Replication Data for: Orient Express: Using Frobenius to Express Oriented Isogenies

We describe a new cryptographic group action built from isogenies, using the Frobenius endomorphism as an accelerator. This dataset consists of SageMath code providing a proof-of-concept implementation of two instantiations of this group action: the "square case" and the "square-free case". The main goal of the code is to help convince the reader that the algorithm really works in practice, and to allow for comparison with similar algorithms. E.g., using this implementation, we have produced the runtimes reported in Table 4 and Table 5.