Patent Publication Number: US-2005141716-A1

Title: Coherent-states based quantum data-encryption through optically-amplified WDM communication networks

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
      This application is a continuation in part of copending application Ser. No. 10/674,241, which is entitled “Ultra-Secure, Ultra-Efficient Cryptographic System”, and which was filed on Sep. 29, 2003 and the instant application claims priority of the following provisional applications: Ser. No. 60/517,422, which is entitled “Coherent-States Based Quantum Data-Encryption Through Optically-Amplified WDM Communications Networks”, and which was filed on Nov. 5, 2003; Ser. No. 60/518,966, which is entitled “Coherent-States Based Quantum Data-Encryption Through Optically-Amplified WDM Communications Networks, and which was filed on Nov. 10, 2003; and Ser. No. 60/546,638, which is entitled “Quantum Noise Protected Data Encryption for WDM Networks”, and which was filed on Feb. 20, 2004, and the entirety of these applications is hereby incorporated herein by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH  
      The United States Government has certain rights to this invention pursuant to Grant No. F30602-01-2-0528 from Defense Advanced Research Projects Agency (DARPA) to Northwestern University. 
    
    
     BACKGROUND OF THE INVENTION  
      Field of the Invention—The present invention relates generally to information security, and more particularly to a method and system for achieving the cryptographic objectives of data encryption and key expansion/generation/distribution.  
      Problems associated with information security have become a major issue in this still emerging openly accessible information society. While cryptography is an indispensable tool in addressing such problems, there are both questions of security and efficiency with the standard cryptographic techniques. The usual cryptographic algorithms utilizing private keys have yet to catch up with the data speed of the Internet fiber backbone, not to mention the projected increase of the fiber data rates in the future. The ones utilizing dual keys are even much slower. The private key algorithms, including DES and AES, are not proved to be secure against all attacks within their key-size limits. The public-key algorithms all rely on the presumed complexity of certain computational problems. Both types of algorithms are vulnerable to advances in computer technology, especially if a quantum computer becomes available. Additional problems arise in their use in a network environment, including key management issues as well as the usefulness and design of the public-key infrastructure.  
      The currently available quantum cryptographic techniques, based primarily on the well known techniques, have many intrinsic limitations that make them too slow and impractical for long-distance or network communications. The most famous of these proposals was made by Bennett-Brassard (BB84) in C. Bennett and G. Brassard, “Quantum crytpgraphy: Public key distribution and coin tossing” in  Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing,  Bangalore India, 1984, pp 175-179. In this scheme, two parties are able to remotely agree on a string of binary random numbers known only to each other. These random numbers are stored by the user for later use in a one-time pad (OTP) data encryption or as cryptographic keys in complexity-based encryption.  
      While OTP encryption does provide provable information-theoritic security on public channels, it is inefficient in the sense that every bit of data to be encrypted requires one bit of the generated one-time pad. This means that the encrypted data transmission rate is limited to the key generation rate. Due to technical and physical limitations, current implementations of BB84 have much lower rate-distance product than is available in traditional telecom channels. One of the major technical problems limiting BB84&#39;s key generation rate, and more importantly the rate-distance product, is the protocol&#39;s requirement for single-photon states. This requirement is a burden for not only in the generation of such states but also in that such states are acutely susceptible to loss, are not optically amplifiable (in general) and are difficult to detect at high rates.  
      For the encryption of data with perfect secrecy that cannot be broken with any advance in technology, one may, in principle, employ a one-time pad with a secret key obtained by Bennett-Brassard quantum cryptographic technique for key expansion. Such an approach may be possible; however, it is slow and inefficient because the key length needs to be as long as the data, and it also requires a nearly ideal quantum communication line that is difficult to obtain in long distance commercial systems such as the Internet core. On the other hand, for both military and commercial applications, there are great demands for secret communications that are fast and secure but not necessarily perfectly secure. There are many practical issues, human as well machine based, that would make theoretical perfect security in specific models not so important in real life.  
      The key lengths of traditional cryptographic algorithms are chosen such that current computers using the best known cracking algorithms will require an unreasonable amount of time to break the cipher. While some algorithms generate keys and/or ciphertext that appear to be secure through computational complexity, only in degenerate cases can any information-theoretic analysis of security be performed. The end result is that cipher cracking algorithms may exist that are much more powerful than a cryptographic protocol is provisioned for. Armed with the inherent measurement uncertainty of non-orthogonal quantum states, several protocols have been proposed offering quantum effects as cryptographic mechanisms. A shortcoming of all these proposed protocols is their inherent inability to be optically amplified.  
      A further consideration is the nature of the transmission network over which quantum encrypted data is being transmitted. Free space or fiber optic links, such as WDM networks are important because they make up the existing optical telecommunications infrastructure. WDM networks are in-line amplified optical fiber links where many independent “streams” or “channels” of data traffic flow simultaneously. In systems in which quantum-noise protected data encryption is based on varying the polarization-state of light, polarization effects in WDM networks affect the polarization-state of light such that the input polarization state of light into a WDM network is not the same as the output polarization state of light. Moreover, this “transformation” happens in a random way that is difficult to track. Consequently, it is desirable to have a cryptographic communications scheme that is independent of the transmission medium, and in particular that is not based on the polarization-state of light. Moreover, it is desirable that such a communication scheme operate seamlessly over WDM networks.  
      It is accordingly the primary objective of the present invention that it provide an improved method and system for transmitting encrypted data between first and second locations.  
      It is another objective of the present invention that it provide a method and system for transmitting encrypted data between first and second locations independently of the transmission medium existing between the two locations.  
