Question: (1) This question is about secret sharing. (a) You set up a (3, 29) Shamir threshold scheme, working modulo the prime 211. Four of the

(1) This question is about secret sharing. (a) You set up a (3, 29) Shamir threshold scheme, working modulo the prime 211. Four of the shares are {1, 4), (2, 5), and (3, 6). Another share is (4,112), but the part denoted by a: is unreadable. Find the correct value of m, the relevant polynomial, and the message. Justify all your steps. (b) In a (4, 31) Shainir threshold scheme, working mod the prime 223. The shares (1, 8), (2, 16), (3, 32), and (4, 64) were given to Alice, Bob, Jerry, and Charles. Calculate the corresponding interpolation polynomial p(2:) modulo 223; that is, write 33(3) = 043 +a1$ #11211?2 + (132:3 with (19, a1, 0.2, :13 E Z223. Also, identify the secret

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