The idea described in this tech memo is to accelerate rainbow table searches inside the SSD SoC.
A "rainbow table" is a data structure containing precomputed "chains" for reversing cryptographic hash functions, usually for cracking password hashes. A good yet simple instruction of the rainbow table by Kestas can be found at http://kestas.kuliukas.com/RainbowTables/.
RainbowCrack (http://project-rainbowcrack.com/) is a project that generates rainbow tables (for various hash algorithms) and creates tools for cracking hashes using rainbow tables. As can be seen from the page http://project-rainbowcrack.com/buy.php, rainbow table files are generally big, if not enormous, in size (the aforementioned page contains several TB of data). Because of this, rainbow tables are usually stored in non-volatle memory, and (partially) loaded to the host PC's main (volatile) memory when cracking hashes.
As far as rainbow table search is concerned, a rainbow table contains (unliked "reduced") hash values, and the bulk of a search operation is to find a match between the hash value to crack and existing hash values in the rainbow table. Note that a rainbow table can be sorted so that a binary search can be facilitated.
PIS-RT (Processing In Storage-Rainbow Table) is the approach that performs the above table lookup operation (i.e., matching a hash in the rainbow table) inside the disk (SSD in particular), possibly with a hardware module that does a linear (if rainbow table is not sorted) or binary (if rainbow table is sorted) search. This will significantly save I/O cost between the device (SSD) and the host (PC), and thus seems to be an architecture that fits the hash cracking application.