11,1751465 22,8375276 33,2902948 44,126321 55,3311225 66,4197480 77,349514 88,3831672 99,6506980 111,6366157

3 Shamir Secret Sharing Consider a (5, 10) secret sharing scheme working in Zp with p 8675309. The shares are (ToVo) (11, 1751465) (x1, yi)- (22, 8375276) (2.2, y 2) (33, 2902948) (T3, 3) (44, 126321) (4)-(55,3311225) (x5, ys)- (66, 4197480) (2.6. ) (77, 349514) (r)(88, 3831672) (Ts, ys) (99,6506980) (2.9. 9)--(111, 6366157) The shares are also found in the provided shamir.data file. Answer each of the questions. Include the code you used for the computations (or show a trace of the work that leads to he answers) a) Compute the secret s. Do this twice using different subsets of the shares b) Add a new share with ro- 1234. What is its corresponding yio-f(i0)-f(1234) value? c How many values of r E Zp satisfy f(x) 123456