You exchange a one time id with each close proximity. If you test positive, you publish your recorded close proximities ids on a public server. Authorities can

You exchange a one time id with each close proximity. If you test positive, you publish your recorded close proximities ids on a public server. Authorities can supply you with a one time tocken with the test result to append said server. There are certanly more efficient and elegant ways to solve this problem, but it is solvable.