      A further objective of the present invention is that it provide an improved method and system for transmitting encrypted data over WDM networks between first and second locations over any transmission medium such as free-space or optical fiber.  
      A further objective of the present invention is that encrypted signals, where encryption is provided via the present invention, are able to seamlessly propagate with multiplexed conventional unencrypted channels in a free-space or optical fiber network which may or may not be an optically amplified line using erbium, Raman, semiconductor, parametric, or any other optical amplifier in use today.  
      Another objective of the present invention is that it provide an encryption/decryption method and system that reduce the requirements on drive electronics.  
      The apparatus of the system of the present invention must also be of construction which is both durable and long lasting, and it should also require little or no maintenance to be provided by the user throughout its operating lifetime. In order to enhance the market appeal of the apparatus of the present invention, it should also be of inexpensive construction to thereby afford it the broadest possible market. Finally, it is also an objective that all of the aforesaid advantages and objectives be achieved without incurring any substantial relative disadvantage.  
     REFERENCES  
      Background information, together with other aspects of the prior art, including those teachings useful in light of the present invention, are disclosed more fully and better understood in light of the following references, each of which is incorporated herein in its entirety. 
      [1] N. Gisin, G. Ribordy, W, Tittel, and H. Zbinden, “Quantum cryptography,”  Reviews of Modern Physics,  vol. 74, pp. 145-195, 2002.     [2] G. Barbosa, E. Corndorf, P. Kumar, H. Yuen, “Secure communication using mesoscopic coherent states,”  Physics Review Letters,  vol. 90, 2003,     [3] E. Corndorf, G. Barbosa, C. Liang, H. Yuen, and P. Kumar, “High-speed data encryption over 25 km of fiber by two-mode; coherent-state quantum cryptography,”  Optics Letters,  vol. 28, pp. 2040-2042, 2003.     [4] E. Selmer,  Linear Recurrence over Finite Field,  Norway; University Of Bergen, 1996.     [5] N. Zierler and J, Brillhart, “On primitive trinomials (mod 2).”  Journal of Information and Control,  vol. 15, pp. 541-544. 1968.     [6] C. Helstrom,  Quantum Detection and Estimation Theory,  New York; Academic, 1976.     [7] E. Corndorf, G. S. Kanter, C. Liang, and P. Kumar, “Quantum-noise protected data encryption for WDM networks,” presented at the Conference on Lasers and Electro-Optics (CLEO&#39;2004), San Francisco, Calif., May 16-21, 2004; paper CPDD8.     [8] E. Corndorf, C. Liang, G. S. Kanter, P. Kumar, and H. P. Yuen, “Quantum-noise-protected data encryption for WDM fiber-optic networks,” ACM Computer Communication Review: Special Section on Impact of Quantum Technologies on Networks and Networking Research, Vol. 28, October 2004.    

     SUMMARY OF THE INVENTION  
      The disadvantages and limitations of the background art discussed above are overcome by the present invention. With this invention, there is provided a quantum cryptographic protocol using two-mode coherent states that is optically amplifiable, resulting in a polarization independent system that is compatible with the existing WDM infrastructure. The method and system provide secure data encryption suitable for wavelength division multiplexing networks through an in-line amplified line.  
      The present invention provides a method for transmitting encrypted data from a first location to a second location over a communication link that includes a plurality of transmission channels over which a plurality of independent channels of data traffic flow simultaneously, wherein unencrypted data is transmitted over a plurality of the transmission channels transmit. The method includes encrypting a light wave with data to be transmitted; coupling the encrypted light wave onto one of the transmission channels of the communication link at the first location; transmitting the encrypted light wave to the second location over the communication channel; and decrypting the encrypted light wave at the second location to recover the transmitted data. The communication link can include a free-space portion or a fiber-optic wavelength division multiplexing network. The encrypted light wave can be multiplexed onto the transmission channel that is carrying a conventional unencrypted information bearing light wave for transmission over the transmission channel. The encrypted light wave and the unencrypted information bearing light wave can be transmitted at different data rates over the transmission channel. The encrypted light wave can be amplified while the encrypted light wave is being transmitted from the first location to the second location, including being amplified at the first and/or second locations. The method can be implemented over all types of networks, including enterprise, metro, short haul, and long haul networks, and independent of underlying software protocols.  
      Further in accordance with the present invention, there is provided a method and system for transmitting data from a first location to a second location over a communication channel. In accordance with the invention a shared multi-bit secret key K is extended at the transmitting and receiving locations to produce an extended key K′. The extended key K′ is mapped to a function to produce a mapped extended key K″ that is used at the transmitting location, along with the bits of the binary bit sequence to be transmitted, to select a quantum state for each bit to be transmitted to the receiving location. A light wave is modulated with the selected quantum states for transmission to the receiving location over an all optical channel. At the receiving location, using the mapped extended key K″, the modulated light wave transmitted over optical channel is subjected to an all-optical rotation to a state corresponding to the mapped extended key K″, effectively decrypting the optical signal. The signal is demodulated to recover the binary bit sequence, and the binary bit sequence is decoded to recover the binary bit sequence transmitted.  
      When operating in polarization mode, the bases correspond to orthogonal pairs of polarization-states and decoding includes flipping each received data bit as a function of the mapped extended key. When operating in the time mode, the bases correspond to antipodal phase-states and decoding includes differentially flipping each received data bit as a function of the mapped extended key.  
      The system of the present invention is of a construction which is both durable and long lasting, and which will require little or no maintenance to be provided by the user throughout its operating lifetime. The system of the present invention is also of inexpensive construction to enhance its market appeal and to thereby afford it the broadest possible market. Finally, all of the aforesaid advantages and objectives are achieved without incurring any substantial relative disadvantage. 
