Abstract:
Quantum cryptography by polarization ambiguity is generally used but it involves polarization-maintained fibers. This invention proposes an alternative: quantum cryptography by ambiguity in time. It comprises the conversion of K bits to be transmitted into a train of K pulses of particle flows of time width ΔT and whose frequency Tb, is predetermined knowing that each of the K pulses being shifted or not in time such that the k th  pulse is shifted by a duration t 0  respectively t 1 , with respect to the initial instant of the period depending on the value “0”, respectively “1” of the k th  bit, where k is an integer such that 0≦k&lt;K and the shifts t 0  and t 1  are such that 0≦t 0 ,t 1 ≦Tb−ΔT and 0&lt;|t 1 −t 0 |&lt;ΔT.

Description:
FIELD OF THE INVENTION 
   The invention concerns the field of cryptography. 
   RELATED APPLICATIONS 
   The present Application is based on International Application No. PCT/FR01/03500 filed on Nov. 9, 2001, which in turn corresponds to French Application No 00/14488 filed on Nov. 10, 2000 and priority is hereby claimed under 35 USC § 119 based on these applications. Each of these applications are hereby incorporated by reference in their entirety into the present application. 
   BACKGROUND OF THE INVENTION 
   Through the use of cryptography, a message can only be read by its recipient. A key is used to encrypt the message. The owner of the key is the only person who can read the message received. 
   The encryption key must therefore be transmitted by the sender to the recipient of the encrypted message. Transmission is carried out such that only the recipient of the encrypted message receives this encryption key. Interception by a third party of the encryption key is detected by the sender or the recipient. Consequently, the encryption key or the elements of the key detected as having been intercepted are not used to encrypt the message. 
   The principle of transmitting encryption keys is used, for example, in quantum cryptography. It consists of using physical properties to guarantee the integrity of a received encryption key. 
   The encryption key consists of a bit sequence. Generally, a photon polarization state is associated with each bit. The light flow, encoded by polarization, is then attenuated. The probability of detecting two photons associated with the same bit is then negligible. 
   The sender can encode the encryption key on two nonorthogonal states (a given polarization state and a state at 45°). Concerning this subject, Bennett wrote the article “Quantum Cryptography using any two Nonorthogonal states” in Physics Review letters 68 in 1992. In reception, the detection states are chosen in a base with two states. These two detection states are orthogonal respectively to each state of the base used by the sender. During transmission, the transmission and detection states are chosen independently of each other. 
   If the states chosen by the transmitter and the receiver are orthogonal, the detection probability is zero. The measurement result is certain, there is no ambiguity. If they are not orthogonal, there are two possible measurement results since the probability of detecting the photon is 0.5. If the photon is detected, it is certain that the transmitter state is at 45° to the receiver state. There is no ambiguity. Irrespective of the polarization configuration, there is always a possibility of not detecting the photon. This non detection of the photon makes deducing the choice of transmitter polarization, using the receiver state, ambiguous. 
   This ambiguity concerning the polarization is used in quantum cryptography. A non recipient cannot reproduce the message since it is impossible to avoid losing information. 
   This type of quantum cryptography is known as “polarization ambiguity quantum cryptography” since it uses photon polarization states. A certain number of problems are to be faced. They concern the encoding of the encryption key on the polarization states of the photons in a light flow. During transmission, there is a problem of polarization distortion. For example, transmission by optical fibers requires complex systems which are difficult to implement and very expensive. For example,
         either the use of polarization-maintained fibers, which are expensive and difficult to implement,   or the use of complex systems implementing, for example, Faraday rotators.       

   SUMMARY OF THE INVENTION 
   This invention proposes an alternative: quantum cryptography by ambiguity in time. It is easier to implement since protected, amongst other things, against problems of transmission by optical fibers. Two photons transmitted successively with a time difference Δt will be received in the transmission order with the same time difference Δt, independently of the transmission medium. 
