Examples
The block cipher Rijndael/AES uses a key of up to 256 bits, resulting in a key space containing over 2256 (or 1.1579 × 1077) keys. This makes it computationally unfeasible to check each possible key by brute force.
In the DES block cipher, a 56-bit key is used, resulting in a relatively small key space of size 256 (or 7.2058 x 1016).
Searching for passwords using lists of dictionary words and other common selections can often produce the correct answer in far less time than a brute force search of all character combinations.
The ROT13 cipher is only intended to prevent people from accidentally reading messages (e.g. movie plot details). While it would appear that there is no key (the key space being therefore empty), in fact a constant key, implied in the algorithm, is used. The key space has therefore exactly one key, and it has dimension zero, so that no bits are required to select it (the key parameter is the empty vector).
Read more about this topic: Key Space (cryptography)
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