3.Suppose that cryptosystem (K, E, D) is perfectly secure. Show that for any possible plaintext Po and anypossible ciphertext C, it holds thatPr[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 .

Perfect security in a cryptosystem means that the ciphertext does not reveal any information about…

Answered: 3. Suppose that cryptosystem (K, E, D)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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[Algebraic Cryptography] How do you solve this question?
Question 4
12. Determine which of the following functions are one-to-one. (a) r:Z36 → Z36; r(n) = 5n (mod 36). (b) s: Z10 → Z10; s(n) = n+5 (mod 10). (c) t: Z10 → Z10; t(n) = 3n + 5 (mod 10).
7. Suppose that X is a real valued random variable and : R → R is continuous. Show that if X and (X) are independent, then (X) must be deterministic (i.e. there is a real number a so that P((X) = a) = 1).
Let f:{0,1}* → {0,1}" and g:{0,1}* → {0,1}™ be two cryptographic hash functions. Let h = fOg, that is, each string h(x) is obtained from the strings f (x) and g(x) by bitwise addition modulo 2. Is h also a cryptographic hash function? Explain your answer.
2.18. Solve each of the following simultaneous systems of congruences (or explain why no solution exists). (a) x = 3 (mod 7) and x = 4 (mod 9). (b) x 137 (mod 423) and x = 87 (mod 191). (c) x = 133 (mod 451) and x = 237 (mod 697). (d) x = 5 (mod 9), x = 6 (mod 10), and x = 7 (mod 11). (e) x 37 (mod 43), x = 22 (mod 49), and x = 18 (mod 71).
(b) A computer room has 36 computers, numbered from 0 to 35. Assign a computer to each of the following students by the hashing function h(k)= k mod 36 where k is the class number of the student. Solve the problem when a collision occurs (In case of collisions, the computer number will usually be assigned to the next available storage location). (i) Student number of Jerry: 138 (ii) Student number of Ray: 36 (iii) Student number of Ivy: 34 (iv) Student number of Lucy: 66 (v) Student number of Ivan: 124
1.3. For this exercise, use the simple substitution table given in Table 1.11. (a) Encrypt the plaintext message The gold is hidden in the garden. (b) Make a decryption table, that is, make a table in which the ciphertext alphabet is in order from A to Z and the plaintext alphabet is mixed up. (c) Use your decryption table from (b) to decrypt the following message. IBXLX JVXIZ SLLDE VAQLL DEVAU QLB
5
12. A parking lot has visitor spaces, numbered from 0 to 30. Visitors are assigned parking spaces using the Hashing function h(k) = k mod 31, where k is the number formed from the license plate. Which spaces are assigned by the Hashing function to cars that have the following license plates: 317, 007, 102, 111, 918 ? (x2 + 1) mod 15, show how the data 5, 8, 20, 32 and 13. For the Hashing function h(x) 40 would be inserted in the order given in initially empty cells indexed 0 to 14.
7. Suppose n is a natural number that is greater than 100. Alex and Jerry each compute the gcd(4n. 20n2 + 15) and obtain different answers. Alex's computation has 12 divisions and Jerry's has 19. (a) Can we conclude that Alex's calculation contains an error? (b) Can we conclude that Jerry's calculation contains an error?

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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 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.