Which type of encryption algorithm uses two different keys: a public key for encryption and a private key for decryption?

Asymmetric encryption, also known as public-key cryptography, is designed to use a pair of mathematically related keys. One key, the public key, is made available to anyone and is used to encrypt messages. The second key, the private key, is kept secret by its owner. A message encrypted with the public key can only be decrypted by the corresponding private key. This two-key system is a fundamental principle of asymmetric algorithms like RSA and ECC, providing confidentiality, authentication, and non-repudiation.

A. Hashing algorithm: This is a one-way function that generates a fixed-length hash value from input data; it is not reversible and is used for integrity, not encryption.

B. HMAC algorithm: This uses a cryptographic hash function and a single secret key to generate a message authentication code for integrity and authenticity, not for encryption.

D. Symmetric encryption: This method uses a single, shared secret key for both the encryption and decryption of data, unlike the two-key system described.

1. Cisco Systems, Inc., "Next-Generation Cryptography," Cisco Public White Paper, 2016. In the "Asymmetric Algorithms" section (p. 3), it states: "Asymmetric algorithms (also called public-key algorithms) use two different keys, a public key and a private key... Data encrypted with the public key can be decrypted only with the private key."

2. Kaufman, C., Perlman, R., & Speciner, M., Network Security: Private Communication in a Public World (2nd ed.). Prentice Hall, 2002. Chapter 6, "Public Key Algorithms," Section 6.1 "Introduction to Public Key Algorithms," explains that in a public key system, "encryption and decryption keys are different. The encryption key... can be made public. The decryption key... is kept private."

3. Rivest, R. L., "Lecture 15: Public-Key Cryptography, RSA," MIT OpenCourseWare, 6.046J Design and Analysis of Algorithms, Spring 2015. The lecture notes explicitly define public-key cryptography: "Each user has a public key P and a private key S... To encrypt a message M for user A, Bob computes C = PA(M)... To decrypt C, Alice computes M = SA(C)." This demonstrates the use of two distinct keys.