[Trae Johnson]

Three Encryption Methods are symmetric, asymmetric, and hash functions, each play a vital role with their application in information technology. Determining which one is to be used depends on the nature of specific security requirements. Whether it be for speed, key exchange, or integrity verification of key data. The efficient application of these encryption methods will make certain that data confidentiality, integrity, and authenticity are guaranteed in several applications.

1. Symmetric Key Encryption
Symmetric key encryption, also known as private key encryption, is a process in which the same key is used to encrypt and decrypt data. Some of the generally utilized symmetric encryption algorithms are Advanced Encryption Standard, Data Encryption Standard, and Triple DES. Among them, AES is utilized because of its efficiency and security to protect sensitive data of customers.

Symmetric encryption is appropriate in the encryption of large volumes of data, since it has a relatively fast processing speed. It is applied in the encryption of data at rest, such as on hard drives and in databases. Applications include file system security, database encryption, and data transfer within secure networks where both sender and receiver share the secret key. However, symmetric encryption requires a secure method for key exchange, which might be challenging to realize.

2. Asymmetric Key Encryption
Asymmetric key encryption, or public key encryption, involves a pair of keys: one for the actual encryption, a so-called public key, and another for its decryption, a private key. This hence provides better security since the public key can be distributed without worrying about its secrecy while the private key remains safe. The common algorithms used in this regard are RSA, or Rivest-Shamir-Adleman, ECC or Elliptic Curve Cryptography, and Diffie-Hellman key exchange.

Asymmetric encryption is used in applications that require the exchange of keys over an insecure network. It is widely used for securing e-mail through PGP/GPG, for establishing secure web connections, SSL/TLS, and for digital signatures for authentication and integrity verification, among others, in e-commerce and other online transactions. Asymmetric encryption is much slower than symmetric encryption. It is generally used with symmetric encryption so as to take advantage of both security and efficiency.

3. Hash Functions
Hash functions refer to those forms of cryptographic encryption that convert input data into a fixed-size hash value representing the unique contribution of that data. The most common hash functions include SHA-256, or Secure Hash Algorithm 256-bit, and MD5, or Message Digest 5. As opposed to all other forms of encryption, hash functions are one-way; once an instance is committed to a hash, it is impossible to use the hash function itself to determine the original data in any instance, as elaborated by Schneier (2015).

Appropriate Usage:
They are primarily employed in ensuring data integrity and not necessarily in encrypting the data itself. They ensure that data, even passwords or files, are not tampered with during transfer. Another equally important application where hash functions are put into work is digital signatures, message authentication codes, and blockchains. All these involve ensuring data integrity and verification. -Ferguson, Schneier, & Kohno, 2010.

References
Ferguson, N., Schneier, B., & Kohno, T. (2010). Cryptography engineering: Design principles and practical applications. Wiley.

Katz, J., & Lindell, Y. (2020). Introduction to modern cryptography (3rd ed.). CRC Press.

Menezes, A. J., Vanstone, S. A., & Oorschot, P. C. (2018). Handbook of applied cryptography. CRC Press.

Paar, C., & Pelzl, J. (2010). Understanding cryptography: A textbook for students and practitioners. Springer.

Schneier, B. (2015). Applied cryptography: Protocols, algorithms, and source code in C, 20th anniversary ed., Wiley.

Stallings, W. (2017). Cryptography and network security: Principles and practice, 7th ed., Pearson.