    
    
     DESCRIPTION OF THE DRAWINGS  
      These and other advantages of the present invention are best understood with reference to the drawings, in which:  
       FIG. 1  is a graph illustrating a numerical calculation of Eve&#39;s maximum information acquired via an optimal individual ciphertext-only attack on a message for values of M=1001 and M=2047;  
       FIG. 2  illustrates a plurality of pairs of orthogonal states uniformly spanning a great circle of the Poincare sphere in an embodiment employing polarization mode operation;  
       FIG. 3  illustrates a plurality of pairs of orthogonal phase states uniformly spanning a phase circle in an embodiment employing time mode operation;  
       FIG. 4  is a process flow chart for quantum-noise protected data encryption schemes provided by the present invention;  
       FIG. 5  is a schematic of a quantum data encryption/decryption system using polarization states in an all-optical network in accordance with the invention;  
       FIG. 6  is a schematic of one example of a WDM network including a link over which travels the encrypted data produced by the system of  FIG. 5 ;  
       FIG. 7  is a graph showing the optical spectrum after a first arrayed waveguide grating in the fiber link of the WDM network of  FIG. 6 ;  
       FIG. 8  is an Eye diagram of a pseudo-random bit sequence channel at the start of a WDM fiber link of the WDM network of  FIG. 6 ;  
       FIG. 9  is a graph showing the optical spectrum at the end of the WDM fiber link of the WDM network of  FIG. 6 ;  
       FIG. 10  is an Eye diagram of a pseudo-random bit sequence channel at the end of the 100 km WDM fiber link of the WDM network of  FIG. 6 ;  
       FIG. 11  shows a sequence of bits corresponding to a digital photo of an American flag transmitted from Alice to Bob using the quantum data encryption/decryption system of  FIG. 5 ;  
       FIG. 12  shows the same sequence of the bits shown in  FIG. 11 , but as seen by the attacker, Eve;  
       FIG. 13  is a simplified representation of a polarization independent receiver for use in decryption and demodulation of AlphaEta M-ry time mode encrypted signals in accordance with the present invention;  
       FIGS. 13   a - 13   d  are simplified representations of other polarization independent receivers that are similar to the polarization independent receiver of  FIG. 13 ; and  
       FIG. 14  is a schematic of a realization of a quantum data encryption/decryption system incorporating the receiver of  FIG. 13 . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
      The present invention provides a quantum cryptographic protocol using two-mode coherent states that is optically amplifiable, resulting in a polarization independent implementation that is compatible with the existing WDM infrastructure, and an alternative implementation using polarization states that is particularly suited for free-space applications. Note that either implementation is applicable to both free-space and fiber-optic WDM networks. The present invention provides secure data encryption suitable for wavelength division multiplexing networks through an in-line amplified line. According to the present invention, any number of channels of a transparent WDM network, either in optical fiber or in free space, can be encrypted between two end points and such encrypted communication can be multiplexed with conventional unecrypted communication. The encrypted and unencrypted channels can be at different data rates and can simultaneously pass through optical amplifiers, optical multiplexers and demultiplexers including reconfigurable optical add/drop multiplexers, and any number of other optical networking elements that are used in present day optical communication and networking infrastructure. The encryption methods described in this invention can be implemented over all types of networks, including enterprise, metro, short haul, and long haul, and are independent of underlying software protocols. Furthermore, the time-mode scheme described below can be implemented on an optically amplified fiber line using erbium, Raman, semiconductor, parametric, or any other optical amplifier in use today.  
      Coherent-State Data Encryption: Polarization Implementation  
      We discuss first the polarization mode implementation. The time mode implementation is described starting at paragraph [0062]. The irreducible measurement uncertainty of two-mode coherent states is the key element in the security of applicants&#39; scheme. The two-mode coherent states (polarization states) employed in this scheme are 
 
|ψ m   (a) &gt;=|α&gt; I   {circle over (×)}|αe   iθ &gt; y ,   (1) 
 
|ψ m   (b) &gt;=|α&gt; r   {circle over (×)}|αe   i(θ     m+)   &gt; y ,   (2) 
 
 where θ m =πm/M, mε{0, 1, 2, . . . (M−1)}, and M is odd. Viewed on the Poincaré sphere, these 2 M polarization states form M bases that uniformly span a great circle as shown in  FIGS. 2 and 3 . Using a publicly known key extension algorithm, for example, an s-bit linear feedback shift-register (LSFR) with judiciously chosen feedback terms, the transmitter (Alice) extends an s-bit secret-key, K, to a (2 s −1) bit extended key, K′, which is then deterministically mapped on to (1-to-1) different 10-bit sequences producing a mapped, extended key K″. The extended and mapped key K″ is grouped into disjointed blocks of r-bit running keys, R, where r=log 2  (M) and s&gt;&gt;r. Depending on the data bit and the running-key R, the state in equation (1) or equation (2) is transmitted, where m is the decimal representation of R and the data bits are defined differentially. Specifically, if m is even, then (0,1)→(|ψ m   (a) &gt;, |ψ m   (b) &gt;) , and if m is odd, then (0,1)→(|ψ m   (b) &gt;, |ψ m   (a) &gt;). Stated in another way, logical zero is mapped to (|ψ m   (a) &gt; |ψ m   (b) &gt;) if the previously transmitted state was from the set (|ψ m   (a) &gt; |ψ m   (b) &gt;) and logical one is mapped to (|ψ m   (b) &gt; |ψ m   (a) &gt;) if the previously transmitted state was from the set (|ψ m   (b) &gt; |ψ m   (a) &gt;). This results in the mapping of the symbols on the phase circle to be interleaved 0,1,0,1, . . . , as shown in  FIG. 2 . 
