[3][4] Cocks was educated at Manchester Grammar School and went on to study the Mathematical Tripos as an undergraduate at King's College, Cambridge.

He continued as a PhD student at the University of Oxford, where he specialised in number theory under Bryan Birch, but left academia without finishing his doctorate.

Several people had attempted creating the required one-way functions, but Cocks, with his background in number theory, decided to use prime factorization,[8] and did not even write it down at the time.

Only at the end of the evolution from Berners-Lee [in 1989] designing an open internet architecture for CERN, its adaptation and adoption for the Arpanet ... did public key cryptography realise its full potential.

[11] In 1987, the GCHQ had plans to release the work, but Peter Wright's Spycatcher MI5 memoir caused them to delay revealing the research by ten years.

In 2001, Cocks developed one of the first secure identity-based encryption (IBE) schemes, based on assumptions about quadratic residues in composite groups.

[17] With James Ellis and Malcolm Williamson, Cocks was honoured for his part in the development of public-key cryptography by the Institute of Electrical and Electronics Engineers (IEEE)[18] in 2010 and by induction into the Cryptologic Hall of Honor in 2021.