Problem 7: Consider the Shamir secret sharing scheme in Lecture 15, where t > 3. Two variants (denoted by Scheme 1 and S

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Problem 7 Consider The Shamir Secret Sharing Scheme In Lecture 15 Where T 3 Two Variants Denoted By Scheme 1 And S 1 (219.28 KiB) Viewed 55 times

Problem 7: Consider the Shamir secret sharing scheme in Lecture 15, where t > 3. Two variants (denoted by Scheme 1 and Scheme 2, respectively) of the Shamir secret sharing scheme are obtained by replacing the original polynomial a(x) with the following q1) () = (s – a1x + a222 – 43x3 + ... +(-1)-107–121–1) mod p a(x at a (20 t t- а = and a2)(x) = (at-1 + a2x + 02.12 +03:23 22x2 + +...+04-224-2 – sx-1) mod p, at2X respectively. Consider the following two statements: -1 (1) Scheme 1 must be a (t, n)-threshold scheme. 2 (2) Scheme 2 must be a (t, n)-threshold scheme. 2 10 marks Which of the following statements is true? (A) Statement (1) is true, but Statement (2) is false. (B) Statement (2) is true, but Statement (1) is false. (C) Both Statements (1) and (2) are true. (D) Both Statements (1) and (2) are false.