   The invention concerns a digital data encoding method intended for transmission by particle flow such that the probability of transmitting two particles per period is negligible, wherein it includes the transformation of the sequence of K bits of digital data in a train of K pulses of particle flows of time width ΔT whose frequency Tb is predetermined, knows that each of the K pulses being shifted or not in time such that the k th  pulse is shifted by a duration t 0 , respectively t 1 , with respect to the initial instant of the period depending on the value “0”, respectively “1” of the k th  bit, where k is an integer such that 0≦k&lt;K and the shifts t 0  and t 1  are such that 0≦t 0 ,t 1 ≦Tb−ΔT and 0&lt;|t 1 −t 0 |&lt;ΔT. 
   Still other objects and advantages of the present invention will become readily apparent to those skilled in the art from the following detailed description, wherein the preferred embodiments of the invention are shown and described, simply by way of illustration of the best mode contemplated of carrying out the invention. As will be realized, the invention is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the invention. Accordingly, the drawings and description thereof are to be regarded as illustrative in nature, and not as restrictive. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention proposes a method to decode digital data encoded according to the procedure wherein, given Δt=ΔT−lt 1 −t 0   l , it comprises:
         observation of the flow of particles received on one or two time windows for each bit reception period of duration Tb,   detection of particles in the time observation window(s) generates either a bit of value “0” or “1”, or a signal indicating ambiguity.       

     The advantages and features of the invention will be clearer on reading the following description, given as an example, illustrated by the attached figures representing in: 
       FIG. 1 , the representation of the value of a bit transmitted as a pulse according to the invention, 
       FIG. 2 , the time observation windows of the decoder according to the invention, 
       FIG. 3(   a ), a first example of realization of a second variant of the encoder  1  according to the invention, 
       FIG. 3(   b ), the representation of the value of a bit to be transmitted as control signal of the modulator included in the encoder  1  of  FIG. 3(   a ). 
       FIG. 4 , a third variant of the encoder  1  according to the invention, 
       FIG. 5 , a second example of realization of the second variant of the encoder  1  according to the invention, 
       FIG. 6 , the disc of the mechanical chopper of the third and fourth examples of realization of the second variant of the encoder  1  according to the invention, 
       FIG. 7(   a ), a third example of realization of the second variant of the encoder  1  according to the invention, 
       FIG. 7(   b ), a representation of the light flow at the input of the modulator of the encoder  1  of  FIG. 6 . 
       FIG. 8 , a fourth example of realization of the second variant of the encoder  1  according to the invention, 
       FIGS. 9(   a ) and  9 ( b ), the Mach-Zender interferometer of encoder  1  of  FIG. 8  in its two different states, 
       FIG. 10 , a first example of realization of the quantum cryptography transmission system according to the invention, 
       FIGS. 11  ( a ) and  11  ( b ), two variants of the decoder according to the invention, 
       FIG. 12 , a second example of realization of the quantum cryptography transmission system according to the invention. 
   

   DETAILED DESCRIPTION OF THE EMBODIMENTS 
   The principle of this invention is based on the reproduction of the state of the art polarization ambiguity arrangement in the time domain. 
   The information is encoded in pulses of time width ΔT as shown on  FIG. 1 . These pulses may, for example, be light pulses. Generally, they may be pulses of particle flows (photons, electrons, positrons, etc.). The transmitter produces two types of pulse, representing t 0  and t 1 , respectively separated by a time shift of, for example, lt 1 −t 01 =ΔT/2 16. One bit of the digital data representing the information to be encoded is associated with each time period of duration Tb. One of the pulses is associated with the bit of value “0” (that shifted by to with respect to the initial instant of the period of duration Tb), the other with the bit of value “1” (that shifted by t 1 ). The duration Tb is such that it satisfies the following relation Tb≧ΔT+lt 1 −t 0   l . The two pulses are shifted so that they overlap for a time interval Δt=ΔT−lt 1 −t 0   l  (=ΔT/2 16, in our example) &gt;0. On the example of  FIG. 1 , the pulse associated with the bit of value “1” is delayed with respect to the pulse associated with the bit of value “0” and t 0 =0. Generally, t 0  and t 1  are such that 0≦t 0 ,t 1 ≦Tb−ΔT and 0&lt;lt 1 −t 0   l &lt;ΔT. If the receiver detects a photon during the period of overlap, it cannot know which type of pulse it comes from, and consequently the value “0” or “1” of the bit which was transmitted. To detect the bit value unambiguously, only the photons received in the two time windows given on  FIG. 2  are observed. One window is used to observe the first half of the first pulse and the other the second half of the second pulse. Consequently, the photons reaching the receiver during the overlap interval Δt are not observed. 
