4. Show that for the one-time pad, if M and K are uniformly distributed over {0,1}, Pr[M=0C=c] = Pr[M = 1|C = c].
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This is a lesson from applied cryptography (institute of
![4. Show that for the one-time pad, if M and K are uniformly distributed over {0,1},
Pr[M=0C=c] = Pr[M = 1|C = c].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F747ab200-c676-4ed9-b814-dae7641fcf0c%2Fefa045d5-9cf1-402d-b3b3-61fb6c6575cf%2Fvgmus8b_processed.jpeg&w=3840&q=75)
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- Minimize the function using Karnaugh map method. F(A, B, C, D) = E(1, 2, 3, 8, 9, 10, 11, 14) + Ed(7, 15).For f(a, b) = (a | b) | b (a) Simplify f(a, b). (b) Find DNF for f(a, b). (c) Is f(a, b) satisfiable?For f (a, b) = (a | b) | b(a) Simplify f (a, b).(b) Find DNF for f (a, b).(c) Is f (a, b) satisfiable?
- Let f ∈ C+ 2π with a zero of order 2p at z. Let r>p and m = n/r. Then there exists a constant c > 0 independent of n such that for all nsufficiently large, all eigenvalues of the preconditioned matrix C−1 n (Km,2r ∗ f)Tn(f) are larger than c.Simplify the boolean function using carno map in it.Consider a function f : S→ T defined by f(n) = n², where the domain is the set of consecutive integers S = {-7,..., -2, -1, 0, 1, 2, ..., 7} and the range is the set of consecutive squares T = {-64,...,-9, -4,-1,0, 1, 4, 9, ..., 64}. Which one of the following choices correct describes f? O one-to-one, but NOT onto Oonto, but NOT one-to-one O one-to-one and onto O neither one-to-one nor onto O none of these
- Prove that f(n)= {floor function of sqrt(n)} - { floor function of sqrt(n-1)} is a multiplicative function, but it is not completely multiplicative.give set of R(x): x < x^2 where the domain is ZLet f (n) and g(n) be functions with domain {1, 2, 3, . . .}. Prove the following: If f(n) = O(g(n)), then g(n) = Ω(f(n)).