Q2 Consider four parties and for each i = 1, 2,3, 4, party a; has a sensitive number 3;. Assume that 2:1 = 0.8, m2 = 0.3, $3 = 0.4, and 3:4 = 0.7. Dene an ER function 91 (2:) = W, where the set A = [0.2, 0.6] and 1,4(33) denotes the indicator function that equals 1 if a: 6 A and 0 otherwise. Use the ER algorithm with the ER function 91 (1:) = 14F! to securely compute the following empirical probability: 2:1 11403:\") ep := . 4 Please provide all the details in the implementation of each step of the ER algorithm like what are provided on pages 42-44 in Example 2 (Computing Variance Securely) of Lecture 3. Example 2: Computing Variance Securely . Assume that X1 = 0.2, X2 = 0.9, and X3 = 0.6. . Then its true sample variance is equal to Ci=1 (xi - x) 2 = 0.123333333333333. 2 . Substep E.1: Party / computes g1 (x;) and g2(x;) for i = 1,2, 3. 91 (X1 ) = 0.2, 91 (X2) = 0.9, 91 (X3) = 0.6, 92 (X1 ) = 0.04, 92(X2) = 0.81, 92(X3) = 0.36. Ning Cai, HKUST Privacy-Preserving Technologies for Data Analysis 42/54\fExample 2: Computing Variance Securely . Subtep E.3: Party i uses (2) to compute S;(1) and Si(2) for i = 1, 2,3; S1 (1 ) S2 (1 ) S3 (1 ) 2.233212630267172 1.041391527098832 1.425395842633996 S1 (2 ) S2 (2) S3 (2) 0.871244385052784 1.357940193077597 1.980815421869619 . R-Step: The central administration uses (3) to compute Q(1) = 1.700000000000000 (= X1 + X2 + X3) Q(2) = 1.210000000000000 (= X7 + X2 + x3 ) . Final Step: The central administration uses (4) to compute Q (2) - (Q (1) ) 2/ m = 0.123333333333333 m - 1 Ning Cai, HKUST Privacy-Preserving Technologies for Data Analysis 44/54Example 2: Computing Variance Securely . Due to high-dimension, only show (S1 (2), S2(2), S3(2)), which has a uniform distribution over its range. Samples of (S,(2), S,(2), S,(2) when m=3 0.5 E Ning Cai, HKUST Privacy-Preserving Technologies for Data Analysis 45/54