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CSCI-477JC1 of 2CSEC-462- Spring 2017Homework 3 (Total 60 points)Note: Include your explanations to the questions and show all the intermediate stepsappropriately.1.We will now analyze a pseudorandom number sequence generated by a LFSRcharacterized by (p2 = 1, p1 = 0, p0 = 1. This is the tap sequence).a.What is the sequence generated from the initialization vector (s2 = 1, s1 = 0, s0 =0)?(6 points)b.What is the sequence generated from the initialization vector (s2 = 0, s1 = 1, s0 =1)?(6 points)2.Question: What is the polynomial representation of the LFSR of degree m = 4 and the feedbackcoefficients p3 = 1, p2=1, p1=1, p0=1?(5 points)3.Based on the following figure, what are the values formand the feedback coefficientspi?(5points)4.Draw the corresponding LFSR for each of the three polynomials. Determine thesequences generated by: (12 points; 4 + 4 + points)a.x4+ x + 1b.x4+ x2+ 1c.X4+ x3+ x2+ x + 15.If we take the linear congruential algorithm with an additive component of 0 (i.e. c = 0)Xn+1= (aXn)modmThen it can be shown that ifmis prime and if a given value ofaproduces a maximumperiod ofm-1, thenakwill also produce the maximum periodprovided thatkis lessthanmandkandm -1 are relatively prime. Show this statement is true by using X0= 1andm= 5 and producing sequences for ak= 3, 32,and33.(Total 9 points (3 + 3 + 3)6.With linear congruential algorithm, some parameters that provide full period do notnecessarily provide a good random sequence as we saw in class lecture. For exampleconsider the following two generators:(Total 10 points; 5 + 5 points)a.Xn+1= (6Xn)mod 13b.Xn+1= (7Xn)mod 13Start with an initial seed of 1. Write out the two sequences to show that both are fullperiod (that is uptom-1, wherem= 13). Which appear more random to you? Why?7.Using the Blum Blum Shub (BBS) pseudorandom number generator algorithm below,generate the binary digits.What is the maximum period of sequence before numbers starts repeating?(7 points)

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