Quantum cryptography

November 14, 2005
Quantum cryptography, which taps properties of photons to represent information, can, in theory, provide perfectly secure communications.

Alice, for instance, can send Bob perfectly secure messages using quantum key distribution because the method allows them to tell for sure whether the encryption keys they are using to lock and unlock messages have been copied.

Quantum key distribution systems use single photons to represent the binary numbers, or bits, that make up encryption keys. The use of single photons is what guarantees security. If there were two or more photons per bit, eavesdropper Eve could siphon off extra photons to make a copy of a key without being detected.

The systems use polarized photons to represent bits. Photons have both electric and magnetic fields. The electric field of ordinary photons vibrates in all directions perpendicular to the photon’s course. Polarized photons have electric fields that vibrate in only one of four directions: vertical, horizontal and the two diagonals.

Two pairs of polarizations, vertical and horizontal, and the two diagonals, can each be used to represent the 1s and 0s of digital information. For example, vertical could represent 1 and horizontal could represent 0.

To send an encryption key to Bob, Alice transmits a string of randomly polarized photons and records how each photon was polarized. Bob measures the photons, but because of a quirk of quantum physics-the Heisenberg uncertainty principle-he can only look for one of the two pairs of states in each photon. Bob has to choose which type of polarization to look for, and he only gets one look because the act of measuring the photon destroys it.

Bob randomly chooses whether to look for vertical and horizontal or the diagonal orientations. He tells Alice, over a regular unsecure communications channel, how he measured the photons and she tells him which ones he chose correctly.

Alice and Bob use this common string of photon polarizations as a binary encryption key. Alice uses the key to encrypt a message, then sends the encrypted message to Bob over an open channel. Bob then uses the bit string to decrypt the message. Because the bit string was generated at random, there is no mathematical basis for decoding the message without knowing the key. And by using a new encryption key for every message, Alice and Bob can thwart code breakers who deduce keys by looking for common patterns across messages.

The quirky nature of photons makes it impossible for an eavesdropper to intercept single photons and successfully replace them. This is because, like Bob, Eve has to guess which way to measure the photons. If she chooses to measure a photon to see if it is a 1 or 0 based on the vertical and horizontal orientations but Alice encoded the bit in the diagonal orientations, Eve will get a false reading.

This means Eve could correctly measure about half of the photons she intercepts, and so half of the substitutes she sends to Bob would be polarized randomly. By chance, half of the randomly polarized photons would be correct, making about 25 percent of the substitute bits wrong.

Alice and Bob check the error rate by comparing a few of the bits Bob chose correctly. If the error rate is higher than even one percent, they can decide that the chance that Eve has intercepted their key is too high, and throw it out and transmit another.

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