This chapter provides a general overview of AI methods used to support the design of cryptographic primitives and protocols. After giving a brief introduction to the basic concepts underlying the field of cryptography, we review the most researched use cases concerning the use of AI techniques and models to design cryptographic primitives, focusing mainly on Boolean functions, S-boxes and pseudorandom number generators. We then point out two interesting directions for further research on the design of cryptographic primitives where AI methods could be applied in the future.