Logjam works like rainbow tables, but for prime fields. Supposing that a way to reverse the function (a hash in rainbow table case, discrete logarithm in prime

Logjam works like rainbow tables, but for prime fields. Supposing that a way to reverse the function (a hash in rainbow table case, discrete logarithm in prime fields) in time X for a single case, you can instead pre-compute something in time P, which allows computing a specific instance in time Y. P + Y is longer or equal to X, and Y is significantly less than X. To compute n inversions takes nX for the first case, and P + nY for the second. However, the single instance case X still needs to be solvable. For a large enough prime field, X is still incredibly difficult, so P + Y is going to be incredibly difficult as well. It's much more significant that Logjam changes the field to something weak, than all of the servers use the same prime field.