Case b ( refer Figure 1 From The chapter Message Authentication Codes in William Stallings )is an example of digital signature.

Cryptographic hash functions are mathematical algorithms that convert plaintext data into a unique identifier. They are used in cryptography for a variety of purposes, including: Encryption, Password management, Digital signatures, Bitcoin creation, Message security, Password security, Cryptocurrency.  Here are some other uses for hash functions: Identifying files: Hashes are used to identify files on peer-to-peer filesharing networks. Load balancing: Hashing is used in load-balancing algorithms to distribute requests to servers in a network. Blockchain: Hashing is used in blockchain... Show more

Cryptographic hash functions are mathematical algorithms that convert plaintext data into a unique identifier. They are used in cryptography for a variety of purposes, including: Encryption, Password management, Digital signatures, Bitcoin creation, Message security, Password security, Cryptocurrency. 

Here are some other uses for hash functions:
Identifying files: Hashes are used to identify files on peer-to-peer filesharing networks.
Load balancing: Hashing is used in load-balancing algorithms to distribute requests to servers in a network.
Blockchain: Hashing is used in blockchain technology to secure the integrity and consensus of the blockchain. 

Hash functions can also be applied in:
Public Key Infrastructure (PKI) for digital signature creation
IPsec for data integrity and authentication
Wi-Fi Protected Access (WPA) for securing wireless networks 

Hash Functions Based on Cipher Block Chaining: The hash function takes an input message and partitions it into L fixed-sized blocks of b bits each. If necessary, the final block is padded to bits. The final block also includes the value of the total length of the input to the hash function. The inclusion of the length makes the job of the opponent more difficult.

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