   More explicitly, the decoding comprises:
         observation of the flow of particles received on one or two time windows for each bit reception period of duration Tb,
           if t 0 &lt;t 1 , the first time observation window starts at instant t 0  (inclusive) and ends at instant t 1  (exclusive), the second observation window starts, if necessary, at instant t 1 +Δt (exclusive) and ends at instant t 1 +T (inclusive) or vice versa,   if t 1 &lt;t 0 , the first time observation window starts at instant t 1  (inclusive) and ends at instant t 0  (exclusive), the second observation window starts, if necessary, at instant t 0 +Δt (exclusive) and ends at instant t 0 +T (inclusive) or vice versa,   
           detection of particles in the time observation window(s) generates:
           a bit of value “0”:
               if t 0 &lt;t 1 , when a particle is detected in the window starting at t 0  of period k,   if t 1 &lt;t 0 , when a particle is detected in the window starting at t 0 +Δt of period k,   
               a bit of value “1”:
               if t 1 &lt;t 0 , when a particle is detected in the window starting at t 1  of period k,   if t 0 &lt;t 1 , when a particle is detected in the window starting at t 1 +Δt of period k,   
               a signal indicating an ambiguity on the bit value if no particle was detected in the first, and if necessary, in the second observation window.   
               

   In our example, the bits are transmitted according to the format of  FIG. 1  and the observation windows of the receiver are given by  FIG. 2 . 
   The particle flow pulses carrying the information to be transmitted in time shifted format are, for example:
         [ENCODER A] Either produced directly by an encoded pulse source  11   +3  (for example, a laser generating a discontinuous laser beam according to the diagram of encoded pulses shown on  FIG. 1 ),   [ENCODER B] Or shifted in time by t 0  or t 1  depending on the data to be encoded by a controllable delay gate  13  receiving a particle pulse flow from a pulse source  11   +2 ,   [ENCODER C] Or chopped with the appropriate time shift (t 0  or t 1 ) depending on the data to be encoded by an encoded pulse chopper  12   +3  at frequency Tb in a continuous beam from a laser  11 ,   [ENCODER D] Or chopped by a pulse chopper  12  at frequency Tb in a continuous beam from a source  11  then given a time shift of t 0  or t 1  depending on the data to be encoded by a controllable delay gate  13 ,       

   The various encoders  1  and decoders  3  considered on  FIGS. 3 to 12  are given as examples. They illustrate encoding on light beam. More generally, any type of particle flow (photons, electrons, positrons, etc.) may be considered. 
   [ENCODER A] The first variant of encoder  1  is not illustrated. Encoder  1  includes at least one encoded pulse source  11   +3 . It produces particle flow pulses of time width ΔT and frequency Tb. In addition, the pulses from this source are shifted by t 0  or t 1  depending on the value of the data bits to be encoded. The values of the time shifts t 0  and t 1  are such that 0≦t 0 ,t 1 ≦Tb−ΔT and 0&lt;lt 1 −t 0   l &lt;ΔT. In our example, the source  11   +3  is a laser, for example a mode-locked laser producing light pulses according to the diagram on  FIG. 1  with t 0 =0. 
