In cryptography, a key is a piece of information (a parameter) that determines the functional output of a cryptographic algorithm. For encryption algorithms, a key specifies the transformation of plaintext into ciphertext, and vice versa for decryption algorithms. Keys also specify transformations in other cryptographic algorithms, such as digital signature schemes and message authentication codes. In cryptography, a key is a piece of information (a parameter) that determines the functional output of a cryptographic algorithm. For encryption algorithms, a key specifies the transformation of plaintext into ciphertext, and vice versa for decryption algorithms. Keys also specify transformations in other cryptographic algorithms, such as digital signature schemes and message authentication codes. In designing security systems, it is wise to assume that the details of the cryptographic algorithm are already available to the attacker. This is known as Kerckhoffs' principle — 'only secrecy of the key provides security', or, reformulated as Shannon's maxim, 'the enemy knows the system'. The history of cryptography provides evidence that it can be difficult to keep the details of a widely used algorithm secret (see security through obscurity). A key is often easier to protect (it's typically a small piece of information) than an encryption algorithm, and easier to change if compromised. Thus, the security of an encryption system in most cases relies on some key being kept secret. Trying to keep keys secret is one of the most difficult problems in practical cryptography; see key management. An attacker who obtains the key (by, for example, theft, extortion, dumpster diving, assault, torture, or social engineering) can recover the original message from the encrypted data, and issue signatures. Keys are generated to be used with a given suite of algorithms, called a cryptosystem. Encryption algorithms which use the same key for both encryption and decryption are known as symmetric key algorithms. A newer class of 'public key' cryptographic algorithms was invented in the 1970s. These asymmetric key algorithms use a pair of keys—or keypair—a public key and a private one. Public keys are used for encryption or signature verification; private ones decrypt and sign. The design is such that finding out the private key is extremely difficult, even if the corresponding public key is known. As that design involves lengthy computations, a keypair is often used to exchange an on-the-fly symmetric key, which will only be used for the current session. RSA and DSA are two popular public-key cryptosystems; DSA keys can only be used for signing and verifying, not for encryption. Part of the security brought about by cryptography concerns confidence about who signed a given document, or who replies at the other side of a connection. Assuming that keys are not compromised, that question consists of determining the owner of the relevant public key. To be able to tell a key's owner, public keys are often enriched with attributes such as names, addresses, and similar identifiers. The packed collection of a public key and its attributes can be digitally signed by one or more supporters. In the PKI model, the resulting object is called a certificate and is signed by a certificate authority (CA). In the PGP model, it is still called a 'key', and is signed by various people who personally verified that the attributes match the subject. In both PKI and PGP models, compromised keys can be revoked. Revocation has the side effect of disrupting the relationship between a key's attributes and the subject, which may still be valid. In order to have a possibility to recover from such disruption, signers often use different keys for everyday tasks: Signing with an intermediate certificate (for PKI) or a subkey (for PGP) facilitates keeping the principal private key in an offline safe. Deleting a key on purpose to make the data inaccessible is called crypto-shredding. For the one-time pad system the key must be at least as long as the message. In encryption systems that use a cipher algorithm, messages can be much longer than the key. The key must, however, be long enough so that an attacker cannot try all possible combinations. A key length of 80 bits is generally considered the minimum for strong security with symmetric encryption algorithms. 128-bit keys are commonly used and considered very strong. See the key size article for a more complete discussion.