In this paper the authors propose steganographic method of bitwise information hiding, which allows embedding information in vector images by splitting point-defined curves into segments. Due to the invariance property of the curves of this type (B-splines, NURB curves, Bezier curves, Hermite curves), the proposed method will provide resistance to active attacks based on affine transformations. On the basis of the proposed method and the properties of the Bezier curves, StegoBIT algorithm was realized. This algorithm allows to embed information in the Bezier curves of the third degree and provides resistance to active attacks based on affine transformations. An experimental study of the stability of proposed algorithm for affine transformations was carried out. 30 arbitrary SVG images were selected for the experiment. Their structural configuration contained parameters for constructing Bezier curves. The information of different sizes was hidden in the curves, by way of its gradual division into visually identical sets of segments. The affine transformations such as transfer, rotation, almost rotation, biasing for the abscissa and ordinate axis and proportional and disproportional scaling was gradually carried out with the obtained steganocontainer. The obtained results of the experiment demonstrate the effectiveness and stability of the proposed StegoBIT algorithm to various transformations that are based on affine transformations.