Recall that we define a cipher to be secure if the best known attack is an exhaustive key search. If a cipher is secure and the key space is large, then the best known attack is computationally...

Recall that we define a cipher to be secure if the best known attack is an exhaustive key search. If a cipher is secure and the key space is large, then the best known attack is computationally infeasible—for a practical cipher, this is the best possible scenario. However, there is always the possibility that a clever new attack could change a formerly secure cipher into an insecure cipher. In contrast, Naor and Shamir's visual secret sharing scheme is information theoretically secure, in the sense that there is no possibility of a shortcut attack—it is guaranteed to be secure (by our definition) forever.

a. Consider the "2 out of 2" visual secret sharing scheme discussed in this chapter. Why can't Alice determine any information about the secret from her share of the secret?

b. How might a more general "m out of n" visual secret sharing scheme work?

c. For an "m out of n" visual secret sharing scheme, what would happen to the contrast of the recovered image for large m, with n a small value? For large n with m small? For large m and n?