1. Suppose that the following are the five shares in a (3,5)- Shamir Threshold Scheme implemented in Z101. 2 Xi Yi 1 1 35 2 15 47 32 69 4 29 23 53 (a) Determine the secret? (8 Pts.) 8 (b) Having determined the secret, compute the share that can be given to a new participant with an x value of 10. Note that we still want to make sure that any group of 3 or more participants can determine the secret and any group of less than 3 participants can learn nothing about the secret. [Hint: This can be done without really starting all over and without really computing the whole secret polynomial a(x).] (7 Pts.)