Key management deals with the secure generation, distribution, and storage of keys. Secure methods of key management are extremely important. Once a key is randomly generated (see Question 220.127.116.11), it must remain secret to avoid unfortunate mishaps (such as impersonation). In practice, most attacks on public-key systems will probably be aimed at the key management level, rather than at the cryptographic algorithm itself.
Users must be able to securely obtain a key pair suited to their efficiency and security needs. There must be a way to look up other people's public keys and to publicize one's own public key. Users must be able to legitimately obtain others' public keys; otherwise, an intruder can either change public keys listed in a directory, or impersonate another user. Certificates are used for this purpose (see Question 18.104.22.168). Certificates must be unforgeable. The issuance of certificates must proceed in a secure way, impervious to attack. In particular, the issuer must authenticate the identity and the public key of an individual before issuing a certificate to that individual.
If someone's private key is lost or compromised, others must be made aware of this, so they will no longer encrypt messages under the invalid public key nor accept messages signed with the invalid private key. Users must be able to store their private keys securely, so no intruder can obtain them, yet the keys must be readily accessible for legitimate use. Keys need to be valid only until a specified expiration date but the expiration date must be chosen properly and publicized in an authenticated channel.