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 ideal situation. However, there is always the possibility that a clever new attack could change a formerly secure cipher into an insecure cipher. In contrast, Shamir's polynomial-based secret sharing scheme is information theoretically secure, in the sense that there is no possibility of a shortcut attack. In other words, secret sharing is guaranteed to be secure forever.

a. Suppose we have a "2 out of 2" secret sharing scheme, where Alice and Bob share a secret S. Why can't Alice determine any information about the secret from her share of the secret?

b. Suppose we have an "m out of n" secret sharing scheme. Any set of m — 1 participants can't determine any information about the secret S. Why?