Question

Problem 1. Bob decides it is time to use RSA public key encryption to share secret messages with his friends. Bob is loyal to Alice and will never knowingly reveal her messages to anyone. Eve is also Bob's friend and wants to decipher the message that Alice sent Bob. Eve knows that Bob will not reveal Alice's plaintext. But she convinces Bob to agree to decipher a string of bits that is different from Alice's ciphertext. Bob agrees. Eve is thrilled because now she can decipher Alice's message! Explain how Eve can do this. To get started, let (n, e) and (n, d) be Bob's public and private keys. Let Alice's plaintext message be m so that the corresponding ciphertext (which Eve can see) is c = m^e (mod n). Now, if Eve gives Bob a string of bits X, he will give Eve X^d (mod n). Knowing c, how should Eve construct X so that from Bob's response she can recover m?

          Problem 1. Bob decides it is time to use RSA public key encryption to share secret messages with his friends. Bob is loyal to Alice and will never knowingly reveal her messages to anyone. Eve is also Bob's friend and wants to decipher the message that Alice sent Bob. Eve knows that Bob will not reveal Alice's plaintext. But she convinces Bob to agree to decipher a string of bits that is different from Alice's ciphertext. Bob agrees. Eve is thrilled because now she can decipher Alice's message! Explain how Eve can do this. To get started, let (n, e) and (n, d) be Bob's public and private keys. Let Alice's plaintext message be m so that the corresponding ciphertext (which Eve can see) is c = m^e (mod n). Now, if Eve gives Bob a string of bits X, he will give Eve X^d (mod n). Knowing c, how should Eve construct X so that from Bob's response she can recover m?

Problem 1. Bob decides it is time to use RSA public key encryption to share secret messages with his friends. Bob is loyal to Alice and will never knowingly reveal her messages to anyone. Eve is also Bob's friend and wants to decipher the message that Alice sent Bob. Eve knows that Bob will not reveal Alice's plaintext. But she convinces Bob to agree to decipher a string of bits that is different from Alice's ciphertext. Bob agrees. Eve is thrilled because now she can decipher Alice's message! Explain how Eve can do this. To get started, let (n, e) and (n, d) be Bob's public and private keys. Let Alice's plaintext message be m so that the corresponding ciphertext (which Eve can see) is c = m^e (mod n). Now, if Eve gives Bob a string of bits X, he will give Eve X^d (mod n). Knowing c, how should Eve construct X so that from Bob's response she can recover m?

Added by Michael B.

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