Spline-wavelet robust code under non-uniform codeword distribution

Robust codes are new nonlinear systematic error detecting codes that provide uniform protection against all errors, whereas classical linear error-detection code detects only a certain class of errors. Therefore, defence by the linear codes can be ineffective in many channels and environments, when error distribution is unknown. This drawback makes the linear codes vulnerable to side channel attacks. In turn, resistance of the robust code to side channel attacks can deteriorate if codeword distribution is non-uniform. The probability of error masking can increase depending on codeword distribution. However, mapping the most probable codewords to a predefined set can reduce the maximum of the error masking distribution, thus preventing attackers from using this vulnerability. In this paper, we propose a general approach to the algorithm construction of spline-wavelet decompositions of linear space over an arbitrary field. This approach is based on the generalization of calibration relations and functional systems, which are biorthogonal to basic systems of relevant space. The obtained results permit the construction of spline-wavelet robust code. The algorithm proposed in this paper is based on the second-order wavelet decomposition of B-splines under non-uniform nets. The encoding function of the obtained code construction was investigated. In this article, we prove that this encoding function is a bent-function. We also provide a proof that the proposed spline-wavelet robust code is optimal. This paper explores the characteristics of the code in the case of non-uniform codeword distribution.