Topic: Cryptography and Network Security
An RSA crypto system selects two primes $p=11$ and $q=13$. If the private key is $d=7$ which of the following can be the value of the public key 'e'?
- A. 103
- B. 143
- C. 21
- D. 19
Answer: A. 103
Explanation: In RSA, $n = p \times q = 11 \times 13 = 143$.
The totient $\phi(n) = (p-1)(q-1) = 10 \times 12 = 120$.
The public key $e$ and private key $d$ are related by $e \times d \equiv 1 \pmod{\phi(n)}$.
Given $d = 7$, we need to find $e$ such that $(e \times 7) \pmod{120} = 1$.
Testing the options:
(a) $103 \times 7 = 721$. $721 \pmod{120} = 1$ (since $120 \times 6 = 720$). This is correct.
(b) $143 \times 7 = 1001$. $1001 \pmod{120} \neq 1$.
(c) $21 \times 7 = 147$. $147 \pmod{120} = 27$.
(d) $19 \times 7 = 133$. $133 \pmod{120} = 13$.