On what mathematical basis is RSA cryptography primarily built?

On what mathematical basis is RSA cryptography primarily built?

• A. The difficulty of factoring large integers and Euler's totient properties.
• B. The difficulty of solving discrete logarithms.
• C. Hash function preimage resistance.
• D. Quantum entanglement properties.

Answer: (A)

RSA cryptography rests on the fact that multiplying two primes to form a large number is easy, but factoring that large number back into the primes is hard. When you generate keys, you compute n = p q and φ(n) = (p−1)(q−1). The public key uses n and an exponent e chosen so that e and φ(n) are compatible, and the private key is the modular inverse d of e modulo φ(n). The security comes from not knowing p and q, so φ(n) and thus d cannot be derived from the public information alone. If someone could factor n, they could compute φ(n) and then determine d, breaking the system. This is why the difficulty of factoring large integers, together with the Euler totient relationships used to connect the public and private keys, is the fundamental basis of RSA. The other ideas correspond to different areas: discrete logarithms relate to other protocols, hash preimage resistance is about hashing, and quantum entanglement is not used to build RSA (though quantum computing could threaten RSA by enabling factoring).

RSA cryptography rests on the fact that multiplying two primes to form a large number is easy, but factoring that large number back into the primes is hard. When you generate keys, you compute n = p q and φ(n) = (p−1)(q−1). The public key uses n and an exponent e chosen so that e and φ(n) are compatible, and the private key is the modular inverse d of e modulo φ(n). The security comes from not knowing p and q, so φ(n) and thus d cannot be derived from the public information alone. If someone could factor n, they could compute φ(n) and then determine d, breaking the system. This is why the difficulty of factoring large integers, together with the Euler totient relationships used to connect the public and private keys, is the fundamental basis of RSA. The other ideas correspond to different areas: discrete logarithms relate to other protocols, hash preimage resistance is about hashing, and quantum entanglement is not used to build RSA (though quantum computing could threaten RSA by enabling factoring).