(a) You set up a (3, 37) Shamir threshold scheme, working modulo the prime 227. Three...

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(a) You set up a (3, 37) Shamir threshold scheme, working modulo the prime 227. Three of the shares are (1,4), (2,8), and (3, 16). Another share is (5,x), but the part denoted by x is unreadable. Find the correct value of x, the relevant polynomial, and the message. Justify all your steps. (b) In a (4,41) Shamir threshold scheme working modulo the prime 229, the shares (1,9), (2, 27), (3,81), and (4,243) were given to Alice, Bob, Jerry, and Charles. Calculate the corresponding Lagrange interpolation polynomial p(x) modulo 229; that is, write p(x) = a₁ + a₁x + a₂x² + a3x³ with ao, a1, A2, A3 € Z229. Also, identify the secret. (c) Verify the solutions of Parts (a) and (b) in sagemath. (a) You set up a (3, 37) Shamir threshold scheme, working modulo the prime 227. Three of the shares are (1,4), (2,8), and (3, 16). Another share is (5,x), but the part denoted by x is unreadable. Find the correct value of x, the relevant polynomial, and the message. Justify all your steps. (b) In a (4,41) Shamir threshold scheme working modulo the prime 229, the shares (1,9), (2, 27), (3,81), and (4,243) were given to Alice, Bob, Jerry, and Charles. Calculate the corresponding Lagrange interpolation polynomial p(x) modulo 229; that is, write p(x) = a₁ + a₁x + a₂x² + a3x³ with ao, a1, A2, A3 € Z229. Also, identify the secret. (c) Verify the solutions of Parts (a) and (b) in sagemath.

Answer rating: 100% (QA)

a The correct value of X is 75 To find the relevant polynomial we can use Lagrange interpolation Thi... View the full answer