9.10. Let F be a secure block cipher with blocklength 2. Below is an encryption scheme for plaintexts M = {0, 1}². Formally describe its decryption algorithm and show that it does not have CCA security. Enc(k, m): re {0,1}^ c1 := F(k,r) C2 := r O F(k, m) return (c1, c2) KeyGen: k+ {0, 1}^ return k

9.10. Let F be a secure block cipher with blocklength 2. Below is an encryption scheme for plaintexts M = {0, 1}². Formally describe its decryption algorithm and show that it does not have CCA security. Enc(k, m): re {0,1}^ c1 := F(k,r) C2 := r O F(k, m) return (c1, c2) KeyGen: k+ {0, 1}^ return k

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Alice computes the Secret prefix MAC (page 322: secret prefix MAC(x) = h(key || x)) for the message ”GD” (in ASCII) with key “H” (in ASCII) that both Alice and Bob know. The hash function that is used is h(x1x2x3)= g(g(x1 XOR x2) XOR x3 ) where each xi is a character represented as 8 bits, and g(x) is a 8-bit string that is equal to the complement of bits in x. For example, g(10110011) = 01001100. The MAC is 8 bits. (8-bit ASCII representation of characters is available at https://www.asciitable.com/ Take the Hexa equivalent and convert it to 8 bits each. For example character "A" is hexa 41 or 0100 0001 in bits) What is the Secret prefix MAC computed by Alice? Show the MAC as the single character. What information is sent by Alice to Bob?
Suppose Alice computes the Secret suffix MAC (page 322: secret suffix MAC(x) = h(x || key)) for the message ”AM” with key “G” that both Alice and Bob know. The hash function that is used is h(x1x2x3)= g(g(x1 XOR x2) XOR x3 ) where each xi is a character represented as 8 bits, and g(x) is a 8-bit string that is equal to the complement of bits in x. For example, g(10110011) = 01001100. The MAC is 8 bits. (8-bit ASCII representation of the characters is given below.) What is the Secret suffix MAC computed by Alice? Show the MAC as the single character. What information is sent by Alice to Bob.
Write a Python script that implements the CHF (the Casual Hash Function.) The input data should be split into blocks of 32 bits. If the last block is smaller than 32 bits, the remaining bits should be filled with 1 followed by as many zeros as required. A and B are 2 buffers with specific values (see below). Each block in the message should be combined as shown in the image below. All resulting blocks (i.e. FBI) should be combined with "&" to produce the digest. The size of the digest is 64 bits. Calculate the digest for the string: "Alright, but apart from the sanitation, the medicine, education, wine, public order, irrigation, roads, the fresh-water system, and public health, what have the Romans ever done for us?" steps on how are in the attached pictures
Write a Python script that implements the CHF (the Casual Hash Function.) The input data should be split into blocks of 32 bits. If the last block is smaller than 32 bits, the remaining bits should be filled with 1 followed by as many zeros as required. A and B are 2 buffers with specific values (see below). Each block in the message should be combined as shown in the image below. All resulting blocks (i.e. FBI) should be combined with "&" to produce the digest. The size of the digest is 64 bits. Calculate the digest for the string: "Alright, but apart from the sanitation, the medicine, education, wine, public order, irrigation, roads, the fresh-water system, and public health, what have the Romans ever done for us?"
