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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 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. In in-band key exchange, keys are exchanged through the same communication channel that will be encrypted. In out-of-band key, keys are exchanged through a channel else than the one that will be encrypted.
The key exchange problem is how to exchange whatever keys or other information are needed so that no one else can obtain a copy. Historically, this required trusted couriers, diplomatic bags, or some other secure channel. With the advent of public key / private key cipher algorithms (i.e., asymmetric ciphers), the encrypting key (AKA, the public key of a pair) could be made public, since (at least for high quality algorithms) no one without the decrypting key (AKA, the private key of that pair) could decrypt the message.
In principle, the only remaining problem was to be sure (or at least confident) that a public key actually belonged to its supposed owner. Because it is possible to 'spoof' another's identity in any of several ways, this is not a trivial or easily solved problem, particularly when the two users involved have never met and know nothing about each other.
In 1976, Whitfield Diffie and Martin Hellman published a cryptographic protocol called the Diffie–Hellman key exchange (D–H) based on concepts developed by Hellman's PhD student Ralph Merkle. The protocol enables users to securely exchange secret keys even if an opponent is monitoring that communication channel. The D–H key exchange protocol, however, does not by itself address authentication (i.e. the problem of being sure of the actual identity of the person or 'entity' at the other end of the communication channel). Authentication is crucial when an opponent can both monitor and alter messages within the communication channel (AKA man-in-the-middle or MITM attacks) and was addressed in the fourth section of the paper.
Public key infrastructures (PKIs) have been proposed as a way around this problem of identity authentication. In their most usual implementation, each user applies to a 'certificate authority' for a digital certificate which serves for other users as a non-tamperable authentication of identity, at the risk of compromising every user in case the CA itself is compromised.
Several countries and other jurisdictions have passed legislation or issued regulations encouraging PKIs by giving (more or less) legal effect to these digital certificates. Several commercial firms, and a few government departments, have established such certificate authorities. VeriSign is the most prominent commercial firm.
This does nothing to solve the problem though, as the trustworthiness of the CA itself is still not guaranteed for any particular individual. It is a form of argument from authority fallacy. For actual trustworthiness, personal verification that the certificate belongs to the CA and establishment of trust in the CA are required. This is usually not possible.
For those new to such things, these arrangements are best thought of as electronic notary endorsements that “this public key belongs to this user”. As with notary endorsements, there can be mistakes or misunderstandings in such vouchings. Additionally, the notary itself can be untrusted. There have been several high-profile public failures by assorted certificate authorities.
At the other end of the conceptual range is the web of trust system, which avoids central Certificate Authorities entirely. Each user is responsible for getting any certificate from another before using that certificate to communicate with, vet digital signatures from, ... the user claimed to be associated with the particular public key in a certificate. PGP (and GPG, an implementation of the OpenPGP Internet Standard) employ just such a web of trust mechanism. Together they are the most widely used high quality cryptographic system in the world.
The BB84 key exchange protocol—like any quantum key exchange protocol—exploits certain properties of quantum physics to ensure its security. Since quantum mechanics ensures physical traces as a result of mere observation, it provides protection against man-in-the-middle attacks that cannot, as a matter of physical principle, be circumvented.