The NIST security life cycle components and their activities are correctly matched in option C:
* Implement (1) corresponds with iv. Sets security controls within an enterprise architecture. This involves integrating the selected security controls into the enterprise architecture during the implementation phase.
* Authorize (2) matches with iii. Determines risk to organizational operations and assets. Authorization involves assessing the risks to the organization's operations and assets and determining if the implemented controls are adequate.
* Categorize (3) aligns with v. Defines criticality of information system according to potential worst-case.
Categorization is the process of determining the criticality of information systems based on the potential impact of worst-case scenarios.
* Select (4) is associated with i. Determines security control effectiveness. Selection involves choosing the appropriate security controls and determining their effectiveness in protecting the system.
References: The information provided is based on the NIST guidelines for the system development life cycle, which include security considerations as an integral part of the process1234.

The Birthday Attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. This attack is relevant to the question as it involves attacking cryptographic hash functions based on the probability of collisions. In the context of hash functions, a collision occurs when two different inputs produce the same hash output. The Birthday Attack leverages the fact that in a set of randomly chosen keys, it is probable that two keys will have the same hash value. This is analogous to the birthday paradox, where in a group of people, there's a high probability that two individuals will share the same birthday. The attack does not rely on the strength or weakness of the hash function itself, but on the statistical likelihood of these collisions occurring, which is surprisingly high even for large sets of possible hash values.
References: The explanation is based on the principles of cryptographic hash functions and the birthday problem as described in standard cryptography literature and resources123.