   [ENCODER B]  FIG. 4  shows a second variant of encoder  1  using a modulator  131 . Modulator  131  is electro-optical or acousto-optical, etc. Encoder  1  includes a pulse source  11   +2 . This source  11   +2  generates a particle flow as a train of pulses of time width ΔT and frequency Tb. The pulse source  11   +2  is, for example, a mode-locked laser. Mode-locked lasers produce pulse trains separated by a constant time interval equal to the time for the back and forth movement in the laser cavity. It is difficult to control the laser in order to produce the time shifts required depending on the bits to be encoded. Consequently, in the variant proposed by  FIG. 4 , these shifts are produced outside the laser  11   +2  using a controllable delay gate  13 . The delay gate  13  makes the pulses follow or not a delay line according to the shift required and determined by the bits to be encoded. This type of delay gate  13  can be produced, for example, using a modulator  131  to switch the polarization between two directions specific to the polarizing prisms  132   S  and  132   R  placed downstream. Polarizing prism  132   S  guides the pulses depending on their polarizations to a first or a second path. The second polarizing prism  132   R  brings them back to the output of the delay gate  13 . Depending on the path followed by the pulses, the distance traveled is more or less long. For example, if the pulse is not shifted, if follows a direct path and if it is shifted, it follows an elongated path. 
   [ENCODER C] The first example of realization of the third variant of encoder  1  shown on  FIG. 3(   a ) is simple. The beam generated by the laser  11  goes through a modulator  121 . Modulator  121  has two operating modes: active mode and inactive mode. It can be electro-optical, acousto-optical, etc. Modulator  121  receives a control signal which has two states. One state corresponds to inactive mode, the other state to active mode.  FIG. 3(   b ) shows the control voltage of an electro-optical modulator  121 . It is designed to create pulses of time width ΔT at frequency Tb with a time shift t 0  or t 1  depending on the value “0” or “1” of the bits. When the control voltage reaches a threshold value Vπ, modulator  121  is active. Modulator  121  in active state switches the polarization of the light beam passing through it by 90°. A polarizer  122  is placed downstream from modulator  121 . Polarizer  122  switches off the beam when modulator  121  is not active. In fact, polarizer  122  only allows the beam to pass when its polarization corresponds to that obtained at the output of modulator  121  when active. When idle therefore, no beam is transmitted by the encoded pulse chopper  12   +3 . 
   This first example of realization of the third variant of encoder  1  therefore includes a source  11  producing a continuous flow of particles followed by an encoded pulse chopper  12   +3  with at least one modulator  121  receiving the continuous flow, and a polarizer  122  to allow transmission only during the recorded pulse. 
   Another technique consists of using a mechanical chopper  123  which chops pulses of given time width ΔT at the desired frequency Tb on a continuous particle flow. 
     FIG. 5  shows a second example of realization of the third variant of encoder  1 . It uses a mechanical chopper whose disc  123   1  has only one opening. A phase check device  124  generates a voltage (VCO) to command the speed of rotation of the disc  123   1 . Varying the control voltage dephases more or less the disc rotation and therefore shifts by a duration t 0  or t 1  the creation of a pulse in the beam from laser  11 . 
   A disc  123   2  with two openings like that shown on  FIG. 6  can be used to avoid having to check the disc rotation phase. So that the pulses have the same shape and same duration T, the two openings have identical shapes (triangles, squares, rectangles, etc.). In addition, they are diametrically opposed and shifted by ½ an opening. The two pulses created are therefore shifted by half a width. The advantage is to provide the shift of ΔT/2 independently of the disc rotation spectral width. For a shift other than ΔT/2, the shift is no longer ½ an opening but adapted to the required time shift. 
   The two pulses are created on two separate beams since they have orthogonal polarizations, as shown on  FIGS. 7(   a ) and  8 . To do this, the beam from laser  11  is split into two beams. The polarizations of these two beams are orthogonal. This separation is produced, for example, with a polarizing prism  122   M . Disc  123   2  is positioned so that one beam crosses one of the openings directly. The other beam is guided to the other opening using, for example, a mirror  125 ″. One of the beams then has pulses at instants t 1  and the other beam has pulses at instants t 0 . To encode data, one or other of the two pulses must then be chosen. 
   The third example of realization of the third variant of encoder  1  shown on  FIG. 7(   a ) proposes a first pulse selection device. The two beams are recombined after passing through disc  123   2 . A repolarizing cube  122   V  is used to perform this recombination. It is placed on the path of one of the beams. The other beam is guided to the repolarizing cube  122   V  using, for example, a mirror  125 ′. The recombined beam has the two pulse types t 0  and t 1  each on a given polarization as shown on  FIG. 7(   b ). The selection device is placed on the light beam resulting from the recombination. It includes, for example, a modulator  121  which is activated or not depending on the pulse selected. The modulator  121  places the selected pulses corresponding to the data to be encoded on a given polarization. The selection device then only allows the polarization containing the selected pulses to pass, by using a polarizer  122 . 
