= Cryptographic key
{title2=$k$}
A cryptographic key is a <parameter> selecting a particular transformation from a family of <algorithms> in <cryptography>. For an encryption family, correctness requires
$$
D_k(E_k(m))=m
$$
for every allowed <plaintext> $m$ and appropriate encryption/decryption keys. In <symmetric-key cryptography>, the communicating parties share a secret key. In <public-key cryptography>, the public encryption or verification key is paired with a private decryption or signing key.
For a one-bit example, $E_k(m)=m\mathbin\oplus k$ and $D_k(c)=c\mathbin\oplus k$ recover the message because applying <exclusive or> twice with the same <bit> cancels it. The <one-time pad> extends this to a uniformly random independent key as long as the message. Its secrecy depends on the key distribution and use, not on hiding the XOR algorithm. The number of possible keys gives a brute-force search space, but key length alone does not establish the security of a cryptographic construction.
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