Answer
$701$
Work Step by Step
To decrypt the message 1101 using RSA encryption with private keys \( n = 911 \) and \( d = 5 \), we'll use the following decryption formula:
\[ M = C^d \mod n \]
Where:
- \( M \) is the decrypted message
- \( C \) is the ciphertext (1101 in this case)
- \( d \) is the private exponent
- \( n \) is the modulus
Plugging in the values:
\[ M = 1101^5 \mod 911 \]
We have:
\[ 1101^5 = (911+190)^5 \]
Now, taking the modulus:
\[ 1101^5 \mod 911 = 190^5\mod 911 =(911\cdot 271,900,109+701) \mod 911 = 701 \]
So, the decrypted message \( M \) is 701.
