Definition
Quantum cryptography is an effort to allow two
users of a common communication channel to create a body of shared and secret
information. This information, which generally takes the form of a random string
of bits, can then be used as a conventional secret key for secure communication.
It is useful to assume that the communicating parties initially share a small
amount of secret information, which is used up and then renewed in the exchange
process, but even without this assumption exchanges are possible. The
advantage of quantum cryptography over traditional key exchange methods is that
the exchange of information can be shown to be secure in a very strong sense,
without making assumptions about the intractability of certain mathematical problems.
Even when assuming hypothetical eavesdroppers with unlimited computing power,
the laws of physics guarantee (probabilistically) that the secret key exchange
will be secure, given a few other assumptions. Cryptography is the art of
devising codes and ciphers, and cryptoanalysis is the art of breaking them. Cryptology
is the combination of the two. In the literature of cryptology, information to
be encrypted is known as plaintext, and the parameters of the encryption function
that transforms are collectively called a key. Existing
cryptographic techniques are usually identified as ``traditional'' or ``modern.''
Traditional techniques date back for centuries, and are tied to the the operations
of transposition (reordering of plaintext) and substitution (alteration of plaintext
characters). Traditional techniques were designed to be simple, and if they were
to be used with great secrecy extremely long keys would be needed. By contrast,
modern techniques rely on convoluted algorithms or intractable problems to achieve
assurances of security. There
are two branches of modern cryptographic techniques: publickey encryption and
secretkey encryption. In publickey cryptography, messages are exchanged
using keys that depend on the assumed difficulty of certain mathematical problems
 typically the factoring of extremely large (100+ digits) prime numbers. Each
participant has a ``public key'' and a ``private key''; the former is used by
others to encrypt messages, and the latter by the participant to decrypt them.
In secretkey encryption,
a kbit ``secret key'' is shared by two users, who use it to transform plaintext
inputs to an encoded cipher. By carefully designing transformation algorithms,
each bit of output can be made to depend on every bit of the input. With such
an arrangement, a key of 128 bits used for encoding results in a key space of
two to the 128th (or about ten to the 38th power). Assuming that brute force,
along with some parallelism, is employed, the encrypted message should be safe:
a billion computers doing a billion operations per second would require a trillion
years to decrypt it. In practice, analysis of the encryption algorithm might make
it more vulnerable, but increases in the size of the key can be used to offset
this.
The main practical
problem with secretkey encryption is determining a secret key. In theory any
two users who wished to communicate could agree on a key in advance, but in practice
for many users this would require secure storage and organization of a awkwardly
large database of agreedon keys.
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