bitwise AND, bitwise XOR and circular shift operation.
The key expansion module involves the bitwise AND, bitwise XOR, and circular shift operation.
In the case when m=4 there is an extra step the most significant word [k.sup.i+3] is circular shifted right by 3 and XOR'ed with [X.sup.i+1], circular shifted to the right by 1 and XOR'ed with the constant [C.sup.j.] as [k.sup.i] is the key used in the present round it will no longer be needed and is overwritten in every round.
Clearly, M is a circular shift of L, since [y.sub.i+1] = [x.sub.i] for i = 0,1, 2, 3,4, mod 5.
Then R is a circular shift of L but now this is not a general feature of non-trivial r-colorings on standard diagrams of THK (3,n)'s (see, for instance, the 5-coloring of THK(3,2) on the right-hand side of Figure 4, or the 7-coloring of THK(3, 8) in Figure 6).
For prime r > 5 and odd [psi](r), we construct a non-trivial r-coloring on the standard diagram of THK(3, [psi](r)) such that the R sequence is a circular shift of the L sequence (Theorem 1.3).