RSA is based on which area of mathematics?

RSA is based on which area of mathematics?

• A. Modular arithmetic and prime numbers
• B. Elliptic curves
• C. Discrete logarithm
• D. Hash functions

Answer: (A)

RSA rests on modular arithmetic with large integers built from prime numbers. The modulus is the product of two large primes, and all encryption and decryption operations occur modulo that number. The public key uses an exponent, and the private key is a modular inverse of that exponent modulo φ(n), so decryption with the private key undoes the encryption. The security comes from the difficulty of factoring the product of two large primes; if someone could factor n, they could derive φ(n) and compute the private key. This approach is grounded in prime numbers and modular arithmetic, not elliptic curves, the discrete logarithm problem, or hash functions (which are used in other contexts but not the basis of RSA’s math).

RSA rests on modular arithmetic with large integers built from prime numbers. The modulus is the product of two large primes, and all encryption and decryption operations occur modulo that number. The public key uses an exponent, and the private key is a modular inverse of that exponent modulo φ(n), so decryption with the private key undoes the encryption. The security comes from the difficulty of factoring the product of two large primes; if someone could factor n, they could derive φ(n) and compute the private key. This approach is grounded in prime numbers and modular arithmetic, not elliptic curves, the discrete logarithm problem, or hash functions (which are used in other contexts but not the basis of RSA’s math).