Reduce Functions for Rainbow Tables

Question

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

Answer 1

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

For example, let r be a reduction function (for example, r (x) = x mod N, where N is the size of your input data set), then to generate a family of reduction functions, as is necessary in rainbow tables, you can use r_i (x) = r (x + i).