Number Theory

Encryption with Number Theory



Solving which of the following problems would allow one to break RSA encryption?

Alice chooses a public key of n=187n=187 and e=3e=3. What is her private key?

Bob's public key is 426759435605268851426759435605268851 and e=3e=3. Alice uses ASCII encryption and sends the ciphertext c=298049520771754739c=298049520771754739. Which of the following was Alice's original message?

Mallory discovers many public keys, including the following:

  • n=70441807n=70441807, e=3e=3
  • n=10645627n=10645627, e=17e=17
  • n=63339281n=63339281, e=65537e=65537
  • n=24864431n=24864431, e=257e=257
  • n=89221291n=89221291, e=17e=17

What number can Mallory discover is the prime factor of one (or more) of these keys, without needing to factor any of them, making use of a vulnerability of RSA?

Knowing which of the following would allow an attacker to efficiently break the RSA encryption?


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