Cryptographic keys for encrypted data stored in the cloud should be ______________. Response:

While 128 bits is a common minimum recommended length for symmetric keys, key length alone does not address the critical security concern of key management and storage location.

Storing cryptographic keys with the cloud provider introduces a single point of failure and potential for compromise if the provider's systems are breached. By managing keys externally, such as through a customer-controlled Hardware Security Module (HSM) or a Bring Your Own Key (BYOK) model, organizations retain exclusive control over their encryption keys, significantly enhancing data security and compliance.

Splitting keys into groups for different data sets is a key management practice, but it's secondary to the fundamental principle of not co-locating keys with the encrypted data at the provider.

Generating keys with redundancy is important for availability and disaster recovery of the keys themselves, but it does not address the security concern of where the keys are stored relative to the encrypted data.