Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. There are many kinds of public-key cryptosystems, with different security goals, including digital signature, Diffie–Hellman key exchange, public-key key encapsulation, and public-key encryption. Public key algorithms are fundamental security primitives in modern cryptosystems, including applications and protocols that offer assurance of the confidentiality and authenticity of electronic communications and data storage. They underpin numerous Internet standards, such as Transport Layer Security (TLS), SSH, S/MIME, and PGP. Compared to symmetric cryptography, public-key cryptography can be too slow for many purposes, so these protocols often combine symmetric cryptography with public-key cryptography in hybrid cryptosystems.
Description Before the mid-1970s, all cipher systems used 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 the key 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 – for instance, via a secure channel. This requirement is never trivial and very rapidly becomes unmanageable as the number of participants increases, when secure channels are not available, 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. By contrast, in a public-key cryptosystem, the public keys can be disseminated widely and openly, and only the corresponding private keys need be kept secret. The two best-known types of public key cryptography are digital signature and public-key encryption:
In a digital signature system, a sender can use a private key together with a message to create a signature. Anyone with the corresponding public key can verify whether the signature matches the message, but a forger who does not know the private key cannot generate any message/signature pair that will pass verification with the public key. For example, a software publisher can create a signature key pair and include the public key in software installed on computers. Later, the publisher can distribute an update to the software signed using the private key, and any computer receiving an update can confirm it is genuine by verifying the signature using the public key. As long as the software publisher keeps the private key secret, even if a forger can distribute malicious updates to computers, they cannot convince the computers that any malicious updates are genuine.
In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message. For example, a journalist can publish the public key of an encryption key pair on a website so that sources can send secret messages to the news organization in ciphertext. Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropper reading email on its way to the journalist cannot decrypt the ciphertexts. However, public-key encryption does not conceal metadata like what computer a source used to send a message, when they sent it, or how long it is. Public-key encryption on its own also does not tell the recipient anything about who sent a message—it just conceals the content of the message. Applications built on public-key cryptography include authenticating web servers with TLS, digital cash, password-authenticated key agreement, authenticating and concealing email content with OpenPGP or S/MIME, and time-stamping services and non-repudiation protocols. One important issue is confidence or proof that a particular public key is authentic, i.e., that it is correct and belongs to the person or entity claimed, and has not been tampered with or replaced by some (perhaps malicious) third party. There are several possible approaches to addressing this issue, including: A public key infrastructure (PKI), in which one or more third parties, known as certificate authorities, certify ownership of key pairs. TLS relies upon this. This implies that the PKI system (software, hardware, and management) can be trusted by all involved. A web of trust decentralizes authentication by using individual endorsements of links between a user and their public key. PGP uses this approach, in addition to lookup in the domain name system (DNS). The DKIM system for digitally signing emails also uses this approach.
Hybrid cryptosystems Because asymmetric key algorithms are nearly always much more computationally intensive than symmetric ones, it is common to use a public/private asymmetric key-exchange algorithm to encrypt and exchange a symmetric key, which is then used by symmetric-key cryptography to transmit data using the now-shared symmetric key. PGP, SSH, and the SSL/TLS family of schemes use this procedure; they are thus called hybrid cryptosystems. The initial asymmetric cryptography-based key exchange to share a server-generated symmetric key from the server to client has the advantage of not requiring that a symmetric key be pre-shared manually, such as on printed paper or discs transported by a courier, while providing the higher data throughput of symmetric key cryptography over asymmetric key cryptography for the remainder of the shared connection.
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