**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 \( H : \{0,1\}^* \rightarrow \{0,1\}^n \) be a hash function. Assume that plaintext messages \( m \) all have bit-lengths that are multiples of \( n \); we write \( m = (m_1, m_2, \ldots, m_t) \), i.e., \( m \) is composed of \( t \) blocks \( m_i \) of \( n \) bits each. Consider the following MAC schemes, each using an \( n \)-bit secret key \( k \).1. \( \text{MAC}_k(m) = c_t \), where \( c_0 = 0 \), and \( c_i = c_{i-1} \oplus m_i \oplus E_k(m_i) \) for \( 1 \leq i \leq t \).2. \( \text{MAC}_k(m) = E_k(H(m)) \).Are any of these MAC schemes secure? Justify your answer and clearly state any assumptions you make.

we assume that it is not collision resistant, i.e. we can find a pain of messages x and y where xty…

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 = (m₁, 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) = c₁, where co= 0, and c = c₁-1 m, ⒸE(m) for 1 ≤ i ≤t. 2. MACK(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 = (m₁, 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) = c₁, where co= 0, and c = c₁-1 m, ⒸE(m) for 1 ≤ i ≤t. 2. MACK(m) Ek(H(m)). Are any of these MAC schemes secure? Justify your answer and clearly state any assumptions you make.

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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