 
      Using the same s-bit secret-key and LFSR, the intended receiver (Bob) applies unitary transformations to his received polarization states according to the running-keys. These transformations (polarization rotations) decrypt the received states resulting in either |ηα&gt; x |ηα&gt; y  or |ηα&gt; x |−ηα&gt; y  depending on the logical bit where η is the channel transmissivity. Bob then further rotates the states by π/4 so that the states under measurement are given by equations (3) and (4) as follows: 
 
|ψ m   (a) &gt; =|{square root}{square root over (2)}ηα&gt; I {circle over (×)}|0&gt; y ,   (3) 
 
|ψ m   (b) &gt; =|0&gt; I {circle over (×)}|−{square root}{square root over (2)}ηα&gt; y ,   (4) 
 
 where η is the channel transmissivity. Equations (3) and (4) make up a two-mode, on-off-key signal set, where the logical mapping corresponds to the parity of the running-key, R. The decrypted, logically encoded states are then detected using two-mode difference photodetection. 
 
      Without knowledge of the secret-key and lacking the plain-text, an eavesdropper (Eve) is unable to decrypt Alice&#39;s transmission, even when granted ideal detection equipment and all of the transmitted energy. Individual ciphertext-only attacks on the message are thwarted by the irreducible measurement uncertainty of two-mode coherent states. An attack on the message requires Eve to distinguish neighboring polarization states due to the interleaving of the logical bit mappings ( FIG. 2 ). A calculation of Eve&#39;s optimal quantum measurement shows that her information per bit I asymptotically approaches ½ as |α| is decreased for a given value for M, as shown in  FIG. 1 . The inability to distinguish neighboring polarization states also assures computational security of the secret-key, even if Eve possesses a quantum computer, by forcing the search space of possible LFSR states to be exponential in “s”. With the addition of classical randomization at the transmitter, the scheme provides information theoretic security for the secret-key against a ciphertext-only attack.  
      Referring to  FIG. 4 , there is illustrated a flow chart of the quantum-noise protected data encryption scheme for both polarization- and time-mode in accordance with the present invention. The following is a description of the flow chart.  
      The users (Alice and Bob) use a deterministic extension-algorithm, respective blocks  20  and  26 , to extend a shared s-bit secret-key known only to them. Such algorithms may include linear-feedback shift-registers, or existing stream-ciphers. The extended key, now much longer than the s-bit secret-key, then undergoes a deterministic transformation known as “mapping”, respective blocks  21  and  27 . The purpose of this transformation is to spread the errors that an attacker eventually makes when estimating the running keys across the entire extended key are not focused on just a few bits of each running key. An example of such a “mapping function” would be to deterministically map (1-to-1) 10-bit non-overlapping blocks of the extended key to different 10-bit sequences. Further details as to expansion of secret keys for use in quantum encryption/decryption schemes is described in U.S. application Ser. No. 10/674,241, which was filed on Sep. 29, 2003, which is assigned to the same assignee as the present application.  
      Alice then uses her mapped extended-key K″, along with the data bit sequence to be transmitted, encoded by a DPSK encoder function, block  22 , used only in the time-mode scheme, to select a quantum-state to be generated. In contrast to the polarization-mode scheme, the logical bits in the time-mode scheme are defined differentially. The encoding rule is the following: given a sequence of bits X to be differentially encoded into a sequence of bits Y, Y n =XOR(X n , X n−1 ). For example, a data sequence 1001010 would be encoded as 010111. Specifically, consecutive, non-overlapping groups of the extended key (called running keys) are used to select a “basis” on which to encode the data bit, block  23 . These bases correspond to orthogonal pairs of polarization-states in the polarization-mode scheme and antipodal phase-states in the time mode scheme; see  FIG. 3 . Depending on the logical bit to be transmitted (0 or 1), one of the two states that make up a basis is chosen for generation and transmission, block  24 . This mapping of data bits onto polarization or phase-states is done in a geometrically interleaved way 0,1,0,1,0,1 . . . as shown in  FIG. 3 . Optionally, before entering the quantum-state generator, the chosen state to be transmitted can undergo another permutation known as deliberate state randomization (DSR), block  25 . The deliberate state randomization can be carried out by an analog or digital truly random or pseudo random number generator. Under DSR, the selected state to be generated and transmitted undergoes a randomization known only to Alice. This randomization will result in the actual state that is generated to be within ±θ that is less than or equal π/2 (on the “circle”) with respect to the pre-DSRed state (FIG.  3 ). The magnitude of such θ value is an adjustable parameter which controls the level of security in the AlphaEta scheme. After the optional step of DSR, the chosen state to be transmitted is sent to the quantum-state generator for optical-state encoding for transmission over an optical channel to the receiving location (Bob).  
      On receiving the quantum-state transmission, the receiver (Bob) uses his mapped, extended-key to apply an all-optical rotation to the state corresponding to his mapped, extended-key (which is the same as Alice&#39;s). This rotation effectively decrypts the optical signal, block  28 . The optical signal then enters an optical demodulator/detector, block  29 , where the optical signal is converted into an electrical signal and a bit decision is made and the detected bits are passed to a post-coder function, block  30 .  
      Digressing, before a description of the post-coder function can be given, a little more information on the encoding process is required. At the transmitter (Alice) sufficient electrical voltage (power) is required to be able to generate all of the possible quantum-states in either the polarization-mode or time-mode schemes by driving optical phase-modulators. In the time-mode scheme, this corresponds to a phase modulation from 0 to 2π radians and in the polarization-mode scheme, this corresponds to a full “great circle” polarization-state rotation. In either  30  case, the corresponding voltages required are 0 to 2 V π  volts where V π  is a characteristic voltage of the phase modulator.  
