Use the information below from Dominion IT Budget and infrastructure summary to answer the following questions 4.
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Use the information below from Dominion IT Budget and infrastructure summary to answer the following questions
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4. [25 Points] Assume Larry, Moe and Curly all use the encryption exponent 3, with 3 differ- 30929. I sent the same two messages ent moduli, larry = 25777,1moe = 22879 and ncurly = to all three of them. Assume an attacker, Mallory, was able to see the encrypted messages that I sent to Larry, Moe and Curly. C1larry c1moe C1 curly C2Larry = 19052 (mod narry) = 4546 (mod nmoe) = 29722 (mod ncurly) = 1708 (mod narry) = 11733 (mod nmoe) = 17059 (mod ncurly) C2moe C2 curly Without factoring the moduli, recovering the decryption exponent or performing a brute force attack, recover the two messages, m and m2. These messages are encoded using the same methods as Exercise 1. Hint: Are nlarry, n moe and ncurly relatively prime? Note: You can solve these using spreadsheets or you can write a script to help out as well. If you write a script in Python, I may suggest using Python3.10. You can use the pow function to calculate exponentials and inverses modulo n. pow (a, 2, n) pow (a,-1, n) 4. [25 Points] Assume Larry, Moe and Curly all use the encryption exponent 3, with 3 differ- 30929. I sent the same two messages ent moduli, larry = 25777,1moe = 22879 and ncurly = to all three of them. Assume an attacker, Mallory, was able to see the encrypted messages that I sent to Larry, Moe and Curly. C1larry c1moe C1 curly C2Larry = 19052 (mod narry) = 4546 (mod nmoe) = 29722 (mod ncurly) = 1708 (mod narry) = 11733 (mod nmoe) = 17059 (mod ncurly) C2moe C2 curly Without factoring the moduli, recovering the decryption exponent or performing a brute force attack, recover the two messages, m and m2. These messages are encoded using the same methods as Exercise 1. Hint: Are nlarry, n moe and ncurly relatively prime? Note: You can solve these using spreadsheets or you can write a script to help out as well. If you write a script in Python, I may suggest using Python3.10. You can use the pow function to calculate exponentials and inverses modulo n. pow (a, 2, n) pow (a,-1, n)
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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