RSA signature Scheme question: Cryptosystem 7.1: RSA Signature Scheme Let n = pq, where p and q are primes. Let P = A - Zn, and define K={{n, p, q, a, b): n = pq, p, q prime, ab = 1 (mod o(n))}. The values n and b are the public key, and the values p, q, a are the private key. For K (n. p, q, a, b), define - and sigk(z) = z mod n verk (2, y) = true z = y (mod n) (x,y Zn). Refer to page 283, CS 7.1. Suppose Alice's RSA modulus is m = 91, her encryption exponent is e = 7 and her decryption exponent is d = 31. a. Bob receives a message-signature pair from Alice (not related to the above) and decrypts it, and gets (x=89, y-54). Does he regard the pair as likely to be authentic, or does he know that the pair has been altered? Show your work. b. Alice wants to sign the message x = 21 Calculate her signature. The RSA Cryptosystem You have set up a public key cryptosystem; your public encoding function is: E(x) = x5 (mod 26) Dr. Ecco, using this encoding function, has sent you the following ciphertext: PQKKP Two prime numbers are kept private for your public key cryptosystem they are: p = 2,q = 13 The decoding function is: D(x) = Find the decoding function and the plaintext. The plain text is: "On a typical day, more than 500 million tweets are sent" @raffi