Researchers have made a significant breakthrough in neural network field theory by incorporating topological effects, enabling the formulation of field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. This extension allows for the inclusion of discrete parameters that label the topological quantum number, effectively recovering the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of topological defects1. The study demonstrates the power of neural network field theory in capturing complex topological phenomena, which has significant implications for the development of post-quantum cryptography. As quantum computing advancements accelerate, the need for cryptographic migration to post-quantum cryptography becomes increasingly urgent, making this research crucial for informing PQC planning and implementation strategies. The findings of this study underscore the importance of considering topological effects in neural network field theory, which will be essential for developing robust and secure cryptographic systems.