A Quick Background on Perfect Rainbow Tables

Rainbow tables allow us to find plaintexts to cryptographic hash algorithms quickly. They are based off of Hellman Martin’s “A Cryptanalytic Time – Memory Trade-Off“. By including the step in the reduction function, Phillipe Oechslin was able to improve on Hellman Martin’s method, and we came up with Rainbow Tables, the “Faster Cryptanalytic Time – Memory Trade-Off“.

If you are unfamiliar with rainbow tables, it is suggested you become familiar before continuing.

Even rainbow tables are not perfect. They still merge, and merges mean wasted information, wasted space, wasted time. What we really want are perfect rainbow tables. In perfect rainbow tables, each chain has a unique endpoint. We have no merges. They give us nearly the same percentage to find a plaintext as non-perfect rainbow tables, but are much smaller.
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