Module Three Homework

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Apr 3, 2024

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How M,MAT 260 – Cryptology Dejah Crews-Siler March 17, 2024 Section 5.4: Exercise Problem 5 Section 5.5: Computer Problem 1, 3 Section 6.6: Exercise Problems 2 ,6, 8 Section 6.7: Computer Problems 1 Section 5.4: Exercise Problem 5 Suppose we build an LFSR machine that works mod 3 instead of mod 2. It uses a recurrence of length 2 of the form 𝑥 𝑛+2 ≡ ? 0 𝑥 𝑛 + ? 1 𝑥 𝑛+1 (mod 3) To generate the sequence 1,1,0,2,2,0,1,1. Set up and solve the matrix equation to find the coefficients ? 0 𝑎𝑛? ? 1 . ANSWER: 1 = [0,1] x [1] + [co, c] x [1] mod3 1 = [0,1] x [1] + [co, c] x [1] mod3 0 = [0,1] x [0] + [co, c] x [0] mod3 2 = [0,1] x [0] + [co, c] x [1] mod3 2 = [0,1] x [2] + [co, c] x [1] mod3 0 = [0,1] x [2] + [co, c] x [0] mod3 1 = [0,1] x [0] + [co, c] x [2] mod3 1 = [0,1] x [1] + [co, c] x [2] mod3 This implies that ? 0 = 1 and ? 1 = 1

Section 5.5: Computer Problem 1, 3 1. The following sequence was generated by a linear feedback shift register. Determine the recurrence that generated it. 3. The following sequence ciphertext was obtained by XORing an LSFR output with the plaintext. Suppose you know the plaintext starts Find the plaintext. 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0

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