Exercise 2 (MAC schemes derived from block ciphers( Let E denote the family of encryption functions for a block cipher where plaintext blocks, ciphertext blocks, and keys are each n = 80 bits in length. Let H: {0, 1} {0, 1}" be a hash function. Assume that plaintext messages m all have bit-lengths that are multiples of n; we write m = (my, m₂,...,m), i.e. m is composed of t blocks m, of n bits each. Consider the following MAC schemes, each using an n-bit secret key k. 1. MAC (m) = ₁, where co= 0, and c, =c-1m, E(m) for 1 ≤ i ≤t. 2. MAC (m) = Ek (H(m)). Are any of these MAC schemes secure? Justify your answer and clearly state any assumptions you make.

Exercise 2 (MAC schemes derived from block ciphers( Let E denote the family of encryption functions for a block cipher where plaintext blocks, ciphertext blocks, and keys are each n = 80 bits in length. Let H: {0, 1} {0, 1}" be a hash function. Assume that plaintext messages m all have bit-lengths that are multiples of n; we write m = (my, m₂,...,m), i.e. m is composed of t blocks m, of n bits each. Consider the following MAC schemes, each using an n-bit secret key k. 1. MAC (m) = ₁, where co= 0, and c, =c-1m, E(m) for 1 ≤ i ≤t. 2. MAC (m) = Ek (H(m)). Are any of these MAC schemes secure? Justify your answer and clearly state any assumptions you make.

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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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…