In asymmetric cryptography, what cannot be derived from the public key?

In asymmetric cryptography, what cannot be derived from the public key?

• A. The Private Key
• B. The Public Key
• C. The Algorithm
• D. The Hash

Answer: (A)

In asymmetric cryptography, the private key cannot be derived from the public key because they are connected by a one-way, trapdoor function: the public key is designed to reveal nothing about the secret key, while the secret key is needed to decrypt or sign. For example, in RSA, the public key uses a modulus and exponent (n, e); the private key depends on a value d that satisfies a relation with φ(n). Without factoring n or knowing φ(n), computing d is computationally infeasible, so the private key cannot be recovered from the public key. The other items can be determined or computed from the public key. The public key itself is the public material. The algorithm used (RSA, ECC, etc.) is typically identifiable from the key's format or accompanying data. A hash of the public key can be computed directly by applying a hash function to the key. Therefore, the only value that cannot be derived is the private key.

In asymmetric cryptography, the private key cannot be derived from the public key because they are connected by a one-way, trapdoor function: the public key is designed to reveal nothing about the secret key, while the secret key is needed to decrypt or sign. For example, in RSA, the public key uses a modulus and exponent (n, e); the private key depends on a value d that satisfies a relation with φ(n). Without factoring n or knowing φ(n), computing d is computationally infeasible, so the private key cannot be recovered from the public key.

The other items can be determined or computed from the public key. The public key itself is the public material. The algorithm used (RSA, ECC, etc.) is typically identifiable from the key's format or accompanying data. A hash of the public key can be computed directly by applying a hash function to the key. Therefore, the only value that cannot be derived is the private key.