Crypotography Questions:

1. A message m was encrypted using the RSA algorithm with n=899 and e=13. The ciphertext is 706. Find the message m. Show all the work from the scratch, including finding 1/e(using the extended Euclidean algorithm) and the resulting modular exponentiation...

In the following problem #1 has to be done manually. For problems #2-4 you may use a CAS (computer algebra system) such as Maple or Wolfram Alpha. 1. A message m was encrypted using the RSA algorithm with n-899 and e-13.The ciphertext is 706. Find the message m. Show all the work from the scratch, including finding 1/e (using the extended Euclidean algorithm) and the resulting modular exponentiation. 2. Let (n,e)-(14351, 17) for an RSA encryption. (a) Encrypt the plaintext "jack" (b) Decrypt the ciphertext 12900. Convert the plaintext to plain English. The RSA public encryption key consists of (n,e) (2966193773,65537). (a) Encrypt the plaintext "don" (b) Decrypt the ciphertext c-2896921917. Convert the plaintext to plain English. The number 81842353880865 is the numerical value of a short expression converted from ASCII characters. What is the expression? Explain how you got the answer. In the following findx. If a solution does not exist, state why. (a) 2* E 3 mod 17 (b) 3x 3. 4. 5. 7 mod 17