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2. Consider a spy. (a) The spy learns that messages m are encrypted to m' using m' = am mod 97 for some a. He discovers that m = 13 is encrypted to m' = 74. What is a? What is the decryption formula? (b) The spy knows that messages m are encrypted to m' using m' = am+b mod 251. He discovers that m₁ = 14 is encrypted to m₁ = 111 and that m2 = 73 is encrypted to m2 = 14. What is a and b? What is the decryption formula? (c) The spy knows that messages m are encrypted to m' using m' m² mod 1189. Without knowing the factorization of 1189, explain how the spy could determine the decryption key d so that m (m')d mod 1189?

2. Consider a spy. (a) The spy learns that messages m are encrypted to m' using m' = am mod 97 for some a. He discovers that m = 13 is encrypted to m' = 74. What is a? What is the decryption formula? (b) The spy knows that messages m are encrypted to m' using m' = am+b mod 251. He discovers that m₁ = 14 is encrypted to m₁ = 111 and that m2 = 73 is encrypted to m2 = 14. What is a and b? What is the decryption formula? (c) The spy knows that messages m are encrypted to m' using m' m² mod 1189. Without knowing the factorization of 1189, explain how the spy could determine the decryption key d so that m (m')d mod 1189?

Computer Networking: A Top-Down Approach (7th Edition)
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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2. Consider a spy. (a) The spy learns that messages m are encrypted to m' using m' = am mod 97 for some a. He discovers that m = 13 is encrypted to m' = 74. What is a? What is the decryption formula? (b) The spy knows that messages m are encrypted to m' using m' = am + b mod 251. He discovers that m₁ = 14 is encrypted to m₁ = 111 and that m₂ = 73 is encrypted to m2 = 14. What is a and b? What is the decryption formula? (c) The spy knows that messages m are encrypted to m' using m' = m mod 1189. Without knowing the factorization of 1189, explain how the spy could determine the decryption key d so that m = (m')d mod 1189?
Transcribed Image Text:2. Consider a spy. (a) The spy learns that messages m are encrypted to m' using m' = am mod 97 for some a. He discovers that m = 13 is encrypted to m' = 74. What is a? What is the decryption formula? (b) The spy knows that messages m are encrypted to m' using m' = am + b mod 251. He discovers that m₁ = 14 is encrypted to m₁ = 111 and that m₂ = 73 is encrypted to m2 = 14. What is a and b? What is the decryption formula? (c) The spy knows that messages m are encrypted to m' using m' = m mod 1189. Without knowing the factorization of 1189, explain how the spy could determine the decryption key d so that m = (m')d mod 1189?
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