1. We have defined a symmetric cryptography algorithm using the XOR operator. Assume our messages (before encryption) consist of only uppercase and lowercase letters, digits and blank character. In addition, assume the key size is only one byte which is an integer between 0 and 255 (inclusive). The pseudocode of the proposed encryption algorithm is as follows: Read the message // for example message=”Hi” Read the key // for example key=10 Cipher_text=[] //an empty list for i=1 to len(message): Cipher_text= Cipher_text.append(XOR(message[i],key)) Return Cipher_text Assume XOR function, takes a character and the key, then returns the result of bitwise XOR of ASCII code of the letter with the key as an (one byte) integer. For example, if message=”Hi” and key=10, then we should first calculate the ASCCI code of “H” which is 72 and find the result of (72 XOR 10) which is 66. Then the ASCCI code of “i” is 105, so the result of (105 XOR 10) is 99. Thus the Cipher_text would be…
1. We have defined a symmetric cryptography algorithm using the XOR operator. Assume our messages (before encryption) consist of only uppercase and lowercase letters, digits and blank character. In addition, assume the key size is only one byte which is an integer between 0 and 255 (inclusive). The pseudocode of the proposed encryption algorithm is as follows: Read the message // for example message=”Hi” Read the key // for example key=10 Cipher_text=[] //an empty list for i=1 to len(message): Cipher_text= Cipher_text.append(XOR(message[i],key)) Return Cipher_text Assume XOR function, takes a character and the key, then returns the result of bitwise XOR of ASCII code of the letter with the key as an (one byte) integer. For example, if message=”Hi” and key=10, then we should first calculate the ASCCI code of “H” which is 72 and find the result of (72 XOR 10) which is 66. Then the ASCCI code of “i” is 105, so the result of (105 XOR 10) is 99. Thus the Cipher_text would be…
Now consider the opposite problem: using an encryption algorithm to construct a oneway hash function. Consider using RSA with a known key. Then process a message consisting of a sequence of blocks as follows: Encrypt the first block, XOR the result with the second block and encrypt again, etc. Show that this scheme is not secure by solving the following problem. Given a two-block message B1, B2, and its hash RSAH(B1, B2) = RSA(RSA (B1) +B2) Given an arbitrary block C1, choose C2 so that RSAH(C1, C2) = RSAH(B1, B2). Thus, the hash function does not satisfy weak collision resistance.
What is the security requirement on password hashing? Given a password w, its hash is calculated as . This question is about the security requirement on function h. (a) Can we use any function as h for password hashing? For example, can we use the "mod 100" function, which is a common computer science function? (Given any integer value x, "mod 100" function works by "x mod 100," which is a value between [0, 99]; for example, if x = 105, x mod 100 = 5; x = 1000000, x mod 100 = 0;) (b) If not, what is the security requirement on h?
The parity function is a very simple hash function producing a one-bit digest, which is 0 if the number of bits in the message is even and 1 if it is odd. Consider a communication system that uses 7 bits out of every byte to transmit data, and reserves the 8th bit (the one on the right) to transmit the parity of the other seven bits, for purposes of error checking. Below is the binary representation of some bytes that were transmitted using this system. For each one, tell whether there is a reason to suspect an error in transmission, giving the reason for your answer. 10110011 11101111 10101100 00110011
In a special case of a permutation cipher, we take a message, M, and write its letters in an s× t table, in a row-major fashion, and then let the ciphertext be a column-major listing of the entries in the table. For example, to encrypt the message ATTACKATDAWN, using a 3 × 4 table, we would write the message as ATTA CKAT DAWN and then write down the ciphertext as ACDTKATAWATN. The secret key in this cryptosystem is the pair (s, t). How is decryption done in this cryptosystem? Also, how hard would it be to attack this cryptosystem using a ciphertext-only attack?
This question relates to hash functions for block ciphers Block size = 4 bits Hash size = 4 bits Encryption function: Divide the key into two halves: LK and RK; Divide the plaintext into two halves: LT and RT; Then ciphertext= LC||RC where LC=LK XOR RT; and RC = RK XOR LT; where LC, RC, LT, and RT are each 2 bits; Plaintext and ciphertext are each 4 bits. g(H) = a 4-bit string that is equal to the complement of bits in H; For example, if H=A (Hexa) = 1010 (binary); then g(H)= 0101 H0 = Initial hash = C (in Hexa) Given message M: D9 (in Hexa); a. Determine the hash (in hexadecimal) of the message M using Martyas-Meyer-Oseas hash function b. Determine the hash (in hexadecimal) of the message M using Davis-Meyer hash function c. Determine the hash (in hexadecimal) of the message M using Migayuchi-Preneel hash function
Suppose the economies of the world use a set of currencies C1, . . . , Cn; think of these as dollars, pounds, Bitcoin, etc. Your bank allows you to trade each currency Ci for any other currency Cj, and finds some way to charge you for this service. Suppose that for each ordered pair of currencies (Ci, Cj ), the bank charges a flat fee of fij > 0 dollars to exchange Ci for Cj (regardless of the quantity of currency being exchanged). Describe an algorithm which, given a starting currency Cs, a target currency Ct, and a list of fees fij for all i, j ∈ {1, . . . , n}, computes the cheapest way (that is, incurring the least in fees) to exchange all of our currency in Cs into currency Ct. Also, justify the its runtime. [A description or pseudocode (either is OK) of the algorithm, as well as a brief justification of its runtime.]