Introduction to Cryptography with Coding Theory, 3rd Edition

17.4 Computer Problems

1. Alice, Bob, and Charles have each received shares of a secret that was split using the secret splitting scheme described in Section 17.1. Suppose that $n=2110763$. Alice is given the share $M-r-s=1008369$, Bob is given the share $r=593647$, and Charles is given the share $s=631870$. Determine the secret $M$.

2. For a Shamir (4,7) secret sharing scheme, take $p=8737$ and let the shares be

   $$(1\text{,}214)\text{,}(2\text{,}7543)\text{,}(3\text{,}6912)\text{,}(4\text{,}8223)\text{,}(5\text{,}3904)\text{,}(6\text{,}3857)\text{,}(7\text{,}510)\text{.}$$

   Take a set of four shares and find the secret. Now take another set of four shares and verify that the secret obtained is the same.

3. Alice, Bob, Charles, and Dorothy use a (2, 4) Shamir secret sharing scheme using the prime $p=984583$. Suppose that Alice gets the ...