Modular exponentiation raises an integer to a power and reduces the result modulo a specified integer. In RSA, encryption computes c = m^e mod n, while decryption computes m = c^d mod n. section 8.3.2
RSA message recovery
With p = 193, q = 727, n = 140311, e = 17653, and d = 77533, Bob encrypts m = 1337 as c = 1337^17653 mod 140311 = 133682. Alice recovers 1337 by calculating 133682^77533 mod 140311. section 8.3.2
Equation 8.10
\[\begin{aligned} \begin{aligned} c &= \text{Encrypt}(m, \text{PubKey}_{\text{Alice}}) \\ c &= m^e \bmod n \end{aligned} \label{equation:bob-rsa-encrypt} \end{aligned}\]Shows the RSA encryption equation that applies modular exponentiation to a plaintext using a public key. section 8.3.2
Equation 8.11
\[\begin{aligned} \begin{aligned} m &= \text{Decrypt}(c, \text{PrivKey}_{\text{Alice}}) \\ m &= c^d \bmod n \end{aligned} \label{equation:alice-rsa-decrypt} \end{aligned}\]Shows the corresponding decryption equation using the private exponent. section 8.3.2
