I'm trying to understand how routers that offer AES encryption manage their symmetric keys. I thought I'd be able to find some information in the NIAP security targets, but I can't figure it out. Are these keys self-generated and last for the life of the device? Are they generated via passphrase? Some other way?
Long story short, it looks like the document you linked to is referring to the NSA Suite B cryptography standard, RFC 6379. It links to these two documents, which are monsters. Checking out IPsec, IKE and ISAKMP would be more useful I think, but, if you're looking for the dirty details:
NIST Special Publication 800-56A : https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Ar2.pdf
NIST Special Publication 800-56B : https://csrc.nist.gov/publications/detail/sp/800-56b/archive/2009-08-28
Briefly, generation of AES keys depends on what AES is being used for. A good example, in the IPsec framework for VPNs, a router uses IKE (Internet Key Exchange) to create an ISAKMP security association (Internet Security Association and Key Management Protocol). IKE negotiates the hash, authentication, Diffie-Hellman group, lifetime of security of association and, what you're looking for: the encryption. (A nice mnemonic is HAGLE)
security association - Instance of security policy and keying material applied to a data flow.
Diffie-Hellman in IKEv1 or IKEv2 generate the asymmetric keys that protect the negotiation of the symmetric keys that are used for encryption, such as AES, DES(deprecated), or 3DES(legacy), some other symmetric key. IKEv2 can be found in RFC 4306. AES symmetric keys are used rather than the DH asymmetric keys because symmetric encryption is far more efficient.
Internet Security Association and Key Management Protocol : Internet IPsec protocol that negotiates, establishes, modifies, and deletes security associations. It also exchanges key generation and authentication data (independent of the details of any specific key generation technique), key establishment protocol, encryption algorithm, or authentication mechanism. Defined in RFC 2408.
It looks like the document you linked to is referring to the same/similar process on page 23 section 5.2.2. NIST Special Publication 80056A. The DH algorithm uses Discrete Logarithm Cryptography. Sounds Suite B to me: RFC 6379.
“Recommendation for PairWise Key Establishment Schemes Using Discrete Logarithm Cryptography” for elliptic curve based key establishment schemes and implementing “NIST curves” P256, P384 and [P521] (as defined in FIPS PUB 186 3, “Digital Signature Standard”)
NIST Special Publication 80056B, 'Recommendation for PairWise Key Establishment Schemes Using Integer Factorization Cryptography'for RSA based key establishment schemes]
Where elliptic curve-based key establishment could refer to Diffie-Hellman elliptic curve (DHEL), it's groups 19,20 and 24 use elliptic curve.