Cryptography

Cryptography is an interdisciplinary subject, drawing from several fields. Older forms of cryptography were chiefly concerned with patterns in language. More recently, the emphasis has shifted, and cryptography makes extensive use of mathematics, particularly discrete mathematics, including topics from number theory, information theory, computational complexity, statistics and combinatorics. Cryptography is also considered a branch of engineering, but it is considered to be an unusual one as it deals with active, intelligent and malevolent opposition (see cryptographic engineering and security engineering). Cryptography is a tool used within computer and network security.

Public key cryptography

Main article: Public key cryptography / Asymmetric key algorithm

Related Topics:
Public key cryptography - Asymmetric key algorithm

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Symmetric key encryption has a troublesome drawback — two people who wish to exchange confidential messages must share a secret key. The key must be exchanged in a secure way, and not by the means they would normally communicate. This is usually inconvenient, and public-key (or asymmetric) cryptography provides an alternative. In public key encryption there are two keys used, a public and a private key, with the public key for encryption and the private key for decryption. It must be difficult to derive the private key from the public key. This means that someone can freely send their public key out over an insecure channel and yet be sure that only they can decrypt messages encrypted with it.

Related Topics:
Private key - Channel

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Public key algorithms are usually based on hard computational problems. RSA, for example, relies on the (conjectured) difficulty of factorisation. For efficiency reasons, hybrid encryption systems are used in practice; a key is exchanged using a public-key cipher, and the rest of the communication is encrypted using a symmetric-key algorithm (which is typically much faster). Elliptic curve cryptography is a type of public-key algorithm that may offer efficiency gains over other schemes.

Related Topics:
Public key algorithm - Hard computational problems - RSA - Conjecture - Factorisation - Elliptic curve cryptography

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Asymmetric cryptography also provides mechanisms for digital signatures, which are a way to establish with high confidence (under the assumption that the relevant private key has not been compromised in any way) that the message received was sent by the claimed sender. Such signatures are often, in law or by implicit inference, seen as the digital equivalent of physical signatures on paper documents. In a technical sense, they are not as there is no physical contact nor connection between the "signer" and the "signed". Properly used high quality designs and implementations are capable of a very high degree of assurance, likely exceeding any but the most careful physical signature. Examples of digital signature protocols include DSA and ElGamal signatures. Digital signatures are central to the operation of public key infrastructure and many network security schemes (e.g., Kerberos, most VPNs, etc). Like encryption, hybrid algorithms are typically used in practice; rather than signing an entire document, a cryptographic hash of the document is signed instead.

Related Topics:
Digital signature - DSA - ElGamal signatures - Public key infrastructure - Kerberos - VPN - Cryptographic hash

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Asymmetric cryptography also provides the foundation for password-authenticated key agreement and zero-knowledge password proof techniques. This is important in light of empirical and theoretical proof that secure password-only authentication over a network cannot be achieved with just symmetric cryptography and hash functions.

Related Topics:
Password-authenticated key agreement - Zero-knowledge password proof

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