RSA Public Key cryptography uses a secret pair of prime numbers p and q to determine . The modulus m = pq, . The public key a, which is any number relatively prime to (p - 1) x (q 1), and . The private key B, which is the inverse of a modulo (p-1) x (g-1). Use the following table to convert capital English letters to numbers B D E 3 4 5 6 7 R 0 P Q 16 17 18 19 A 2 N 15 F G H K T J 10 11 8 9 12 13 S T U V W X Y 20 21 22 23 24 25 26 27 Helpful Hints: (a) Your MATH1081 friend gives you the modulus m = 493, their pubic key a = 39, and shows you how to encrypt the word MATH as a sequence of numbers. Letter Number x Encrypted Number x39 (mod 493) Encrypt the message AXIS using the method above. Enter your answer as a sequence of digits such as [1,2,3,4] BA 256 = 2556 E 10112 20112 E M 14 Z M A T H 14 2 21 9 414 366 200 138 = 1 (mod 493). (b) Your friend tells you that their public key uses the prime number 17. Use this information to deduce: 1. The other secret prime Number 2. Their private key = Number Encrypt the message AXIS using the method above. Enter your answer as a sequence of digits such as [1,2,3,4] Helpful Hints: 256 2556 = 10112 = 20112 = 1 (mod 493). = (b) Your friend tells you that their public key uses the prime number 17. Use this information to deduce: 1. The other secret prime Number 2. Their private key = Number (c) Anyone who knows the private key can decrypt secret messages by taking each encrypted number to the power and evaluating modulo 493. For example Encrypted number y Number y (mod 493) Letter What does the secret message [334, 366, 75, 473] say? 414 14 M 366 200 138 2 21 A T 9 H Helpful Hints: 3112 = 256 = 1216 = 6112 = 1 (mod 493).