gen-define-modular-exponentiation-in-rsa-and-give-one-short-work-a584

Define modular exponentiation in RSA and give one short worked example.

# Modular Exponentiation in RSA **Modular exponentiation** is the core operation in RSA encryption and decryption. It computes: $$c = m^e \bmod n$$ where: - **m** = message (plaintext or ciphertext) - **e** = exponent (public or private key) - **n** = modulus (part of the key) - **c** = result The operation raises a number to a power, then finds the remainder when divided by the modulus. ## Worked Example **Given:** - Message: m = 5 - Public exponent: e = 3 - Modulus: n = 14 **Encryption:** $$c = 5^3 \bmod 14$$ **Steps:** 1. Calculate: 5³ = 125 2. Divide by modulus: 125 ÷ 14 = 8 remainder **13** 3. Result: c = **13** **Verification:** 14 × 8 = 112, and 125 - 112 = 13 ✓ --- *Note: Real RSA uses much larger numbers (2048+ bits). For decryption, you'd compute m = c^d mod n using the private exponent d.*