Reduction functions for rainbow tables

Question

Since chains of rainbow tables are very long, are there many different reduction functions used to reduce each hash, or are there only a handful, while using indexes to prevent merging? or something else?

Answer 1

The reduction functions of a rainbow table are all different (one per column), but are generally built as an extension of a single reduction function.

For instance, let r be a reduction function (say, r(x) = x mod N, where N is the size of your input set), then to generate a reduction function family, as one needed in rainbow tables, one could use r_i(x) = r(x+i).