Error management for long distance quantum key distribution and symmetrical key distribution
Methods and systems for performing secure quantum key distribution (QKD) over noisy channels are disclosed. A first computing device generates a challenge set using a secret seed, applies the challenges to its CRP, and receives an ordered set n responses, where n has the same number of bits as the key. It then sends only those responses in positions that correspond to 1s in the key to the second computing device. Those responses are sent under a QKD protocol such as BB84. The second computing device generates the same challenges and recovers the same responses with a mirror CRP mechanism. It also receives the subset of responses from the first computing device. Generated responses that match received responses correspond to 1s in the key, and 0s are assigned to all other positions.
1 . A method to distribute a secret key from a first computing device to a second computing device comprising:
at a first computing device,
generating a secret key of length n;
generating a first set of challenges;
applying the first set of challenges to a first challenge response pair mechanism (CRP) and receiving a first set of ordered n responses of length p;
selecting from the first set of ordered n responses a subset of m responses that occupy positions in the ordered set also occupied by a first binary value in the secret key;
transmitting the m responses to a second computing device over a quantum data transmission channel;
at the second computing device;
receiving the subset of m responses;
generating the first set of challenges;
applying the first set of challenges to a second CRP to generate second set of ordered n responses;
comparing the second set of ordered n responses to the subset of m responses to determine the positions in the second set of ordered n responses that match responses in the subset of m responses, and
generating a key by assigning the first binary value to positions in the key corresponding to positions in the second set of ordered n responses for which there are matching responses in the subset of m responses and assigning a second binary value to the remaining positions in the key.
2 . The method of claim 1 , wherein transmitting the m responses to a second computing device over a quantum data transmission channel comprises encoding the m responses into first and second polarization states of photon and transmitting the photons over an optical transmission channel.
3 . The method of claim 2 , wherein the optical transmission channel is an optical fiber.
4 . The method of claim 2 , wherein encoding the m responses into first and second polarization states is performed in accordance with a QKD protocol.
5 . The method of claim 4 , wherein the QKD protocol is one of Decoy, Eker, EPR, MDI, or Phase Matching.
6 . The method of claim 4 , wherein the QKD protocol is BB84.
7 . The method of claim 2 , further comprising generating a random number Ra, selecting a first or second polarization basis dictated by sequential binary values of Ra, and transmitting each photon with a polarization dictated by the value of the bit to be encoded and transmitted and the polarization basis.
8 . The method of claim 7 , wherein receiving the subset of m responses comprises:
generating a random number Rb, selecting a first or second polarization basis dictated by sequential binary values of Ra, receiving each photon in the first computing device's transmission through a polarization filter having a first polarization orientation or a second polarization orientation, dictated by sequential values of Rb.
9 . The method of claim 8 , further comprising, at the second computing device receiving Ra, comparing Ra and Rb, and blanking bits in a received bitstream of the subset of m responses at positions where a binary value of Ra does not match a binary value of Rb, resulting a set of m bit-reduced responses of length pi.
10 . The method of claim 9 , wherein comparing the second set of ordered n responses to the subset of m responses to determine the positions in the second set of ordered n responses that match responses in the subset of m responses comprises, using Ra and Rb to blank bits in a bitstream of the second set of ordered n responses at positions where a binary value of Ra does not match a binary value of Rb, resulting in a set of n bit-reduced responses of length pi and comparing each of the m bit reduced responses of length pi to each of the n bit-reduced responses of length pi to determine the positions of responses in the second set of ordered n responses for which there is a match.
11 . The method of claim 1 , wherein determining the positions in the second set of ordered n responses that match responses in the subset of m responses comprises determining that compared responses match to an extent above some predetermined threshold.
12 . The method of claim 1 , wherein generating a first set of challenges at a first computing device comprises generating a first set of challenges with a random number.
13 . The method of claim 12 , further comprising generating a first set of challenges at a first computing device by concatenating the random number with a known number and providing the result to an expanded output function.
14 . The method of claim 12 , wherein generating the first set of challenges at the second computing device comprises receiving the random number from the first computing device and using the random number to generate the first set of challenges.
15 . The method of claim 1 , wherein the second CRP is a PUF array and the first CRP is an image of the PUF array.
16 . A method of receiving a secret key from a first computing device, comprising:
at a second computing device:
receiving a first set of m responses generated by a first CRP mechanism at a first computing device, the set of m responses being quantum encoded and transmitted over a quantum channel;
generating a set of challenges to a CRP mechanism at the second computing device;
applying the set of challenges to the CRP mechanism at the second computing device, and receiving a second set of n responses;
comparing each response in the first set of m responses to each response in the second set of n responses and, on the basis of the comparison, determining positions of responses within the second set of n responses that match responses in the first set of m responses, and
building a key by assigning a first binary symbol to positions in the key that correspond to positions of responses in the second set of n responses for which there is a matching response in the first set of m responses, and assigning a second binary symbol for other positions.
17 . The method of claim 16 , wherein one of the CRP mechanisms at the first or second computing devices is a PUF array, and wherein the other of the CRP mechanisms at the first or second computing devices is an image of the PUF array.
18 . The method of claim 16 , wherein generating a set of challenges comprises receiving a message digest from the first computing device, and using the message digest to generate the set of challenges, and wherein the message digest was generated using a random number.
19 . The method of claim 16 , wherein the first set of m responses were transmitted in accordance with BB84 QKD, and wherein receiving the first set of m responses comprises:
generating a random number Rb;
selecting a first or second polarization basis dictated by sequential binary values of Ra;
receiving each photon in the transmission of the first set of m responses through a polarization filter having a first polarization orientation or a second polarization orientation, dictated by sequential values of Rb;
receiving a number Ra from the first computing device, where the length of Ra equals Rb, identifying positions in Ra that do not match corresponding positions in Rb, and building a filter on the basis of matching positions and unmatching positions in Ra and Rb;
aligning the filter to a received bitstream for the first set of m responses and blanking bits that have positions in the bitstream that correspond to positions of bits in Ra that do not match corresponding positions in Rb, resulting in a set of bit reduced m responses.
20 . The method of claim 19 , comprising, applying the filter to the received second set of n responses prior to comparing responses in the first set of m responses and responses in the second set of n responses.