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In cases such as digital enrolment via mobile and online services, identity document verification is critical in order to efficiently detect forgery and therefore build user trust in the digital world. In this paper, an authentication model for identity documents based on forgery detection of guilloche patterns is proposed. The proposed approach is made up of two steps: feature extraction and similarity measure between a pair of feature vectors of identity documents. The feature extraction step involves learning the similarity between a pair of identity documents via a convolutional neural network (CNN) architecture and ends by extracting highly discriminative features between them. While, the similarity measure step is applied to decide if a given identity document is authentic or forged. In this work, these two steps are combined together to achieve two objectives: (i) extracted features should have good anticollision (discriminative) capabilities to distinguish between a pair of identity documents belonging to different classes, (ii) checking out the conformity of the guilloche pattern of a given identity document and its similarity to the guilloche pattern of an authentic version of the same country. Experiments are conducted in order to analyze and identify the most proper parameters to achieve higher authentication performance. The experimental results are performed on the MIDV-2020 dataset. The results show the ability of the proposed approach to extract the relevant characteristics of the processed pair of identity documents in order to model the guilloche patterns, and thus distinguish them correctly. The implementation code and the forged dataset are provided here (https://drive.google.com/id-FDGP-1)