      On the receiving end (Bob), the need to rotate the phase or polarization-state of the incoming signal, which corresponds to a drive voltage of 0 to 2 V π  volts, is still present in order to properly decrypt the arriving optical signal. The post-coder function, block  30 , helps to alleviate the voltage (power) requirements on Bob&#39;s phase modulator(s) by introducing a coding scheme whereby the voltage required to drive Bob&#39;s phase modulator(s) is cut in half from 0 to 2 V π  volts to 0 to V π  volts.  
      In the polarization-mode scheme, the post-coder function, block  30 , simply corresponds to “flipping” each received data bit as a function of the mapped extended-key. Specifically, if the last bit of a running key corresponding to a particular data bit were 0, then nothing should be done to the data bit. If, on the other hand, the last bit of a running key corresponding to a particular data bit were 1, then the data bit should be flipped.  
      In the time-mode scheme, the post-coder function, block  30 , is slightly more complicated that in the polarization-mode scheme. A similar flipping of data bits is required as a function of the last bit of each running key with an addition. Due to the fact that the data bits are differentially encoded at the transmitter, the post-coder function, block  30 , requires a “differential flipping rule” which essentially states that if the two consecutive data bits “need” to be flipped according to the last bit of the running key, then flip the first bit, don&#39;t flip the second bit, and flip the third bit. The same rule applies for n consecutive bits that “need” to be flipped; flip the first bit, don&#39;t flip the next (n−1) bits, and flip the (n+1) bit.  
      Again, the purpose of the post-coder function, block  30 , is simply to reduce the voltage (power) required to drive the phase modulator(s) at the receiver and to improve the quality of the transitions in the received signal. This technique cannot be used at the transmitter (Alice).  
      Experimental Setup of the Polarization Implementation  
       FIG. 5  is a schematic of a quantum data encryption/decryption system  40  in accordance with the invention, including a quantum data-encryption transmitter  42  coupled to a receiver  44  over an all-optical network, such as a wavelength division multiplexing (WDM) network  46  over which the encrypted data travels.  
      The transmitter (Alice)  42  includes a laser  48 , a polarization-control-paddle (PCP)  50 , a phase modulator  52  and an optical amplifier  53 . The transmitter further includes an extended key generator which can be implemented by a personal computer (PC)  54 , or alternatively by a microprocessor embedded in an field-programmable gate array. The output of the PC  54  is coupled through a digital-to-analog (D/A) converter  56  and an amplifier  58  to the phase modulator  52 .  
      The laser  50  can be a distributed-feedback (DFB) laser. The phase modulator  52  can be a 10 GHz-bandwidth fiber-coupled LiNbO3 phase modulator that is driven by the output of the D/A converter  56  amplified by the amplifier  58 . The output of the phase modulator  52  is coupled to an all optical network through the optical amplifier  53 . The D/A converter  56 , which can be a 12-bit digital-to-analog converter, introduces a relative phase (0 to 2π radians) between the two polarization modes. The extended key generator can be a linear feedback shift register (LFSR) implemented in software on a personal computer (PC)  56 , or alternatively by a microprocessor embedded in an field-programmable gate array.  
      The receiver (Bob)  44  includes an optical wave amplifier  60 , a phase modulator  62 , a second PCP  64 , and a polarizing beam splitter  66 . In addition, the receiver includes a pair of detectors  68  and  69  having associated amplifiers  70  and  71 , respectively, and an analog to digital converter (A/D)  72 , which is interposed between the outputs of the amplifiers  70  and  71  and a personal computer (PC)  74 . The receiver  44  further includes a digital to analog converter (D/A)  76  and an electrical signal amplifier  78  through which the output of the PC  74  is applied to the phase modulator  62 .  
      The optical wave amplifier  60  can be an erbium-doped fiber amplifier (EDFA) having approximately 30 dB of small signal gain and a noise figure very close to the quantum limit (NF≅3 dB). The phase modulator  62  can be a LiNbO3 phase modulator. The PCP  64  is interposed between the optical wave amplifier  60  and the phase modulator  62  for canceling the polarization rotation caused by the fiber in an optical fiber communication link of the WDM network  46  over which the encrypted data is transmitted from the transmitter  42  to the receiver  44 . The beam splitter  66  can be a fiber-coupled polarization beam splitter (FPBS) oriented at π/4 radians with respect to the principal axes of the phase modulator  62 . The extended key generated by the software implemented LFSR in the PC  74  is applied via the D/A converter  76  and amplifier  78  to the phase modulator  62 . The detectors  68  and  69  can be 1 GHz-bandwidth InGaAs PIN photodiodes. The electrical signal amplifiers  70  and  71  can be 40 dB-gain amplifiers.  
      Referring now to  FIG. 6 , there is shown a schematic of a WDM network which can implement the WDM network  46  of  FIG. 6 , effectively simulating random, real-world data traffic. The WDM network  46  includes a WDM link  80  representing a portion of the WDM network  46  over which the encrypted data produced by the system  40  of  FIG. 5  travels. Along with the quantum-noise encrypted data, classical data traffic also propagates through the described WDM link  80 . For simulating other “data traffic”, light from two DFB lasers  82  on the 100 GHZ ITU grid (1546.9 nm and 1553.3 nm) is mixed on a 3 dB coupler  84  where one output is terminated and the other enters a 10 GHz-bandwidth fiber-coupled LiNbO3 intensity modulator (Mach-Zender)  86 . The intensity modulator  86  is driven by the amplified output of a 10 Gbps pseudo-random bit sequence (PRBS) generated by a 10 Gbps pattern generator/BERT  88  with PRBS period 2 31 −1 bits. The PRBS modulated ITU grid channels (hereafter referred to as the PRBS channels) then pass through an EDFA amplifier  95  to compensate for losses before entering, and being spectrally separated by, an arrayed-waveguide grating (AWG)  90 . By introducing a one meter fiber length difference between the separated PRBS channels before launching them into the 100 km WDM link  80 . As shown in  FIG. 6 , the 100 km WDM link  80  consists of two 100 GHz-spacing 40-channel arrayed-waveguide gratings (AWG)  91  and  92 , two 50 km spools of single-mode fiber (such as Corning SMF-28e type fiber)  93  and  94 , and an in-line amplifier (EDFA)  95  with an output isolator. The amplified, group-velocity-dispersion compensated PRBS channel is detected using an InGaAs PIN-TIA receiver  98  and measured by the 100 Gbps BERT  88 .  
