The model for chaotic signal masking is proposed in the article. The digital signal in the bit representation is encoded using a family of orthogonal functions. Random white noise is superimposed on the resulting analog signal. The white noise amplitude is significantly greater than the amplitude of the signal. The functions orthogonal property is used to retrieve a useful signal. The advantage proposed this model is that it is not necessary to match the noise generators in the source and in the receiver of the message. The integration operation is required to retrieve the message. The using a simple rectangle scheme is discussed. The comparative computer experiment is based on two families of orthogonal functions: simple trigonometric functions and orthogonal Lagrange polynomials. It has been shown that using the trigonometric function family results in fewer errors when retrieving a message.

1. Downes P.T. Secure communication using chaotic synchronization. Proceed-ings of SPIE, 1993, vol. 2038, pp. 227–234. 2. Perez G., Cerderia H.A. Extracting messages masked by chaos. Physical Re-view Letters, 1995, vol. 74, pp. 1970–1973. 3. Short K.M. Unmasking a modulated chaotic communication scheme. Inter-national Journal of Bifurcation and Chaos, 1996, vol. 6, no. 2, pp. 367–375. 4. Ponomarenko V.I., Prokhorov M.D. Extracting information masked by the chaotic signal of a time-delay system. Physical review. E, Statistical, Nonlinear, and Soft Matter Physics, 2002, vol. 66, p. 026215. 5. Kolumban G., Vizvari G.K., Schwarz W., Abel A. Differential chaos shift keying: a robust coding for chaos communication. Proceedings International Workshop on Non-linear Dynamics of Electronic Systems (NDES’96), Sevilla, Spain, 1996, pp. 92–97. 6. Galias Z., Maggio G.M. Quadrature chaos-shift keying: theory and perfor-mance analysis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2001, vol. 48, no. 12, pp. 1510–1519. 7. Kaddoum G. Design and performance analysis of a multiuser OFDM based differential chaos shift keying communication system. IEEE Transactions on Com-munications, 2016, vol. 64, no. 1, pp. 249–260. 8. Yang H., Tang W.K.S., Chen G. System design and performance analysis of orthogonal multi-level differential chaos shift keying modulation scheme. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2016, vol. 63, no. 1, pp. 146–156. 9. Wren T.J., Yang T.C. Orthogonal chaotic vector shift keying in digital com-munications. IET Communications, 2010, vol. 4, no. 6, pp. 739–753. 10. Wang L., Cai G., Chen G. Design and performance analysis of a new multi-resolution M-ary differential chaos shift keying communication system. // IEEE Transaction on Wireless Communications. – 2015. - Vol. 14, N 9. - P. 5197–5208. 11. Kaddoum G., Soujeri E., Arcila C., Eshteiwi K. I-DCSK: An improved noncoherent communication system architecture. IEEE Transactions on Circuits and Systems II: Express Briefs, 2015, vol. 62, no. 9, pp. 901–905. 12. Xu W.K., Wang L., Kolumban G. A novel differential chaos shift keying modulation scheme. International Journal of Bifurcation and Chaos, 2011, vol. 21, no. 3, pp. 799–814. 13. Huang T., Wang L., Xu W., Lau F.C. A multilevel code-shifted differential chaos-shift-keying system. IET Communications, 2016, vol. 10, no. 10, pp. 1189–1195. 14. Escribano F.J., Kaddoum G., Wagemakers A., Giard P. Design of a new differential chaos-shift-keying system for continuous mobility. IEEE Transactions on Communications, 2016, vol. 64, no. 5, pp. 2066–2078.