what is the original message (number)encrypted using the RSA system with n= 77 and e = 43 if the encrypted message is 0202

Question

what is the original message (number)encrypted using the RSA system with n= 77 and e = 43 if the encrypted message is 0202...............................

need solution with explinations

Answer 1

Hi Muhammad, essentially what this boils down to is brute force cracking of RSA encryption. That is possible in this case because of the small message size, small key size, and lack of padding.

Your question is a bit unclear as to whether the message is 130 (0202, in octal), 202 base 10, or a string "0202". I'm going to assume it is octal 202 (the integer 130 in base 10) for my example.

The formula for RSA encryption is c = m^e % n, where c is the ciphertext (encrypted message) and m is the original message. So to brute force the original message, the method would involve iterating through all possible messages and checking if the result of the encryption formula matches the encrypted message.

Here's a simple python script that can do this. If I'm incorrect regarding my interpretation of the message value, you'll need to modify this script accordingly.

# Known values

e = 43

n = 77

c = 130

# Iterate through possible messages, and check if result of encryption

# matches known ciphertext

for i in range(0, 999):

if i^e % n == c:

print(i)