With advancements in quantum computing, the search for efficient algorithms for synthesising gates (the building blocks of quantum algorithms) using cost-effective gate sets has become an important area of research. Interestingly, the problems underlying gate synthesis have a number of connections with cryptography. The first half of this talk will cover the history of research in this area and an overview of the main concepts. In the second half, I will present recent advancements in quantum gate synthesis, which adapt path-finding results from cryptography. This talk is aimed at researchers without a background in quantum computing, so will be fairly introductory.