V. I. Korzhik, A. S. Ushmotkin, A. V. Razumov, G. A. Bespalov

Today copyright relations in computer networks are very important matter. Due to some technical features it6 is not simple to prove somebody-s rights on digital images in court. Besides, traitors use many ways to made it impossible. The main scheme observed in this paper is collusion attack, when violators collude in group to redistribute illegal copy. this work providel the method which helps to detect colluders through analysis of illegal copy of digital imge. The main idea is in using special digital watermark called fingerprints, which is embedded in digital images by its owner or legal distributor. In this article authors propose to use random superimposed codes (SIC), introduces by Ericson and Gyorfi, as sequences for collusion-resistant fingerprints. This approach seems to be more suitable in comparison with the use of some regular sequences (like WBE-sequences) against watermark removal attacks. there is represented the evaluation of the probability of erroneous colluder detection for randomly shosen SIC in its work. Then authors observe the sphere decoding algorithm (SDA) which is used for tracing traitors. There is represented SDA decision tree. Authors note 2 ways for embedding fingerpreints: in order of stegokey and in blocks of pixels in order of pseudo random sequence. Either of the advantage of the second method is "blind" decoder usage capability. The performance evaluation of the proposed methods is presented in the work. Simulation results show a good efficiency of the proposed codes. The conclusion of work underlines the improvement of collusion resistance using SIC sequences and SDA method.