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→Practical Considerations
* Public key cryptography is very susceptible to the manipulation of public keys by an attacker interposed between the two parties at the time that the public keys are shared (e.g., when someone is downloading your public key from your website). This is called a ''Man in the Middle'' (MIM) attack.
* Public key cryptography is susceptible to theft of the private key (e.g., hacking your system, or stealing your laptop). The private key is therefore often protected with a passphrase.
* Cryptographic systems can be broken by guessing the key. The easiest way to do this is to sequentially try all possible key values. As computers become faster, more keys can be tested in a reasonable length of time, so keys must be made longer. Each bit added to the length of the key doubles the number of possible key values, doubling the average length of time that it will take to guess the key.
== Uses for Public Key Cryptography ==