   The selection device described by the fourth example of realization of the third variant of encoder  1  on  FIG. 8  is produced using another technique. It is an optical routing technique. It uses, for example, a Mach-Zender interferometer i set to zero step difference. The interferometer has two input and output channels that are arranged in a known configuration as shown on  FIGS. 9(   a ) and  9 ( b ). Depending on the dephasing introduced in one arm of the interferometer (e.g. 0 for t 0  or π for t 1 ), one of the input channels is connected to one of the output channels. This dephasing is easy to achieve by mounting one of the mirrors  125   i ′″ on a piezo-electric block  127   i . This is used to elongate the length of one arm by a distance equal to one wavelength. A half-wave plate  126  can be used on one of the input channels of the interferometer i. The polarizations of the two beams are then identical at the input of the interferometer i. 
   The examples of realization of the third variant of encoder  1  on  FIGS. 7 and 8  show an encoded pulse chopper  12   +3  which has a given structure. The encoded pulse chopper  12   +3  includes at least one particle flow separator  122   M  on two channels. A chopper  123  as such is used to chop on the particle flow pulses shifted by t 0  on the first channel and by t 1  on the second channel. A device ( 121 + 122  or i) is used to select at each period the pulse shifted by t 0  or by t 1  depending on the value “0” or “1” of the bit to be encoded on this period. 
   [ENCODER D] The fourth variant of encoder  1  is not illustrated. It includes a source supplying a continuous particle flow (single mode laser, etc.) Pulses of time width ΔT are chopped at frequency Tb in the continuous flow. They are produced by a pulse chopper  12  generating pulses either not shifted, or all shifted by t (0≦t≦Tb−ΔT). The structure of the pulse chopper  12  may, for example, be similar to that of the encoded pulse choppers  12   +3  described above. The pulses are then shifted or not by a delay gate  13  (for example similar to that of the second variant of encoder  1 ). The pulses output from the delay gate  13  then carry the data to be transmitted according, for example, to the diagram on  FIG. 1 . 
   Once the data is encoded as pulses shifted or not by an encoder  1  including, for example, an encoded pulse chopper  12   +3  on the particle flow from a continuous source  11 , it must be attenuated. The probability that the decoder  3  represented on  FIG. 10  detects two photons on the same pulse must be negligible. It is this principle which brings in the quantum dimension of the cryptography. The attenuator  2  is positioned after encoder  1  in the transmitter. It includes a half-wave plate  21  followed by a polarizer  22  which produces two beams: a “key” attenuated beam and a secondary beam. The intense beam leaving by the secondary channel can also be transmitted to the receiver. It is used, for example, to create a “sync” reference signal to synchronize the receiver clock. In particular, it is used to synchronize the decoder  3 . The “sync” signal is transmitted either directly in optical format or as a microwave signal, etc. 
   A first variant of the decoder  3  shown on  FIG. 11  ( a ) includes a photon counter  31 ′ activated only during the observation windows shown on  FIG. 2 . Following the detection of a photon in the “key” quantum signal by the photon counter  31 ′ in either of the observation windows, the decoder  3  decides whether a bit of value “0” or “1” has been transmitted. If the photon counter  31 ′ does not detect any photons in either observation window, the decoder  3  decides that there is non-reception. It cannot determine whether this non-reception is due to poor quality transmission or to interception by a third party. 
