Key exchange (also key establishment) is a method in cryptography by which cryptographic keys are exchanged between two parties, allowing use of a cryptographic algorithm.
If the sender and receiver wish to exchange encrypted messages, each must be equipped to encrypt messages to be sent and decrypt messages received. The nature of the equipping they require depends on the encryption technique they might use. If they use a code, both will require a copy of the same codebook. If they use a cipher, they will need appropriate keys. If the cipher is a symmetric key cipher, both will need a copy of the same key. If it is an asymmetric key cipher with the public/private key property, both will need the other's public key.
Key exchange is done either in-band or out-of-band.
The key exchange problem describes ways to exchange whatever keys or other information are needed for establishing a secure communication channel so that no one else can obtain a copy. Historically, before the invention of public-key cryptography (asymmetrical cryptography), symmetric-key cryptography utilized a single key to encrypt and decrypt messages. For two parties to communicate confidentially, they must first exchange the secret key so that each party is able to encrypt messages before sending, and decrypt received ones. This process is known as the key exchange.
The overarching problem with symmetrical cryptography, or single-key cryptography, is that it requires a secret key to be communicated through trusted couriers, diplomatic bags, or any other secure communication channel. If two parties cannot establish a secure initial key exchange, they won't be able to communicate securely without the risk of messages being intercepted and decrypted by a third party who acquired the key during the initial key exchange.
Public-key cryptography uses a two-key system, consisting of the public and the private keys, where messages are encrypted with one key and decrypted with another. It depends on the selected cryptographic algorithm which key—public or private—is used for encrypting messages, and which for decrypting.
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