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Math 180, problem set #8
(1) There is a rational number r, with denominator less than 50, whose
expansion begins 1.2941176470588 . . .. Express r as a fraction . (You may need
to use a calculator to compute a continued fraction.)
For the next three problems an RSA cipher is set up with
modulus N = 12091 =
107 113 and encryption exponent e = 3.
(5) Encrypt the message 2107.
(6) What is the decryption exponent ?
(7) Suppose the encrypted message (ciphertext) received is 9812. Decrypt it.
In the Diffie-Hellman key exchange, Alice and Bob (being
agree to use the prime modulus 101 and the primitive root 2. Alice chooses the secret
exponent 20 and Bob chooses the secret exponent 41.
(8) What does Alice send to Bob?
(9) What does Bob send to Alice?
(10) What is the shared secret?