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Public-key cryptography


Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. The generation of such keys depends on cryptographic algorithms based on mathematical problems to produce one-way functions. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security.

Public key algorithms are fundamental security ingredients in modern cryptosystems, applications and protocols assuring the confidentiality, authenticity and non-repudiability of electronic communications and data storage. They underpin various Internet standards, such as Transport Layer Security (TLS), S/MIME, PGP, and GPG. Some public key algorithms provide key distribution and secrecy (e.g., Diffie–Hellman key exchange), some provide digital signatures (e.g., Digital Signature Algorithm), and some provide both (e.g., RSA).

Before the mid-1970s, all cipher systems were using symmetric key algorithms, in which the same cryptographic key is used with the underlying algorithm by both the sender and the recipient, who must both keep it secret. Of necessity, the key in every such system had to be exchanged between the communicating parties in some secure way prior to any use of the system - a secure channel. This requirement is never trivial and very rapidly becomes unmanageable as the number of participants increases, or when secure channels aren't available for key exchange, or when, (as is sensible cryptographic practice), keys are frequently changed. In particular, if messages are meant to be secure from other users, a separate key is required for each possible pair of users.

The most obvious application of a public key encryption system is in encrypting communication to provide confidentiality – a message that a sender encrypts using the recipient's public key can be decrypted only by the recipient's paired private key.

Because asymmetric key algorithms are nearly always much more computationally intensive than symmetric ones, in many cases it is common to exchange a key using a key-exchange algorithm, then transmit data using that key and a symmetric key algorithm. PGP, SSH, and the SSL/TLS family of schemes use this procedure, and are thus called hybrid cryptosystems.

All public key schemes are in theory susceptible to a "brute-force key search attack". Such attacks are however impractical if the amount of computation needed to succeed – termed the "work factor" by Claude Shannon – is out of reach of all potential attackers. In many cases, the work factor can be increased by simply choosing a longer key. But other algorithms may have much lower work factors, making resistance to a brute-force attack irrelevant. Some special and specific algorithms have been developed to aid in attacking some public key encryption algorithms – both RSA and ElGamal encryption have known attacks that are much faster than the brute-force approach.

Another potential security vulnerability in using asymmetric keys is the possibility of a "man-in-the-middle" attack, in which the communication of public keys is intercepted by a third party (the "man in the middle") and then modified to provide different public keys instead. Encrypted messages and responses must also be intercepted, decrypted, and re-encrypted by the attacker using the correct public keys for different communication segments, in all instances, so as to avoid suspicion.

For example, the certificate authority issuing the certificate must be trusted to have properly checked the identity of the key-holder, must ensure the correctness of the public key when it issues a certificate, must be secure from computer piracy, and must have made arrangements with all participants to check all their certificates before protected communications can begin. Web browsers, for instance, are supplied with a long list of "self-signed identity certificates" from PKI providers – these are used to check the bona fides of the certificate authority and then, in a second step, the certificates of potential communicators. An attacker who could subvert any single one of those certificate authorities into issuing a certificate for a bogus public key could then mount a "man-in-the-middle" attack as easily as if the certificate scheme were not used at all. In an alternate scenario rarely discussed, an attacker who penetrated an authority's servers and obtained its store of certificates and keys (public and private) would be able to spoof, masquerade, decrypt, and forge transactions without limit.

During the early history of cryptography, two parties would rely upon a key that they would exchange by means of a secure, but non-cryptographic, method such as a face-to-face meeting or a trusted courier. This key, which both parties kept absolutely secret, could then be used to exchange encrypted messages. A number of significant practical difficulties arise with this approach to distributing keys.