Authentication systems are now an important part of our daily life. Human biological, behavioral, and physical characteristics are usually applied in authenticating a person in various applications. Unimodal biometric systems have a number of limitations, such as noise sensitivity, population coverage, intra-class variations, non-universality, and vulnerability to spoofing. Multimodal biometric systems overcome these limitations and are being widely used in many real-world applications. In this work, to construct a three-dimensional (3-D) shell, we use fingerprint and iris. First, features are extracted from the fingerprint. Then, using a user key set, a two-dimensional spiral curve is generated from fingerprint features. Next, iris features are extracted using a pre-trained VGG-16 model, then feature vector-based random projection is applied to generate an iris feature vector. This generated feature vector is combined with the fingerprint shell to construct a secured 3-D shell. Finally, these fused 3-D templates are saved in the database and are used for matching. Our proposed technique has been evaluated on the three publicly available datasets, showing that it can preserve user privacy while maintaining the accuracy of the system with an equal error rate of 0.09%, 0.032%, and 0.015%.