Cryptanalytic time-memory trade-offs (TMTOs) are techniques commonly used in computer security e.g., to crack passwords. However, TMTOs usually encounter in practice a bottleneck that is the time needed to perform the precomputation phase (preceding to the attack). We introduce in this paper a technique, called distributed filtration-computation, that significantly reduces the precomputation time without any negative impact the online phase. Experiments performed on large problems with a 128-core computer perfectly match the theoretical expectations. We construct a rainbow table for a space N=242 in approximately 8 h instead of 50 h for the usual way to generate a table. We also show that the efficiency of our technique is very close from the theoretical time lower bound.