Skipjack is a symmetric block cipher historically associated with the Clipper chip initiative. Its defining parameters match the question: it operates on 64-bit blocks and uses an 80-bit key. The other options do not fit those exact sizes. Twofish is a 128-bit block cipher with key sizes up to 256 bits. Blowfish is a 64-bit block cipher, but its key size is variable from 32 up to 448 bits and is not fixed at 80 bits as a defining property.
Camellia is a 128-bit block cipher with key sizes of 128, 192, or 256 bits. Skipjack's smaller key size and legacy design make it unsuitable for modern security needs, but the question is purely about identifying the algorithm that matches an 80-bit key and 64-bit blocks. Therefore, the correct answer is Skipjack.

3DES (Triple DES) is a symmetric block cipher that retains DES's 64-bit block size while increasing effective security by applying DES multiple times. The common "two-key 3DES" variant uses two independent 56-bit DES keys (K1 and K2) in an Encrypt-Decrypt-Encrypt (EDE) sequence: Encrypt with K1, Decrypt with K2, then Encrypt again with K1. Because each DES key is 56 bits (ignoring parity bits), the total keying material is 112 bits. This matches the question's "112-bit key size and 64-bit block size." Plain DES uses only a 56-bit effective key and a 64-bit block size, so it does not match the 112-bit key size. AES has a 128-bit block size and key sizes of 128/192/256. IDEA uses a 64-bit block size but has a 128-bit key.
Therefore, the correct algorithm is 3DES. Although 3DES improved on DES, it is now considered legacy due to its small 64-bit block size (birthday-bound issues for large data volumes) and performance overhead compared to AES.

One-way server authentication is the standard model used by most TLS-enabled web services to prove the server's identity to a client. In this model, the server presents an X.509 certificate during the TLS handshake.
The client validates the certificate chain to a trusted root CA, checks hostname binding (CN/SAN), validates validity dates, and may check revocation status. If validation succeeds, the client gains cryptographic assurance that it is communicating with the holder of the private key corresponding to the server certificate's public key, and that the certificate is issued to the expected domain/identity. This proves the server's identity to the customer without requiring the customer to present a certificate. Mutual authentication would require both client and server to authenticate each other using certificates (commonly in certain enterprise APIs), but the question asks specifically about the web service proving its identity to the customer, which is satisfied by server-only authentication. One-way client authentication is the opposite direction (client proves identity to server). "End-to-end authentication" is a broader concept and not the specific TLS identity proof mechanism described here. Thus, one-way server authentication is the correct choice.

Symmetric cryptography uses a single shared secret key for both encryption and decryption. This contrasts with asymmetric cryptography, which uses a key pair (public/private). Symmetric algorithms (like AES, ChaCha20) are efficient and well-suited for bulk data encryption, but they require a secure method for key distribution because both parties must possess the same secret. Hashing is not a keyed operation by default (though HMAC is keyed); it maps arbitrary data to a fixed-size digest and is primarily used for integrity checking, fingerprints, and password hashing constructions. Padding is a data formatting technique (e.g., PKCS#7) used to align plaintext to a block size; it is not a cryptographic "operation" that uses a key.
Therefore, the cryptographic operation characterized by using one key shared between parties is symmetric encryption. In real systems, symmetric encryption is frequently combined with asymmetric methods for key exchange and with MACs/AEAD for integrity, producing the standard hybrid approach used in protocols like TLS and IPsec.

The string format $2a$08$... is a well-known identifier for the bcrypt password hashing scheme. In common password-hash notation, the prefix indicates the algorithm and parameters: "$2a$" denotes bcrypt (version
2a), and "08" indicates the cost factor (work factor) controlling how computationally expensive hashing is.
bcrypt is designed specifically for password storage: it includes a built-in salt and is intentionally slow and adaptive, making brute-force and GPU attacks far more expensive than fast general-purpose hashes like MD5 or SHA-512. NTLM and MD5 are obsolete for secure password storage due to speed and known weaknesses.
SHA-512, while cryptographically strong as a hash, is still too fast for password hashing unless used in a dedicated password-hashing construction (e.g., PBKDF2, scrypt, Argon2) with appropriate parameters and salts. Since the given hash clearly matches bcrypt's encoding, the correct algorithm is bcrypt, which incorporates salting and cost-based key stretching as part of its design.