      Referring again to  FIG. 5 , in operation, the polarization-control-paddle (PCP)  50  is adjusted to project the light from the DFB laser  48  equally into the two polarization modes of Alice&#39;s fiber-coupled phase modulator  52 . The phase modulator  52  is driven by the amplified output of the digital-to-analog converter  56  to introduce a relative phase between the two polarization modes. By way of example, the phase can be 0 to 2π radians. The software-implemented LFSR yields a running-key, that when combined with a data bit, instructs the generation or one of the two states in accordance with equation (1) or (2).  
      On passing through the WDM link  80  of the WDM network  46 , from an input Crypto. In at AWG  91  and to an output Crypto. Out at AWG  92 , the light is amplified by the optical wave amplifier  95 . From the output Crypto. Out, before passing through Bob&#39;s phase modulator  62 , the received light is sent through the PCP  64  to cancel the polarization rotation caused by the fiber in the WDM link  80 . While these rotations fluctuate with a bandwidth on the order of kilohertz, the magnitude of the fluctuations drops quickly with frequency, allowing the use of a manual PCP to cancel the unwanted polarizations. In other implementations, Bob&#39;s measurements can be used to drive an automated feedback control on the PCP.  
      The relative phase shift introduced by the phase modulator  62  is determined by the running-key R generated through the software LFSR in Bob&#39;s PC  74  and applied via the output of the D/A converter  76  amplified by amplifier  78 . After this phase shift has been applied, the relative phase between the two polarization modes is 0 or π, corresponding to a 0 or 1 according to the- running-key: if R is even, then (0, π)→(0, 1) and if R is odd, then (0, π)→(1, 0). With use of a fiber-coupled polarization beam splitter (FPBS)  66  oriented at π/4 radians with respect to the principal axes of the phase modulator  62 , the state under measurement [equations (3) or (4)] is direct-detected by using two photodiodes operating at room temperature, one for each of the two polarization modes. The resulting photocurrents from photodiodes  68  and  69  are amplified by respective electrical signal amplifiers  70  and  71 , sampled by the analog-to-digital (A-D) converter  72 , and stored for analysis. The overall sensitivity of Bob&#39;s preamplified receiver was measured to be 660 photons/bit for 10 −9  error probability.  
      On propagating through the WDM link  80  ( FIG. 6 ), one of the two PRBS channels is amplified with a 20 dB gain EDFA  95  (operating in the linear regime) and group-velocity-dispersion compensated −1530 ps/nm using a dispersion compensation module (DCM). While the group velocity dispersion introduced by the 100 km WDM link  80  is approximately 1700 ps/nm, but can be other value. The amplified, group-velocity-dispersion compensated PRBS channel is detected using an InGaAs PIN-TIA receiver and measured by the 100 Gbps BERT. Bit error rates for each of the PRBS channels are measured separately using the BERT.  
      The 100 km WDM link  80  is loss compensated by the in-line EDFA  95 . The 10 dB power loss of the first 50 km spool of fiber  93  (0.2 dB loss per kilometer) is compensated for by 10 dB of saturated gain from the in-line EDFA  95 . The overall loss of the WDM link  80  is therefore 15 db where 10 dB come from the second 50 km spool of fiber  94  and the remaining 5 dB come from the two AWGs  91 ,  92 ; 2.5 dB of loss each.  
      Experimental Results from the Polarization Implementation  
      Experiments have successfully demonstrated quantum data-encryption through a data bearing 100 km WDM link using the encryption/decryption system including the transmitter/receiver pair of  FIG. 5  coupled together by the WDM link  80  in  FIG. 6 . The experiments have also demonstrated that in the 100 km WDM link, the quantum encrypted channel does not negatively impact the data bearing channels.  FIG. 7  shows the optical spectrum of the 100 km WDM link after the first AWG acquired with a 0.01 nm resolution bandwidth. The launch power in the quantum encrypted channel is −25 dBm and the launch power in each of the PRBS channels, located four 100 GHz ITU grid channels away from the encrypted channel, is 2 dBm. An eye diagram of the 1546.9 nm PRBS channel at launch is shown in  FIG. 8 . Measuring after the first AWG in the 100 km WDM link, neither PRBS channel showed any bit errors in 10 terabits communicated.  
       FIG. 9  shows the optical spectrum (0.01 nm resolution bandwidth) after the second 50 km spool of fiber  94  in the 100 km WDM link  80 .  FIG. 9  clearly shows both 10 dB of loss in the signals as well as a 10 db increase in the amplified-spontaneous-emission dominated noise floor. An eye diagram of the 1546.9 nm PRBS channel, post dispersion compensation, is shown in  FIG. 10 . While some group-velocity-dispersion is clearly visible in the eye diagram, the bit-error rate for each of the PRBS channels is “error free” at only 5e-11. Both the bit-error rates and eye diagrams of the PRBS channels did not change when the quantum encrypted channel was turned off.  
