Solve the problem.
-Given the prime factors p and q, the encrytion exponent e, and the ciphertext C, apply the RSA algorithm to find the plaintext message. $\begin{array}{rccc}
\hline \mathrm{p} & \mathrm{q} & \mathrm{e} & \mathrm{C} \
\hline 23 & 17 & 11 & 114 \
\hline
\end{array}$

A) $9.528097579 \mathrm { e } + 14$
B) 114
C) $3.427189631 \mathrm { e } + 13$
D) 11

Question

Solve the problem.
-Given the prime factors p and q, the encrytion exponent e, and the ciphertext C, apply the RSA algorithm to find the plaintext message. $\begin{array}{rccc}
\hline \mathrm{p} & \mathrm{q} & \mathrm{e} & \mathrm{C} \
\hline 23 & 17 & 11 & 114 \
\hline
\end{array}$

A) $9.528097579 \mathrm { e } + 14$
B) 114
C) $3.427189631 \mathrm { e } + 13$
D) 11

Quizplus · Accepted Answer

To decrypt the message, calculate n = p * q = 23 * 17 = 391. Then, find φ(n) = (p-1)(q-1) = 22 * 16 = 352. The decryption key d is the modular inverse of e mod φ(n), which is 11 mod 352. Using the Extended Euclidean Algorithm, d = 32. Finally, decrypt the ciphertext C using the formula M = C^d mod n = 114^32 mod 391, which results in the plaintext message 11.

Solve the Problem pqeC231711114\begin{array}{rccc}\hline \mathrm{p} & \mathrm{q} & \mathrm{e} & \mathrm{C} \\\hline 23 & 17 & 11 & 114 \\\hline\end{array}p23​q17​e11​C114​​

Solve the Problem $\begin{array}{rccc}\hline \mathrm{p} & \mathrm{q} & \mathrm{e} & \mathrm{C} \\\hline 23 & 17 & 11 & 114 \\\hline\end{array}$