(a) Consider a plaintext space M = {M1, M2, M3, M4}, with corresponding cipherte

Question

(a) Consider a plaintext space M = {M1, M2, M3, M4}, with corresponding ciphertext space C = {C1, C2, C3, C4}. Suppose that each plaintext and each ciphertext is equally likely, i.e. p(Mi) = p(Cj ) = 1/4 for 1 i, j 4. Now suppose that each ciphertext Cj narrows down the choice of corresponding plaintext Mi to two of the four possibilities as follows: C1: M1 or M2 C2: M3 or M4 C3: M2 or M3 C4: M1 or M4 Compute H(M|C).

(b) Suppose a cryptosystem provides perfect secrecy, and that p(M) > 0 for all M M. Prove that H(M|C) = H(M).

(c) Does the example of part (a) provide perfect secrecy? Explain your answer?

Explanation / Answer

import java.io.File; importjava.io.IOException; public class RenameFile { public static void main(String[] args) { try // Here F is the object of the Existing file named with Includehelp which is to be renamed. // { File F=new File("f:/Includehelp.txt"); // Here T is the object of the renamed file of Includehelp which is Include.txt. // File T=new File ("f:/Include.txt"); // Rename the file Includehelp.txt into Include.txt. // F.renameTo(T); // Print the result if file renamed. // System.out.println("File Rename Successfully..."); } // If any error occurs while renaming the file. // catch(Exception e) { System.out.println(e); } } }

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