Biometric-based authentication systems have attracted more attention than traditional authentication techniques such as passwords in the last two decades. Multiple biometrics such as fingerprint, palm, iris, palm vein and finger vein and other biometrics have been introduced. One of the challenges in biometrics is physical injury. Biometric of finger vein is of the biometrics least exposed to physical damage. Numerous methods have been proposed for authentication with the help of this biometric that suffer from weaknesses such as high computational complexity and low identification rate. This paper presents a novel method of scattering wavelet-based identity identification. Scattering wavelet extracts image features from Gabor wavelet filters in a structure similar to convolutional neural networks. What distinguishes this algorithm from other popular feature extraction methods such as deep learning methods, filter-based methods, statistical methods, etc., is that this algorithm has very high skill and accuracy in differentiating similar images but belongs to different classes, even when the image is subject to serious damage such as noise, angle changes or pixel location, this descriptor still generates feature vectors in a way that minimizes classifier error. This improves classification and authentication. The proposed method has been evaluated using two databases Finger Vein USM (FV-USM) and Homologous Multimodal biometrics Traits (SDUMLA-HMT). In addition to having reasonable computational complexity, it has recorded excellent identification rates in noise, rotation, and transmission challenges. At best, it has a 98.2% identification rate for the SDUMLA-HMT database and a 96.1% identification rate for the FV-USM database.