Cryptography is the science of relaying information from one party to another in such a manner that both parties can exchange ideas freely and exclusively. The average person relies on the strength of cryptography every day for such reasons as protecting his or her credit rating, ensuring that his or her money is safe in his bank, and securely checking his or her mail on the internet. Cryptosystems, or the procedures used to encrypt and decrypt messages, have been based in a many different disciplines of study. The twentieth century witnessed the conversion of cryptography from a literary stratagem into a mathematical enigma. In light of mankind’s remarkable advancements in the field of quantum theory, physics will be the discipline through which cryptography enters the twenty-first century via quantum cryptography.

Cryptosystems use keys, or algorithms through which a message is transformed, to encrypt and decrypt their messages. For standard cryptosystems, the encryption key and the decryption key are very closely related, and it is often possible to determine the decryption key from the encryption key. The prevailing cryptosystems of the late twentieth century, however, use formulas assumed by mathematicians to be “one-way” formulas, where it is impossible to figure out the decryption key even if the encryption key is known. Artur Ekert (1995), Professor of Quantum Physics at the University of Cambridge, observes that these “one-way” formulas are not mathematically sound, however, because there exists no theorem that states that the decryption key cannot be discerned from the encryption key. With the advancements of mathematics and computer technology, such cryptosystems will inevitably prove to be unsafe because one day mathematicians (with the help of computers) will discover a method for discerning the decryption key from the encryption key, effectively “cracking” the cryptosystem.

Quantum cryptography uses a somewhat different approach, employing a cryptosystem with a simple, random key to encrypt and decrypt messages. Because the components of the key are randomly selected, it is impossible for an outside party to replicate the key and, therefore, impossible for them to crack the cipher. It is the formation and transmission of this key that employs the ingenuity of quantum mechanics to ensure that no eavesdroppers secretly intercept the key.

In order to provide an absolutely secure key exchange between two parties, it is necessary to transmit the key in such a manner that it cannot be comprehended by anyone but the two parties involved. On the quantum level, we are able to achieve this. It is a tenet of quantum cryptography that it is impossible to distinguish between non-orthogonal states of spin momentum for particles on the quantum level. This is part of the idea behind a concept known as quantum entanglement (Papadakos, 2002, p. 7). With this principle in mind, it is possible to transmit a key using faint laser pulses sending out photons. Each photon has one of four predetermined angles of spin momentum, or polarization (Papadakos, 2002, p. 31). The possible angles of polarization are 0°, 45°, 90°, and 135°. Because of quantum entanglement, the recipient of the photons is able to discern between photons with polarization at 0° and 90° using one technique and between photons with polarization at 45° and 135° using another technique, but does not know which technique is correct for each photon. The recipient arbitrarily chooses which method to apply to each incoming photon, and, with sensitive photon-detecting equipment, records both which method was used and what the results of the method were. After doing this, the recipient declares which method he employed for each photon, and the sender responds by letting the recipient know which method proved accurate for each photon. The key is then generated according to the results of the successfully employed methods in a binary form. (Ekert, 1995)

It is impossible for an eavesdropper to intercept the stream of photons, determine the polarization of each photon, and then retransmit the photons, because the eavesdropper does not know exactly how to send the photons out again. Because of the Heisenberg Uncertainty Principle, it is impossible for the eavesdropper to know exactly the polarization of every photon. Therefore, any tampering with the stream of photons would immediately be noticed by a discrepancy in information between the two parties attempting to communicate. Effectively, where mathematicians were unable to create a sound “one-way” function, physicists utilize the laws of nature to achieve this goal.

The task of creating a practical quantum cryptosystem has been underway since 1989, with the transmission of a code through a distance of 30 centimeters. Since then, scientists have been able to successfully transmit codes through distances of over 40 kilometers. As photon-detecting equipment becomes more sophisticated, scientists may be able to send out codes through existing telecommunication fibers, removing the need for implanting special cables for the purpose of photon transmission (Papadakos, 2002, p. 31).

Cryptosystems play an important role in our daily lives. In our digital world, cryptosystems are so thoroughly integrated into many facets of our life that it is impossible to envision our lives without them. The benefits that would result from having a cryptosystem that has been theoretically proven by the laws of physics to be impregnable are both powerful and far reaching. The prospect of perfecting such an important tool as cryptography is indeed an exciting one. The evolutionary history of cryptography is vast and rich, and is deeply entangled in many facets of history. With the introduction of quantum cryptography, the field of study known as cryptography will have finally reached its conclusion.

Sources:

Papadakos, Nikolaos P. (2002) Quantum Information Theory and Applications to Quantum Cryptography. Retrieved February 1, 2003, from
http://arxiv.org/PS_cache/quant-ph/pdf/0201/0201057.pdf

Quantum Cryptography: Secure Communication over Insecure Channels. Retrieved January 25, 2003, from
http://www.almaden.ibm.com/st/projects/quantum/crypto/

Ekert, Artur (1995). QCQ Introductions: Quantum Cryptography: What is Quantum Cryptography. Retrieved January 25, 2003, from
http://www.qubit.org/oldsite/intros/crypt.html

Wright, Marie A. The Impact of Quantum Computing on Cryptography. Network Security, Volume 2000, Issue 9, 1 September 2000, Pages 13-15.
DOI: 10.1016/S1353-4858(00)09027-9

Serway, R., Moses, C., Moyer, C. (1997). Modern Physics: Second Edition. USA: Thomson Learning Inc.