   If the time width ΔT and the spectral width Δv of the pulses transmitted satisfy the minimum state relation Δv.ΔT=1, a second variant of the decoder  3  proposed by  FIG. 11  ( b ) can be used. The laser  11  used to produce such pulses may be, for example, a mode-locked laser. The photons of the “key” quantum signal received are filtered by a filter  35  of spectral width Δv. The photons of spectral width Δv are observed by the photon counter  31 ′ activated on the observation windows shown on  FIG. 2 . The photons reflected by the filter Δv are also counted by a particle counter  31 ″. The comparator  32  checks whether the number N Δf  of reflected photons is greater than the number N Δv  of photons observed in the observation windows. If this is the case, the decoder  3  decides that the data transmitted has been intercepted by a third party. Otherwise, depending on whether the photon counter  31 ′ detects a photon in one or other of the observation windows, the decoder  3  decides whether a bit of value “0” or “1” has been transmitted. Lastly, if the photon counter  31 ′ does not detect any photons in either observation window, the decoder  3  decides that there is non-reception. It cannot determine whether this non-reception is due to poor quality transmission or to interception by a third party. 
   Depending on the type of source ( 11 ,  11   +2  etc.) used, for example a mode-locked laser, the pulse durations may then lie between 10 ps and 100 fs. These values of much less than the response times of some existing photon counters (typically 1 ns). In this case, the photon counter ( 31 ,  31 ′) cannot distinguish between a shifted pulse and a non-shifted pulse, or between a pulse shifted by t 0  and a pulse shifted by t 1 . This function can then be carried out by using, for example, an optical gate (not shown on the figures) upstream from the photon counter ( 31 ,  31 ′). This gate is electrically controlled It must be fast enough to produce detection gates of sufficiently short duration corresponding to the observation windows of  FIG. 2  if the response time of the photon counter ( 31 ,  31 ′) is too long. 
   The decoder  3  shown on  FIGS. 11  ( a ) and  11  ( b ) therefore includes at least one photon counter  31 ′ activated on the observation windows of  FIG. 2 . If the pulses transmitted by the transmitter have minimum state, the decoder can also include a filter of spectral width Δv upstream from the photon counter  31 ′. It may also include a photon counter  31 ″ on the flow reflected by the filter Δv and a comparator  32  receiving the number of particles detected by the photon counter  31 ′ and photon counter  31 ″ which can detect the interception of the transmission by a third party. 
     FIG. 12  shows a second example of realization of the quantum cryptography transmission system with time encoding according to the invention. A pulse source  11   +2  generates the particle flow as a train of pulses of time width ΔT and frequency Tb. For example, if the pulses are too short with respect to the switching time of a gate and/or for the shift to be detected by a photon counter  31 ′, the transmission system or encoder  1  used may have the structure of an interferometer  17  as shown on  FIG. 12 . In this case, the delay gate  13  includes the separating element  14  of the interferometer  17 . The particle flow is therefore split into two parts sent on the two arms of the interferometer  17 . In one arm, the delay gate  13  may, for example, transmit or not the pulse in a delay line  18  of duration ΔT/2 16 (if t 0 =0, t 1 =T/2) depending on the data to be encoded. The particle flows are attenuated on the two arms by the attenuator  2  before being transmitted as “key” signal. The attenuator may, for example, use the secondary flow as “sync” synchronization signal to synchronize the transmitter with the receiver. The decoder  3  then transmits or not the pulse of the other interferometer arm into a delay line  19  of identical duration ΔT/2 16. If the delay gate  13  and the decoder  3  have chosen the same delay  0  or ΔT/2, then the probability of detecting a photon is 100% in one of the output channels (channel a) and zero in the other channel (channel b). If the delay gate  13  and the decoder  3  have chosen different delays, then the probability of detecting a photon is 50% in each channel. The fact that the counter  31 ′ detects a particle in channel b is used to determine with 100% probability the delay which was chosen by the delay gate  13 . The particle counter  31 ′ may, for example, be replaced by the device shown on  FIG. 11  ( b ) if the pulses generated have minimum state. 
   An additional advantage of time ambiguity cryptography over polarization ambiguity cryptography is that the probability of the decoder  3  detecting a photon is greater when the decoder  3  uses two observation windows. 
   It will be readily seen by one of ordinary skill in the art that the present invention fulfills all of the objects set forth above. After reading the foregoing specification, one of ordinary skill will be able to affect various changes, substitutions of equivalents and various other aspects of the invention as broadly disclosed herein. It is therefore intended that the protection granted hereon be limited only by the definition contained in the appended claims and equivalents thereof.