The type of cryptography in which one key is public and the other is private is called?

The correct answer is Asymmetric Key cryptography. Asymmetric key cryptography, also known as public-key cryptography, is a cryptographic system that uses pairs of keys: a public key, which can be widely distributed, and a private key, which is known only to the owner. Data encrypted with the public key can only be decrypted with the corresponding private key, and vice-versa. This unique design allows for secure communication and digital signatures without the need for a prior secure exchange of a shared secret key, fundamentally solving the key distribution problem inherent in other cryptographic methods. It is the backbone of many secure internet communications, including TLS/SSL protocols.

• Hash cryptography is incorrect because hash functions are one-way mathematical algorithms that produce a fixed-size output (a hash value) from an input of arbitrary size. They are used for data integrity verification and password storage but do not involve a pair of public and private keys for encryption and decryption.
• Symmetric Key cryptography is incorrect because it uses a single, secret key for both encryption and decryption. Both the sender and receiver must possess this same key, which requires a secure method for key exchange prior to communication.
• Quantum cryptography is incorrect because it is an emerging field that uses principles of quantum mechanics, such as superposition and entanglement, to provide secure communication. While it aims to offer stronger security, it describes a different underlying mechanism for key generation and distribution, rather than the specific public/private key pair structure described in the question.