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ABSTRACT
Quantum cryptography uses quantum mechanics to guarantee secure
communication. It enables two parties to produce a shared random bit string known only
to them, which can be used as a key to encrypt and decrypt messages.
An important and unique property of quantum cryptography is the ability of the
two communicating users to detect the presence of any third party trying to gain
knowledge of the key. This results from a fundamental part of quantum mechanics: the
process of measuring a quantum system in general disturbs the system. A third party
trying to eavesdrop on the key must in some way measure it, thus introducing detectable
anomalies. By using quantum superpositions or quantum entanglement and transmitting
information in quantum states, a communication system can be implemented which
detects eavesdropping. If the level of eavesdropping is below a certain threshold a key
can be produced which is guaranteed as secure, otherwise no secure key is possible and
communication is aborted.
The security of quantum cryptography relies on the foundations of quantum
mechanics, in contrast to traditional public key cryptography which relies on the
computational difficulty of certain mathematical functions, and cannot provide any
indication of eavesdropping or guarantee of key security.
Quantum cryptography is only used to produce and distribute a key, not to
transmit any message data. This key can then be used with any chosen encryption
algorithm to encrypt and decrypt a message, which can then be transmitted over a
standard communication channel. The algorithm most commonly associated with QKD is
the one-time pad, as it is provably secure when used with a secret, random key.
KEY WORDS:
qubit, uncertainty, entanglement, bit commitment, BB84 protocol, Ekert
protocol, key distribution, one-time-pad
1. INTRODUCTION
Cryptography is the science of keeping private information from unauthorized
access, of ensuring data integrity and authentication, and other tasks. In this survey, we
will focus on quantum-cryptographic key distribution and bit commitment protocols and
we in particular will discuss their security. Before turning to quantum cryptography, let
me give a brief review of classical cryptography, its current challenges and its historical
development.
Two parties, Alice and Bob, wish to exchange messages via some insecure
channel in a way that protects their messages from eavesdropping. An algorithm, which
is called a cipher in this context, scrambles Aliceâ„¢s message via some rule such that
restoring the original message is hard”if not impossible”without knowledge of the
secret key. This scrambled message is called the ciphertext. On the other hand, Bob
(who possesses the secret key) can easily decipher Aliceâ„¢s ciphertext and obtains her
original plaintext. Figure 1 in this section presents this basic cryptographic scenario.
Fig. 1. Communication between Alice and Bob, with Eve listening.
But unlike traditional cryptology methods -- encoding and decoding information or messages -- quantum cryptology depends on physics, not mathematics.
In this report, we'll get to the bottom of how quantum encryption works, and how it differs from modern cryptology. But first, we'll look at the uses and the limitations of traditional cryptology methods.
Traditional Cryptology
Photo courtesy NSA
A German Enigma machine
Privacy is paramount when communicating sensitive information, and humans have invented some unusual ways to encode their conversations. In World War II, for example, the Nazis created a bulky machine called the Enigma that resembles a typewriter on steroids. This machine created one of the most difficult ciphers (encoded messages) of the pre-computer age.
Even after Polish resistance fighters made knockoffs of the machines -- complete with instructions on how the Enigma worked -- decoding messages was still a constant struggle for the Allies [source: Cambridge University]. As the codes were deciphered, however, the secrets yielded by the Enigma machine were so helpful that many historians have credited the code breaking as a important factor in the Allies' victory in the war.
What the Enigma machine was used for is called cryptology. This is the process of encoding (cryptography) and decoding (cryptoanalysis) information or messages (called plaintext). All of these processes combined are cryptology. Until the 1990s, cryptology was based on algorithms -- a mathematical process or procedure. These algorithms are used in conjunction with a key, a collection of bits (usually numbers). Without the proper key, it's virtually impossible to decipher an encoded message, even if you know what algorithm to use.
There are limitless possibilities for keys used in cryptology. But there are only two widely used methods of employing keys: public-key cryptology and secret-key cryptology. In both of these methods (and in all cryptology), the sender (point A) is referred to as Alice. Point B is known as Bob.
In the public-key cryptology (PKC) method, a user chooses two interrelated keys. He lets anyone who wants to send him a message know how to encode it using one key. He makes this key public. The other key he keeps to himself. In this manner, anyone can send the user an encoded message, but only the recipient of the encoded message knows how to decode it. Even the person sending the message doesn't know what code the user employs to decode it.
PKC is often compared to a mailbox that uses two keys. One unlocks the front of the mailbox, allowing anyone with a key to deposit mail. But only the recipient holds the key that unlocks the back of the mailbox, allowing only him to retrieve the messages.
The other usual method of traditional cryptology is secret-key cryptology (SKC). In this method, only one key is used by both Bob and Alice. The same key is used to both encode and decode the plaintext. Even the algorithm used in the encoding and decoding process can be announced over an unsecured channel. The code will remain uncracked as long as the key used remains secret.
SKC is similar to feeding a message into a special mailbox that grinds it together with the key. Anyone can reach inside and grab the cipher, but without the key, he won't be able to decipher it. The same key used to encode the message is also the only one that can decode it, separating the key from the message.
Traditional cryptology is certainly clever, but as with all encoding methods in code-breaking history, it's being phased out. Find out why on the next page.
Traditional Cryptology Problems
Both the secret-key and public-key methods of cryptology have unique flaws. Oddly enough, quantum physics can be used to either solve or expand these flaws.