$[50$ pts$]$ Problem $2($based on book $5\mathrm{.}34)$

a$)[10$pts$]$ Suppose we have a $"2$ out of $2"$ secret sharing

scheme, where Alice and Bob share a secret S$.$ If

Trudy obtains Alice's secret key what information can

Trudy discover about S and why?

b$)[10$pts$]$ Suppose we want an $"$m out of $n"$ secret

sharing scheme. Mathematically what would you need

to do to create the secret scheme and how would you

generate the $n$ keys?