# Alice and Bob are using RSA to communicate a Alice’s...

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MATH 470.502 Examination 2 Solutions November 26, 2014 1. Alice and Bob are using RSA to communicate. (a) Alice’s public encryption key is ( n, e ) = (133 , 5). Bob wants to encrypt the plaintext message ‘8’ to send to Alice. What is the ciphertext that he sends? (b) What is Alice’s decryption exponent?
2. Bob’s ElGamal public key is ( p, α, β ) = (31 , 3 , 19), and his private key is a = 4. (a) Alice wants to encrypt the message ‘9’ and send it do Bob. She first picks k = 5. What does she send to Bob? (b) In a separate communication, Alice has sent Bob the encrypted ciphertext ( r, t ) = (25 , 28). What is the decrypted message?
3. The following congruences hold: 1334 3826 1 (mod 3827) 2493 3826 1 (mod 3827) (1) 3826 3826 1 (mod 3827) 2495 3826 1592 (mod 3827) (2) 147 885 6352 (mod 7081) 147 1770 366 (mod 7081) (3) 147 3540 6498 (mod 7081) 147 7080 1 (mod 7081)