The requirements are: (1) store an API key that a Lambda function will use, (2) ensure the secret is encrypted at rest using AWS KMS , and (3) the company must control key rotation , which implies using a customer managed KMS key (CMK) rather than an AWS managed key.

Option C meets the requirements by storing the API key in AWS Systems Manager Parameter Store as a SecureString parameter encrypted with a customer managed KMS key . SecureString is designed for sensitive configuration data and integrates with KMS so the organization can choose the CMK, manage its lifecycle, and control rotation policies. The Lambda function can retrieve the parameter at runtime using the AWS SDK, and IAM policies can tightly control access to the parameter and to the KMS key.

Option E also meets the requirements by storing the API key in a Lambda environment variable encrypted with a customer managed KMS key . Lambda encrypts environment variables at rest and allows you to specify a customer managed KMS key for encryption. This gives the company control over key rotation and key policy, satisfying the “must control key rotation” requirement. The function reads the value from the environment at runtime without additional network calls.

Why the other options fail:

A uses an AWS managed KMS key, which does not satisfy the requirement for the company to control rotation (you cannot manage rotation of AWS managed keys in the same way).

B is a plain String parameter, which is not encrypted as a secret and does not meet the at-rest encryption requirement.

D uses an AWS managed KMS key, again failing the company-controlled rotation requirement.

Therefore, the two valid solutions are C (Parameter Store SecureString with a customer managed CMK) and E (Lambda environment variable encrypted with a customer managed CMK).