Discussion
Using RSA algorithm, what is the value of cipher text C, if the plain text M = 5 and p = 3, q = 11 & d = 7 ?
Answer: D
In RSA with p = 3 and q = 11 the modulus is n = pq = 33 and \(\phi(n) = (p-1)(q-1) = 20\). The private exponent d = 7 needs a public exponent e with \(ed \equiv 1 \pmod{20}\), and since \(3 \times 7 = 21 \equiv 1\), e = 3. The cipher text is then
\[ C = M^{e} \bmod n = 5^{3} \bmod 33 \]\[ 125 = 3 \times 33 + 26, \quad C = 26 \]The options 33 (the modulus itself), 5 (the plain text) and 25 do not satisfy this calculation. The keyed answer is 26.
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