How do the constants in this implementation of AES match up with the algorithm? In this file on GitHub, from lines 154 to 169, there are twelve arrays of constants that I've not seen in other AES implementations. How do they relate to the algorithm?
The tables represent the composition of some of the routines from the round function. These tables are used because they facilitate an efficient implementation. These slides and the "Advanced Implementation" section this blog post do a good job of explaining. The table based implementation was also mentioned in the Rijndael AES proposal as well, if I recall correctly.