Measuring ethnic diversity currently amounts simply to counting ethnicities. This makes it impossible to correlate with achievement, to track changes over time or to compare institutions in a meaningful way. It is not clear, for example, whether it is more diverse to have many ethnicities with a large majority in one or two categories, or to have fewer ethnicities with a larger proportion in each. This article is not about race per se, but develops indices from cryptography and ecology to solve the problem of measuring diversity properly. Using data from freedom of information requests and university admissions offices, it analyses the ethnic diversity of undergraduate recruitment at Oxford and Cambridge universities over the past 10 years to resolve one of the most controversial issues in higher education today. It finds that both Oxford and Cambridge universities have increased ethnic diversity by more than 25% over the last decade, but that the problem of under-recruitment of black UK students remains. The article is an important contribution to research methodology, with clear applications in the field of school effectiveness, and informs the debate on social justice in education, particularly in a period of significant demographic change across Europe.