Followup of Modular Functions in Encryption
Prerequisite: physics
Modular functions seems impregnable enough but cryptographer just had to take it one step further, harnessing the random unpredictability of light polarization.
Photons can travel as transverse waves. What a polaroid does is filter out waves that oscillate in other directions. Some polaroids allow many oscillation directions while in this diagram below, the polaroid filters out all light waves except ones that oscillate vertically.. but not really.
Diagonal waves have a 50% chance of passing the filter and becoming vertical at the other side, according to Schrödinger's concept of superposition. Another key feature is that one cannot directly observe the polarization of photons due to Heisenberg's uncertainty principle, but one knows for sure the polarization of photons that come after a polaroid.
Let the madness begin.
As a setup for an example of quantum cryptography:
Message is translated into binary.
For the sake of simplicity, assume four possible wave polarizations.
Vertical ( | ) and horizontal ( - ) waves can pass through rectilinear polaroids (+).
Diagonal waves ( / and \ ) can pass through diagonal polaroids (x).
( | ) and ( / ) represents 1.
( - ) and ( \ ) represents 0.
Alice wants to send a key to Bob, and comes up with a pre-key 10011011.
She sets a scheme of randomly alternating polaroids +x++xx+x, then sends polarized photons ( | \ - | / \ | / ) through specific |, -, /, and \ polaroids to Bob, accordingly with her scheme.
A summary of Alice's transmission:
pre-key: 1 0 0 1 1 0 1 1
scheme: + x + + x x + x
polarization: | \ - | / \ | /
(The only way to detect the polarization of a photon is by trial and error, where there is only one trial. Eve cannot possibly guess which polaroid to use for an upcoming photon, and using the wrong one will either block out or repolarize a photon, neither of which are desired. She cannot even deduce whether she used the correct polaroid or not, since a photon entering an incorrect polaroid has a 50% chance of getting through. Tampering with the photons with polaroids can also reveal Eve's act of eavesdropping).
Bob on the other end tries to receive the photons with a random polaroid scheme of his own.
Alice and Bob then identify where they used the same scheme, which is also where they both know the correct polarizations, and the resulting fragmented sequence can be used to generate their key (1110 in this example):
pre-key: 1 0 0 1 1 0 1 1
Alice's scheme: + x + + x x + x
polarization: | \ - | / \ | /
Bob's scheme: + + x + x x x +
filtered scheme: + + x x
key: 1 1 1 0
Eve can overhear what schemes they filtered out, but she cannot know what Bob correctly observed, which is essentially the key. The only way for Eve to know the key is to use the exact same scheme as Bob, which is highly improbable when the key is extremely long.
The incorporation of photons started with Charles Bennett's idea of quantum foolproof money. Last time I checked, a quantum key was successfully exchanged over one kilometer.
Oh dear mortals, what next?
Let the madness begin.
As a setup for an example of quantum cryptography:
Message is translated into binary.
For the sake of simplicity, assume four possible wave polarizations.
Vertical ( | ) and horizontal ( - ) waves can pass through rectilinear polaroids (+).
Diagonal waves ( / and \ ) can pass through diagonal polaroids (x).
( | ) and ( / ) represents 1.
( - ) and ( \ ) represents 0.
Alice wants to send a key to Bob, and comes up with a pre-key 10011011.
She sets a scheme of randomly alternating polaroids +x++xx+x, then sends polarized photons ( | \ - | / \ | / ) through specific |, -, /, and \ polaroids to Bob, accordingly with her scheme.
A summary of Alice's transmission:
pre-key: 1 0 0 1 1 0 1 1
scheme: + x + + x x + x
polarization: | \ - | / \ | /
(The only way to detect the polarization of a photon is by trial and error, where there is only one trial. Eve cannot possibly guess which polaroid to use for an upcoming photon, and using the wrong one will either block out or repolarize a photon, neither of which are desired. She cannot even deduce whether she used the correct polaroid or not, since a photon entering an incorrect polaroid has a 50% chance of getting through. Tampering with the photons with polaroids can also reveal Eve's act of eavesdropping).
Bob on the other end tries to receive the photons with a random polaroid scheme of his own.
Alice and Bob then identify where they used the same scheme, which is also where they both know the correct polarizations, and the resulting fragmented sequence can be used to generate their key (1110 in this example):
pre-key: 1 0 0 1 1 0 1 1
Alice's scheme: + x + + x x + x
polarization: | \ - | / \ | /
Bob's scheme: + + x + x x x +
filtered scheme: + + x x
key: 1 1 1 0
Eve can overhear what schemes they filtered out, but she cannot know what Bob correctly observed, which is essentially the key. The only way for Eve to know the key is to use the exact same scheme as Bob, which is highly improbable when the key is extremely long.
The incorporation of photons started with Charles Bennett's idea of quantum foolproof money. Last time I checked, a quantum key was successfully exchanged over one kilometer.
Oh dear mortals, what next?
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