       FIG. 11  shows results from 5000 A-D measurements (one of the two polarization modes) of a 9.1 Mb bitmap file transmitted from Alice to Bob, shown in the top portion of  FIG. 11 , and to Eve, shown in the bottom portion of  FIG. 11 , through the 100 km WDM link. The data rate is 250 Mbps. The insets show the respective decoded images. In this experiment, actions of Eve are physically simulated by Bob starting with an incorrect secret-key. Clearly, a real eavesdropper would aim to make better measurements by placing herself close to Alice and implementing the optimal quantum measurement. While  FIG. 11  does not explicitly demonstrate Eve&#39;s inability to distinguish neighboring polarization states, it does, however, show that a simple bit decision is impossible. In one experiment that was conducted, the 12-bit D-A conversion allows Alice to generate and transmit 4094 distinct polarization states (M=2047 bases). The numerical calculation used to plot  FIG. 1  (left side) then shows that for −25 dBm launch power at 250 Mbps and M=2047, Eve&#39;s maximum obtainable information in an attack on the message is less than 1e-12 bits/bit. Note, however, that because of the use of a short secret-key (32-bits), the security of this particular demonstration is weak against attacks on the secret-key through exhaustive search.  
      Coherent-State Data Encryption: Time-Mode Implementation—Polarization Independent Decryptor Compatible With Standard NRZ and RZ Communication Formats  
       FIG. 13  is a simplified representation of a receiver  110  for use in the decryption and demodulation of AlphaEta M-ry two-mode (time-mode) encrypted signals. The receiver  110  is a totally polarization-independent M-ry decryptor  112  followed by a totally polarization-independent two-mode (time-mode) demodulator  114 . The M-ry decryptor  112  is compatible with both standard non-return to zero (NRZ) and return to zero (RZ) communication formats. The receiver  110  is totally polarization insensitive. The receiver  110  includes phase stabilization.  
      More specifically, with reference to  FIG. 13 , only optical components of the receiver  110  are shown for the simplified representation of the receiver  110 . The receiver  110  includes an optical amplifier  116 , a pair of concatenated optical phase-modulators  118  and  120  that are connected with polarization-maintaining fiber  122  and oriented with a 90° rotation, so that the two polarization-modes of the optical signal receive the same amount of optical phase-modulation, thereby making the process of decryption insensitive to the polarization-state of the incoming light. The demodulator  114  includes an optical circulator  124  and a fiber Michelson interferometer formed by a 50/50 optical coupler  126  and two Faraday mirrors (FM)  130  and  131 . A path length difference is provided by a fiber loop  128  in one of the arms. The path length difference in the arms of the interferometer corresponds to the period of an optical symbol (bit). The receiver  110  includes a detector including two PIN photodiodes  132  and  133 . The operation of the receiver  110  is described below with reference to  FIG. 14 .  
      The receiver  140  shown in  FIG. 13   a  is similar to the receivers that are described with reference to FIGS. 18 and 27 in U.S. application Ser. No. 10/674,241, which was filed on Sep. 29, 2003. The receiver  140 , only optical components of which are shown, includes an optical amplifier  116  and asymmetric optical path lengths, including a long arm and a short arm, the long arm including an optical phase-modulator  144  and the short including a polarization-control-paddle (PCP)  145 . The receiver  140  includes a detector formed by two photodiodes  132  and  133 .  
      The receiver  140  produces sub-bit period twin pulses which are not in the NRZ format. The receiver  140  is externally and internally polarization sensitive. In addition, the receiver  140  requires an exotic detection timing and requires stabilization of the interferometer.  
      The receivers  150 ,  160  and  170 , shown in  FIGS. 13   b,    13   c  and  13   d,  respectively, represent receiver designs intermediate the receiver  110  shown in  FIG. 13  and the receiver  140  shown in  FIG. 13   a,  depicting the evolution of the receiver  110  shown in  FIG. 13 . The receiver  150 , only optical components of which are shown, includes phase modulators  152  and  154  separated by a length of polarization maintaining fiber (PMF)  156 . The receiver  150  produces twin pico-second pulses which are not in the NRZ format. The receiver  150  is externally and internally polarization sensitive. In addition, the receiver  150  requires an exotic detection timing.  
      The receiver  160  is totally polarization insensitive. The receiver  160 , only optical components of which are shown, includes an optical circulator  124  and a fiber Michelson interferometer, formed by an optical coupler  126  and two Faraday mirrors  130  and  131  in the manner of receiver  110 . In addition, the receiver  160  requires phase stabilization.  
      The receiver  170 , only optical components of which are shown, includes a pair of concatenated optical phase-modulators  118  and  120  that are connected with polarization-maintaining fiber  122  and oriented with a 90° rotation. Consequently, the two polarization-modes of the optical signal receive the same amount of optical phase-modulation, thereby making the process of decryption insensitive to the polarization-state of the incoming light. The receiver  170  produces 50/50 duty cycle pulses in an NRZ format with the bit rate limited by the bandwidth of the modulator. The receiver  170  includes phase stabilization.  
      The receivers  150 ,  160  and  170 , shown in  FIGS. 13   b - 13   d,  are feasible. However, the receiver  110  shown in  FIG. 13  has several practical advantages and is compatible with standard NRZ and RZ communication formats being used with WDM communications today.  
