3. Suppose that cryptosystem (K, E, D) is perfectly secure. Show that for any possible plaintext Po and any possible ciphertext Co it holds that Pr[Co = Ek (P)|P = Po] = Pr[Co = Ek (P)], where the probability is over the random choice of the plaintext P and the key k.
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![3.
Suppose that cryptosystem (K, E, D) is perfectly secure. Show that for any possible plaintext Po and any
possible ciphertext C, it holds that
Pr[Co = E#(P)|P = Po] = Pr[Co = E#(P)],
where the probability is over the random choice of the plaintext P and the key k .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb26327d-067d-492f-96f4-0df6376ef217%2F9e08d7b2-6dc6-45fe-9bb7-877db415714f%2Fp8po2_processed.png&w=3840&q=75)
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 213. Let (n, e) = (16504217646971, 78893) be Alice's public key, where e represents the encryption key. Suppose Oscar has obtained the decryption key d = 5568617131253. Then Oscar can factor n. Find the factors of n via the Squaring Method.(13) Find two different complete systems of residues modulo 8.
- Suppose the numbers xo, x1, x2, ... are given by the linear recurrence relation Xk+2 = 6xk – Xk+1 , k > 0. Find a formula for xg when xo = 1 and x, = 12 Assume that Pr[A]=0.5, Pr[B]=0.45, and Pr[A′∩B]=0.2. Find the following probabilities: (1) Pr[B′∩A]=Pr[B′∩A]= (2) Pr[A∩B]=Pr[A∩B]= (3) Pr[A′∩B′]=Suppose that the probability of observing |0⟩ in the state |ϕ1⟩ is 1/4 and the probability ofobserving |1⟩ in the qubit |ϕ2⟩ is 1/3.(a) Find the probability of observing |01⟩ in the state |ϕ1ϕ2⟩.
- A. xm=[0.25;0.25] b=[6;-4] L=[0 0;1 0] D=[8 0;0 -6] U=[0 -1;0 0] bdash=inv(L+D)*b; B=inv(L+D)*U; for n=1:5 xm=bdash-B*xm endfor B. xm=[0.2;0.2] b=[6;-4] L=[0 0;1 0] D=[8 0;0 -6] U=[0 -1;0 0] bdash=inv(L+D)*b; B=inv(L+D)*U; for n=1:5 xm=bdash-B*xm endfor C. None of these D. xm=[0.25;0.25] b=[6;-4] L=[0 0;1 0] D=[7 0;0 -5] U=[0 -1;0 0] bdash=inv(L+D)*b; B=inv(L+D)*U; for n=1:5 xm=bdash-B*xm endfor E. xm=[0.25;0.25] b=[6;-4] L=[0 0;1 0] D=[8 0;0 -6] U=[0 -1;0 0] bdash=inv(L+D)*b; B=inv(L+D)*U; for n=1:3 xm=bdash-B*xm endforSuppose that the probability of observing |0⟩ in the state |ϕ1⟩ is 1/4 and the probability ofobserving |1⟩ in the qubit |ϕ2⟩ is 1/3.Within the interval (0,1)we randomly choose two numbers: x and y . Determine the probability that the number (5x+y) is divisible by 3 .
- 2.24 An Affine-Hill Cipher is the following modification of a Hill Cipher: Let m be a positive integer, and define P = C = (Z26)". In this cryptosystem, a key K consists of a pair (L, b), where L is an m x m invertible matrix over Z26, and b € (Z26). For x = (x₁,...,xm) ≤ P and K = (L, b) ≤ K, we compute € y = ek (x) = (y₁ym) by means of the formula y = xL + b. Hence, ifShow that Sn is solvable when n ≤ 4.An electronics store has received a shipment of 25 table radios that have connections for an iPod or iPhone. Twelve of these have two slots (so they can accommodate both devices), and the other thirteen have a single slot. Suppose that five of the 25 radios are randomly selected to be stored under a shelf where the radios are displayed, and the remaining ones are placed in a storeroom. Let X = the number among the radios stored under the display shelf that have two slots. (b) (b) Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2). (Round your answers to four decimal places.) (c) Calculate the mean value and standard deviation of X. (Round your standard deviation to two decimal places.)
