Modular arithmetic is defined as performing calculations within a finite set of numbers.

• A. Performing calculations within a finite set of numbers.
• B. Using symmetric keys to encrypt data.
• C. Verifying identity.
• D. Granting permissions.

Answer: (A)

Modular arithmetic involves doing calculations where results are reduced modulo a fixed number, keeping all results inside a finite range (typically from 0 up to modulus minus one). This wrap-around behavior is what makes the set of possible results finite, so the description “performing calculations within a finite set of numbers” matches exactly how modular arithmetic works. In practice, every operation yields a remainder when divided by the modulus, which is why many cryptographic algorithms rely on arithmetic done modulo some number.

The other options point to different cryptographic concepts rather than the arithmetic framework itself: encryption with a symmetric key, identity verification, and granting permissions are about key management, authentication, and access control, respectively, not about performing arithmetic within a finite set.