Question

Bob wants to send Alice an encrypted message, "BUDDIES." Suppose Bob encodes letters of the alphabet as follows. A = 01, B = 02, C = 03, ..., Z = 26. To encrypt the message, Bob uses an RSA cypher with public key (pq, e) = (55, 3). What is the encrypted message that Alice will receive? (Assume Bob encodes one letter at a time. Enter your answer using a fixed number of digits with a space between each encoded letter: 01 for 1, 02 for 2, ..., 09 for 9.)

Answer 1

The encrypted message "BUDDIES" is converted to numbers and each letter is then encrypted using RSA cipher with the public key (55, 3) resulting in the sequence 08 36 09 09 14 15 04.

Step-by-step explanation:

To encrypt a message using the RSA cipher, Bob must follow several steps. He has the public key (pq, e) = (55, 3), where 'pq' is the product of two prime numbers and 'e' is the exponent. The message "BUDDIES" needs to be encoded by converting each letter into its corresponding two-digit number, starting with A=01, B=02, etc.

Therefore, the word "BUDDIES" becomes 02 21 04 04 09 05 19. For each number, the encryption process involves raising the number to the power of 'e' and then taking the modulo 'pq' result. Since the public key exponent is 3, each number is raised to the third power. The number 55, which is the product of the two primes used in the RSA algorithm, is the modulus. When a number larger than 55 is divided by 55, the remainder of that division is the encrypted value.

Let's solve the mathematical problem completely for each letter:

• 02^3 mod 55 = 8 mod 55 = 08
• 21^3 mod 55 = 9261 mod 55 = 36
• 04^3 mod 55 = 64 mod 55 = 09
• 04^3 mod 55 = 64 mod 55 = 09
• 09^3 mod 55 = 729 mod 55 = 14
• 05^3 mod 55 = 125 mod 55 = 15
• 19^3 mod 55 = 6859 mod 55 = 04

The encrypted message that Alice will receive is: 08 36 09 09 14 15 04.