Estimating the size of a rainbow table

RainbowCrack is probably what you would be using to generate rainbow tables. Rainbow tables are always generated over a keyspace, such as alpha-numeric 5-9 bytes long and the chain length and count which will affect the rate and the size of the resulting tables. If you have an input file, then it's not a rainbow table, it's some other lookup table. A rainbow table is a speical type of lookup table with neat properties. Such as the size of the hash function (sha256 vs sha512) doesn't affect the size of the rainbow table.

There are some matlab scripts floating around to calculate the size of rainbow table, however this site is easier to use.

A rainbow table is characterized by its average chain length. It is a parameter which is chosen at table construction time. Let's call it t.

If the table covers about N tentative passwords, then it will have a size of about N/t "entries", where an entry is a "chain end". The encoded size of a chain end depends on a lot of details, but it will typically be as large, or somewhat larger, than a field which can hold the integer value N. In other words, if N is close to 2⁴⁰, each entry will need at least 5 bytes, but probably a bit more than that, say 8 bytes.

To save on storage cost, you will want to make t as big as possible. However, you cannot make it as big as you want, because it raises other costs. Briefly stated:

• The table construction cost is about 1.7*N evaluations of the hash function.
• The storage cost is N/t chain ends.
• The CPU cost when attacking is about t² evaluations of the hash function.
• The lookup cost when attacking is about t random accesses in the tables.

A modern hard disk allows about 100 lookups per second, so if you want to keep attack time below one minute, you cannot have t higher than 6000. You can have much higher values for t if you use SSD (which allow for many thousands of random accesses per second), but storage cost increases because SSD are quite expensive. Also, if t becomes too high, the quadratic CPU cost can become prohibitive.

The difference between a rainbow table, what existed before (Hellman's time-memory trade-off), and the modern variants which mix ideas from Hellman, Oechslin, Rivest, Biham and a few others, is a factor of at most 2 in CPU and lookup costs.