Heterogeneous Rainbow Table Widths Provide Faster Cryptanalyses

Cryptanalytic time-memory trade-offs are techniques introduced by Hellman in 1980 to speed up exhaustive searches. Oechslin improved the original version with the introduction of rainbow tables in 2003. It is worth noting that this variant is nowadays used world-wide by security experts, notably to break passwords, and a key assumption is that rainbow tables are of equal width. We demonstrate in this paper that rainbow tables are underexploited due to this assumption never being challenged. We stress that the optimal width of each rainbow table should be individually -- although not independently -- calculated. So it goes for the memory allocated to each table. We also stress that visiting sequentially the rainbow tables is no longer optimal when considering tables with heterogeneous widths. We provide an algorithm to calculate the optimal configuration and a decision function to visit the tables. Our technique performs very well: it makes any TMTO based on rainbow tables 40% faster than its classical version.