A more precise specification appears below as pseudocode, although in this form the row / column pattern is more difficult to see . ?" is addition modulo 2 32, x ?" = y is an abbreviation for x = x ?" y.
12.
For another example, every abelian group of order 8 is isomorphic to either "'Z "'8 ( the integers 0 to 7 under addition modulo 8 ), ( the odd integers 1 to 15 under multiplication modulo 16 ), or.
13.
As noted above, since exclusive disjunction is identical to addition modulo 2, the bitwise exclusive disjunction of two " n "-bit strings is identical to the standard vector of addition in the vector space ( \ Z / 2 \ Z ) ^ n.
14.
In the first key-mixing stage, the plaintext block is divided into eight 8-bit segments, and subkeys are added using either addition modulo 256 ( denoted by a " + " in a square ) or XOR ( denoted by a " + " in a circle ).
15.
One reason for this name may be that this is the only root from which you can calculate the rest of the n-1 roots by incrementally adding 2 \ pi / n to the angle and " not " have to calculate the angle additions modulo 2 \ pi.
