RSA Encryption Algorithm: Generating Keys and Encrypting Messages - Prof. John F. Ranelli, Assignments of Computer Science

Download RSA Encryption Algorithm: Generating Keys and Encrypting Messages - Prof. John F. Ranelli and more Assignments Computer Science in PDF only on Docsity! RSA Encryption 1. Randomly choose two prime numbers: p and q. p = 127 q = 211 2. Compute N = pq N = 127 * 211 = 26,797 3. Compute N' = (p – 1)(q – 1) N' = (127 – 1) * (211 – 1) = 26,460 4. Choose e > 1 such that gcd( e , N' ) = 1 (any e that is relatively prime to N' ) i. e. any prime e = 13,379 5. Compute d as the multiplicative inverse of e, mod N' (Fig. 7.18) d = 11,099 since e (13,379) * d (11,099) mod N' (26,460) = 1 6. Destroy p, q, N' 7. Use e and N to encrypt a message. Use d to decrypt. Encryption Example encrypt (int M) = Me (mod N). M is the message to be sent encrypt(10,237) = 10,23713,379(mod 26797) = 8422 (see fig. 7.16) 8422 is the encrypted M Decryption Example decrypt(R) = Rd(mod N) R is the received encrypted message decrypt(8422) = 842211099(26797) = 10,237