A = ( 0 1 ) B = ( 0 0 )
( 0 0 ) ( 1 0 )
acting on a two-component vector
v = ( yes )
( no )
Compute ABv and BAv. Suppose we apply this property to an
access control system with two security checkpoints A and B. If we assign
a matrix-valued security token after authentication to each secure
area, how could we use this property to ensure that only those
who have successfully be authenticated to A and then B (in
that order) will gain access to data?
ABv = yes, BAv = no. Obvious how we could use this? Give each user a
matrix token/ticket on passing through a check point. Combine
these with any matrix-tickets the use already has by multiplying
the tickets at each step. To access a resource, we need to apply
our ticket. If the result is yes, we get access otherwise no.
There are are many possible answers. Here is just one:
( 0 1 0 ) ( 0 0 0 ) ( 1 0 0 ) ( yes )
A = ( 0 0 0 ) B = ( 1 0 0 ) C = ( 0 0 0 ) and v = ( no )
( 0 0 0 ) ( 0 0 0 ) ( 0 0 0 ) ( no )
Can verify that only ABCv = yes. All other combinations give either
"no" or zero for an answer. i.e. if we choose yes = 1, the this is
consistent.