y., Xu D. and Ngo C. W., ―Multi-biometrics based on palmprint and hand geometry‖, Proceeding of theFourth Annual ACIS International Conference on Computer and Information Science 2005, Jeju Island, South Korea,Pages 495–500.[29] Wong K. Y. E., G. Sainarayanan and Ali Chekima, ―Palmprint Identification Using SobelCode‖ Malaysia-JapanInternational Symposium on Advanced Technology 2007, 12-15 November 2007, Kuala Lumpur, Malaysia.[30] Wong, M., Zhang, D., Kong, W. K. and Lu, G., ―Real-time palmprint acquisition system design‖, IEE Proceedings -Vision, Image and Signal Processing, Vol 152, Issue 5, 7 October 2005, Pages 527-534.[31] Wu X. Q., Wang K. Q. and Zhang D., ―Wavelet based palm print recognition‖, Proceedings of InternationalConference on Machine Learning and Cybernetics 2002, Vol 3, 4-5 November 2002, Beijing, China, Pages 1253-1257.[32] Wu X. Q., Wang K. Q. and Zhang D., ―Wavelet Energy Feature Extraction and Matching for Palmprint Recognition‖,Journal of Computer Science and Technology, Vol 20, No. 3, May 2005, Pages 411-418.[33] Wu X. Q., Zhang D., Wang K. Q. and Huang B., ―Palmprint Classification Using Principal Line‖, Pattern Recognition,Vol 37, Issue 10, October 2004, Pages 1987-1998.[34] Xiangqian Wu, Kuan-Quan Wang, David Zhang ―Palmprint Recognition Using Fisher's Linear Discriminant ‖Proceedings of the Second International Conference on Machine Learning and Cybernatics, Vol. 5, 2-5 November2003, Pages 3150-3154.[35] Xiao-Yuan Jing and David Zhang, ―A Face and Palmprint Recognition Approach Based on Discriminant DCT FeatureExtraction‖, IEEE Transactions On Systems, Man, And Cybernetics —Part B: Cybernetics, Vol. 34, issue 6, June 2004,Pages 2405-2415.Issn <strong>2250</strong>-<strong>3005</strong>(online) December| 2012 Page 89
International Journal Of Computational Engineering Research (<strong>ijcer</strong>online.com) Vol. 2 Issue. 8Block Diagram and Formal Mathematical Definition of SteganographicSystemAlexey SmirnovAssociate Professor in the Department of Software, Kirovohrad National Technical University, Kirovohrad, UkraineAbstractThis paper studies a formal mathematical description and the block diagram of the secret system and, by analogy withthe theory of secret systems, introduces the basic elements and mathematical operators, abstractly d escribing steganographicinformation protection system.Keywords: secret systems, steganographic system, formal mathematical definition1. IntroductionMathematical foundations of modern cryptography are laid by the famous American scientist C. Shannon [1-3], who,for the first time, using information-theoretic approach, introduced abstract mathematical definition of a secret system andformalized the procedures for data cryptographic transformation of data. These studies gave a significant boost to thedevelopment of the individual methods of the theory of information security, crypt ography and authentication, digitalsteganography, and digital signal processing techniques and error-correcting coding [4-12].This paper studies a formal mathematical description (in terms of C. Shannon) and the block diagram of the s ecretsystem and, by analogy with the theory of secret systems, introduces the basic elements and mathematical operators, abstractlydescribing steganographic information protection system.2. Block diagram and a formal mathematical definition of cryptographic (secret) systemAbstract secret system is defined as some set of mappings from one space (the set of possible messages) to a differentspace (the set of possible cryptograms) [1-3].Let’s fix a set of possible messages M = {M 1 , M 2 , …, M m } and a set of cryptograms E = {E 1 , E 2 , …, E n }. We will alsofix a set of mappings: = { 1 , 2 , …, k },where: i : M E, i = 1, 2 , …, k.If the sets M and E are equivalent, i.e., n = m, then there is an inverse mapping -1 i : E M, which assigns each-1element of the set E to an element of M. Obviously, i and i are given reciprocally the same mapping of the sets M and E.Let’s now fix a set of keys К = {К 1 , К 2 , …, К k }, so that for all i = 1, 2 , …, k mapping i is uniquely specified bythe key K i , that is:Ki : M E .iEach specific mapping of i from the set corresponds to the way of encryption with a specific key K i .Let’s fix a set of keys К * = {К 1 * , К 2 * , …, К k * }, in general to К К * . All the elements of the inverse mappings: -1 = { 1 -1 , 2 -1 , …, k -1 }are given the appropriate key:1iK * i : E M .Each specific mapping -1 i of the set -1 corresponds to the way of decryption using the key K * i . If the key K * i isknown, then the only one answer is possible as the result of decryption – an element of the set M.Thus, an abstract definition of a secret system includes the following sets of M, E, , -1 , К and К * (the sets of opentexts and cryptograms, sets of direct and inverse mappings, sets of keys). If, in addition, К К * , then the system isasymmetric. On the contrary, if К = К * – the system is symmetric. Fig. 1 represents a block diagram of a s ecret system.Issn <strong>2250</strong>-<strong>3005</strong>(online) December| 2012 Page 90
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