Suppose you have p = 152 and g = 34 = 81 for the Diffie-Hellman key exchange. Without computing any power of g, determine if the order of g is a prime number.
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Suppose you have p = 152 and g = 34 = 81 for the Diffie-Hellman key exchange. Without computing any power of g, determine if the order of g is a prime number.
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- Use the Euclidean algorithm to find the GCD of the following pairs of integers. Also find s and t such that as+bt=gcd(a,b). (a) a=2938 and b=183 (b) a=93182 and b=246 Show all calculations. Does a inverse mod b exist? If yes, what is it.Use strong induction to prove the following:Asymtotic Analysis : Prove the following claims
- Let ap = 1, an = an-1 + 3 be the recurrence relation of algorithm A and T(1) = 1, T(n) = T(n/5)+n be the recurrence relation of algorithm B. 1. Find the solution for both relations. Use any method.3. Let p(n) = Σª a¡n², where a¿ > 0, be a degree-d polynomial in n, and let k be a constant. Prove the following properties. if k ≥ d, then p(n) = 0(nk); if k ≤d, then p(n) = N(nk); if k = d, then p(n) = 0(nk); if k > d, then p(n) = o(n²); if k < d, then p(n) = w(nk); a. b. C. d. e.Express the solution in big-O terms for the following recurrence relation: T(n) = 9*T(n/3) + n^3; T(1)=1; Answer: T(n) = O(......) .
- Please explain your answer for both questions. For the first part n is greater than or equal to zeroA detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that: If the handyman is lying, then so is the butler. The gardener and the handyman cannot both be telling the truth. The cook and the gardener are not both lying. The handyman is telling the truth only if the cook is lying. For each of the four witnesses, can the detective determine whether that person is telling the truth or lying? Use the truth table to explain your reasoning (Give the full truth table). Please use the following notations in your reasoning – B: The butler is telling the truth. C: The cooking is telling the truth. G: The gardener is telling the truth. H: The handyman is telling the truth.Prove or disprove each of the following: [10] 1. (n+a) = 0(nb), for any real constants, where b > 0. 2. 3an = 0(3")
- hi. i got the answer to this question wrong despite asking one of your experts. Please can you give another go and help me by providing a detailed solution to this question. Thank youLet ap = 1, an = an-1 + 3 be the recurrence relation of algorithm A and T(1) = 1, T(n) = T(n/5)+n be the recurrence relation of algorithm B. 1. Find the solution for both relations. Use any method.8. Solve the following recurrence relations. (16 points) a. T(n) = 4T(n-1) + 1 for n > 1; T(1) = 1; b. T(n) = T(n/2) + 3; T(1) = 1; Here you can assume that n=2k for some integer k.