In a system an RSA algorithm with $p = 5$ and $q = 11$, is implemented for data security. What is the value of the decryption key if the value of the encryption key is 27?
- A. 3
- B. 7
- C. 27
- D. 40
Answer: A. 3
Explanation: $n = p \times q = 55$. $\phi(n) = (5-1)(11-1) = 4 \times 10 = 40$.\n$e = 27$.\n$d \times e \equiv 1 \pmod{\phi(n)}$.\n$d \times 27 \equiv 1 \pmod{40}$.\nTry options: \n(a) $3 \times 27 = 81 \equiv 1 \pmod{40}$. Correct.