Answered step by step
Verified Expert Solution
Question
1 Approved Answer
please explain all answers clearly. 4. (30 points) Linear Feedback Shift Register linear attack. In the previous exercise, we saw that the initial state is
please explain all answers clearly.
4. (30 points) Linear Feedback Shift Register linear attack. In the previous exercise, we saw that the initial state is retrievable from n consecutive bits of the output stream. In this exercise, we will extend that attack to show how the initial state is retrievable from any n bits of the output stream. Therefore, consider the n-bit LFSR below. 20 21 22 ... 0 1 2 3 Represent the state after t iterations by a vector st. Let zt denote the tth output bit. It is known that with this cipher, the output stream is decimated and the following bits will be in the output: 22, 25, 29, 213. [You are allowed to compute powers of matrices (e.g., M4) using a computer algebra system.] = 2 pt 10 pt (a) Give the matrix M corresponding to the LFSR, that is the matrix M such that st+1 M st. (b) Let s = (S0, S1, S2, S3), so that zo = 83. Express z2 in terms of s. [Remember that za is the output after applying M two times.] (c) Let z = (22, 25, 29, 213). Find a matrix N such that z = = N.80. (d) As in (c), let z = (1,0,0,1)). Recover the key (that is the initial state s). 10 pt 8 pt 4. (30 points) Linear Feedback Shift Register linear attack. In the previous exercise, we saw that the initial state is retrievable from n consecutive bits of the output stream. In this exercise, we will extend that attack to show how the initial state is retrievable from any n bits of the output stream. Therefore, consider the n-bit LFSR below. 20 21 22 ... 0 1 2 3 Represent the state after t iterations by a vector st. Let zt denote the tth output bit. It is known that with this cipher, the output stream is decimated and the following bits will be in the output: 22, 25, 29, 213. [You are allowed to compute powers of matrices (e.g., M4) using a computer algebra system.] = 2 pt 10 pt (a) Give the matrix M corresponding to the LFSR, that is the matrix M such that st+1 M st. (b) Let s = (S0, S1, S2, S3), so that zo = 83. Express z2 in terms of s. [Remember that za is the output after applying M two times.] (c) Let z = (22, 25, 29, 213). Find a matrix N such that z = = N.80. (d) As in (c), let z = (1,0,0,1)). Recover the key (that is the initial state s). 10 pt 8 ptStep by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started