In AES, the number of rounds is explicitly tied to the key length. AES-128 uses 10 rounds, AES-192 uses 12 rounds, and AES-256 uses 14 rounds. The purpose of additional rounds is to increase diffusion and confusion, strengthening resistance against cryptanalysis as the key schedule and state transformations iterate more times. Although key length primarily affects brute-force resistance, AES's designers and standardization parameters link longer keys with more rounds to maintain security margins across variants, especially considering differences in the key schedule structure. Thus, as key length increases from 128 to 192 to 256 bits, the number of rounds increases correspondingly from 10 to
12 to 14. This relationship is fixed by the AES specification and does not vary dynamically at runtime.
Therefore, the correct correlation is that the number of rounds increases as the key length increases.

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.

Lightweight cryptography is important because many modern systems operate in constrained environments- IoT sensors, embedded controllers, wearables, and mobile devices-where CPU, memory, storage, bandwidth, and battery power are limited. Traditional "heavy" cryptographic suites may be too slow, too energy-intensive, or too large in code footprint for these platforms, leading to insecure workarounds or disabling security entirely. Lightweight cryptographic primitives and profiles are designed to deliver strong security properties (confidentiality and integrity, often via AEAD) while fitting within tight resource budgets and real-time constraints. This is essential as IoT and mobile ecosystems expand, increasing the attack surface and the consequences of compromised devices (botnets, surveillance, physical safety risks). Lightweight cryptography is not meant to "limit encryption tools" or complicate protection; it enables practical, deployable security where otherwise implementations might be weak or absent. High-speed network communication can benefit from efficient crypto too, but the defining modern driver is constrained-device security. Therefore, the correct reason is addressing the security needs of IoT devices and mobile applications.

Data integrity means ensuring that information has not been modified without authorization. Digital signatures are a core cryptographic technique that provides integrity by binding a message (typically its hash) to the signer's private key. The signer creates a signature over the message digest; the verifier checks it with the signer's public key and recomputes the digest. Any change to the message alters the digest and causes verification to fail, revealing tampering. Digital signatures also support authenticity (verifying the signer) and can contribute to nonrepudiation under proper key-management and policy controls, but integrity is a primary guarantee they deliver. "Authentication" is broader and can be achieved by other means, but it is not as directly tied to integrity as signatures in this option set. "Non-repudiation" is an outcome/goal rather than a standalone integrity technique. "Steganography" hides the existence of data and does not inherently protect integrity. Therefore, among these options, digital signatures are the best cryptographic technique for ensuring data integrity.

The value 51 mod 11 is the remainder after dividing 51 by 11. Modular arithmetic is widely used in cryptography to keep computations within a finite set of residues, such as in RSA where values are taken modulo n, or in Diffie-Hellman where exponents and group elements are reduced modulo a prime. To compute 51 mod 11, find the largest multiple of 11 less than or equal to 51. Multiples of 11 are 11, 22, 33, 44, 55. The closest without exceeding 51 is 44. Subtracting gives 51 # 44 = 7, so the remainder is 7. Therefore, 51 mod 11 = 7, matching option "07." This remainder is always in the range
0 through 10 because the modulus is 11. Such residue computations underpin the "wraparound" behavior that makes modular exponentiation and inverse computations well-defined in cryptographic groups.