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4. Suppose two friends Alice and Alicia are using the public key cryptosystem RSA, but are using the same modulus N in their public keys. Assume that Alice's public key is (N, e₁) and Alicia's public key is (N, e₂), where e₁ and e2 are relatively prime. Suppose that a mutual friend Bob, sends both Alice and Alicia the same message m, encrypted using their public keys. That is, Bob sends Alice the ciphertext C₁ = me₁ (mod N), and sends Alicia the ciphertext c₂ = m2 (mod N). Show that if Eve is able to intercept both the ciphertexts, she can recover the value of m.

4. Suppose two friends Alice and Alicia are using the public key cryptosystem RSA, but are using the same modulus N in their public keys. Assume that Alice's public key is (N, e₁) and Alicia's public key is (N, e₂), where e₁ and e2 are relatively prime. Suppose that a mutual friend Bob, sends both Alice and Alicia the same message m, encrypted using their public keys. That is, Bob sends Alice the ciphertext C₁ = me₁ (mod N), and sends Alicia the ciphertext c₂ = m2 (mod N). Show that if Eve is able to intercept both the ciphertexts, she can recover the value of m.

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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4. Suppose two friends Alice and Alicia are using the public key cryptosystem RSA, but are using the same modulus N in their public keys. Assume that Alice's public key is (N, e₁) and Alicia's public key is (N, e₂), where e₁ and e2 are relatively prime. Suppose that a mutual friend Bob, sends both Alice and Alicia the same message m, encrypted using their public keys. That is, Bob sends Alice the ciphertext C₁ = m²₁ (mod N), and sends Alicia the ciphertext c₂ = m²2 (mod N). Show that if Eve is able to intercept both the ciphertexts, she can recover the value of m.
Transcribed Image Text:4. Suppose two friends Alice and Alicia are using the public key cryptosystem RSA, but are using the same modulus N in their public keys. Assume that Alice's public key is (N, e₁) and Alicia's public key is (N, e₂), where e₁ and e2 are relatively prime. Suppose that a mutual friend Bob, sends both Alice and Alicia the same message m, encrypted using their public keys. That is, Bob sends Alice the ciphertext C₁ = m²₁ (mod N), and sends Alicia the ciphertext c₂ = m²2 (mod N). Show that if Eve is able to intercept both the ciphertexts, she can recover the value of m.
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