Public Key cryptography is an essential tool that underpins internet security. The talk describes the origins of public key some 50 years ago and the mathematical techniques involved. The focus then shifts to a variety of applications enabled by public key cryptography, and ends with a discussion about the future and how we are meeting the threat from quantum computing. Cliff Cocks, former Chief Mathematician at GCHQ - the UK's intelligence, security and cyber agency - talks through his key role in the development of public key cryptography, the theory that underpins it and its widespread use now. Cliff was speaking at the G-Research Distinguished Speaker Symposium on Prime Numbers and Cryptography. Cliff was the first of two speakers, alongside James Maynard, Fields Medallist 2022. Interested in attending future Distinguished Speaker Series events? Learn more and sign up for updates here: https://www.gresearch.com/news/distinguished-speaker-symposium-on-prime-numbers-and-cryptography/ Subtitles have been created using AI. As such, there may be some minor errors within the content.