Let (P, C, K, E, D) be a cryptosystem such that #K = #P = #C. Showthat if this cryptosystem has perfect secrecy, then every ciphertext is used withequal probability and every plaintext is used with equal probability.

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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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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.
Let A=0, Z=25
a) Find the sequence of pseudorandom numbers generated by the linear congruential method with modulus m = 9, multiplier a = 34, increment c = 2, and seed Xa= 5. Xat1 = (ax, + c) mod m. b) Which memory locations are assigned by the hashing function h(k) = k mod 101 to the records of insurance company customers with these Social Security numbers? 24735634
(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
Recall that an affine cipher, fa,b(n) = an + b( mod 26), where a, b ∈ {0, 1, 2, . . . , 25}, is said to be valid if gcd(a, 26) = 1. (a)Use the key (a, b) = (3, 0) to come up with the cipher text corresponding to the following plaintext DO WELL. (b) Now use the key (a, b) = (5, 1) to come up with the cipher text for DO WELL. (c) The key (a, b) = (5, 1) was used to generate the following cipher text. Decrypt the message. gbidxv vbfev
1.2. Decrypt each of the following Caesar encryptions by trying the various possible shifts until you obtain readable text. (a) LWKLQNWKDWLVKDOOQHYHUVHHDELOOERDUGORYHOBDVDWUHH (b) UXENRBWXCUXENFQRLQJUCNABFQNWRCJUCNAJCRXWORWMB (c) BGUTBMBGZTFHNLXMKTIPBMAVAXXLXTEPTRLEXTOXKHHFYHKMAXFHNLX
Which memory locations are assigned by the hashing function h(k) = k mod 101 to the records of insurance company customers with these Social Security numbers? a) 104569065 b) 432222165
Decrypt the message EABW EFRO ATMR ASIN, which is the ciphertext produced by encrypting a plaintext message using the transposition cipher with blocks of four letters and the permutation ? of {1, 2, 3, 4} defined by ?(1) = 3, ?(2) = 1, ?(3) = 4, and ?(4) = 2.
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.
Construct an affine cipher that uses only uppercase letters of English alphabet encoded as elements of Z26 as shown in the table below: A|B|C|D E FG|HIJK|L M 0|1|23 45678 a) Choose a proper key k = (a, b) where a # 1 and b # 0 b) Write the encryption function c) Write the decryption function d) Encrypt the first two letters of your name 9 10 11 12 NO|P|Q RST|UVWX|Y|Z 13 14 15 16 17 18 19 20 21 22 23 24 25

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Let (P, C, K, E, D) be a cryptosystem such that #K = #P = #C. Show that if this cryptosystem has perfect secrecy, then every ciphertext is used with equal probability and every plaintext is used with equal probability.