       FIG. 14  is a detailed schematic of a time-mode implementation including a transmitter  108  and the receiver  110  shown in  FIG. 13  and the surrounding functions, and accordingly like components have been given the same reference numbers. The detailed schematic of  FIG. 14  includes optical as well as electronic elements of the decryption/demodulation receiver  110 . The transmitter  108  includes a laser  200 , coupled to a phase modulator  202  by a length of polarization-maintaining fiber (PMF)  204 . The output of the phase modulator  202  is coupled to an all optical network through an optical amplifier  206 . The phase modulator  202  is driven by an electrical drive signal produced by a microprocessor  210 , the output of which is coupled to the phase modulator  202  through a digital-to-analog converter  212  and an amplifier  214 . Inputs to the microprocessor  210  include the secret key, the data bits to be encrypted and a clock signal for synchronization.  
      More specifically, the phase modulator  202  can be a lithium niobate phase modulator. The optical phase of the light is changed by the phase modulator  202  in response to the drive signal applied to the phase modulator  202 . The drive signal, consisting of differential-phase-shift-keyed data-bit information as well as an encryption signal, is the amplified output of a digital-to-analog converter  212  that is driven by a micro-processor/micro-controller  210 .  
      As described above, the receiver  110  is a totally polarization-independent M-ry decryptor  112  followed by a totally polarization-independent two-mode (time-mode) demodulator  114 . The M-ry decryptor  112  is compatible with both standard non-return to zero (NRZ) and return to zero (RZ) communication formats. The receiver  110  includes an optical amplifier  116 , a pair of concatenated optical phase-modulators  118 , 120  that are connected with polarization-maintaining fiber  122  and oriented with a 90° rotation, so that the two polarization-modes of the optical signal receive the same amount of optical phase-modulation, thereby making the process of decryption insensitive to the polarization-state of the incoming light. The receiver  110  includes a demodulator  114  formed by an optical circulator  124  and a fiber Michelson interferometer. The interferometer includes a 50/50 optical splitter  126  and two Faraday-rotator mirrors (FM)  130  and  131 . A path length difference is provided by a fiber loop  128  in one of the arms. The path length difference in the arms of the interferometer corresponds to the period of an optical symbol (bit). The detector of the receiver  110  includes two photodiodes  132  and  133 . The design of the demodulator is chosen to maintain polarization insensitivity using fiber-based components. Other demodulators, such as asymmetric Mach-Zehnder interferometers integrated on an, optical substrate, can also be used.  
      The Michelson interferometer operates as a dither-lock-stabilized interferometer that “decodes” the data bits which are differentially encoded into their original un-encoded form. The arms of the interferometer are set to be  {fraction (1/2)} bit-period off from one another in length ( 1 bit-period round trip), allowing the differentially encoded optical signal to be demodulated, resulting in two outputs from the interferometer. The outputs of the interferometer are detected by the photodiodes  132  and  133  oriented in a “differencing” mode. The differencing mode is strictly not needed, but can improve performance in some cases. Because the interferometer uses faraday-rotator mirrors rather than plain mirrors, the interferometer is made polarization-state independent. That is to say that the interferometer performance is not a function of the polarization-state of the light entering the interferometer.  
      The electrical components of the receiver  110  include an electrical decrypting signal generator  180  including a microprocessor controller  181 , a digital-to-analog converter D/A  182 , an amplifier  183  and a splitter  184 . The electrical components of the receiver  110  further include a trans-impedance amplifier (TIA)  185 , low/high frequency component separator  186 , a piezo-electric stretcher  187  and data/clock recovery circuit  188 . The piezo-electric stretcher  187  includes a piezoelectric (PZT) element  189  connected in one arm of the interferometer and a PZT controller  190  coupled to the output of the low/high frequency component separator  186 .  
      The trans-impedance amplifier (TIA)  185  is located in the circuit before the electronic high-frequency signal (bit information) is separated from the low frequency signal (dither-lock information). The low frequency signal enters a dither-locking circuit which locks the phase of the interferometer. This is achieved with the use of a piezo-electric stretcher  187  on one of the optical-fiber arms of the interferometer. The high frequency electronic signal (data bits) enters a clock/data recovery circuit  188  which electronically “recovers” the data and clock signals. These signals are driven back into the micro-processor/micro-controller  181  for the purpose of maintaining cryptographic synchronization between the two users (Alice and Bob).  
      The electronic voltage signal that drives the concatenated phase modulators  118  and  120  is the same signal where an electronic delay equal to the optical path-length delay between the phase modulators  118  and  120  is required. The voltage signal is the output of the digital-to-analog converter  182  that is then amplified and split into two equal parts, one for each modulator. The digital-to-analog converter  182  is driven by the output of the micro-processor/micro-controller  181 . The micro-processor/micro-controller  181  of the receiver  110  is driven by the secret-key as well as with the arriving encrypted data stream for synchronization purposes.  
      The system of  FIG. 14  is an improvement over the time-mode scheme proposed in FIGS. 18 and 27 of U.S. application Ser. No. 10/674,241. The system illustrated in  FIG. 14  provides quantum-noise protected data encryption in a polarization-state insensitive manner. This differs from the polarization-mode schemes disclosed in FIGS. 6, 22, 23, 24 of U.S. application Ser. No. 10/674,241, in which data encryption is based on varying the polarization state of light.  
      In operation, light from the laser light source  200  is applied via a polarization-maintaining fiber  204  to the phase modulator  202  where it is encrypted by the drive signal produced by the microprocessor  210  producing an M-ry phase encrypted optical signal (RZ or NRZ modulation format) with the bit sequence to be transmitted. The phase-modulated light, amplified by optical amplifier  206  and leaves the transmitter (Alice).  
      On propagating through the all-optical channel, the information-bearing light signal transmitted by Alice arrives at the receiver (Bob) and is first amplified by the optical amplifier  116 . The light then propagates through the pair of concatenated optical phase-modulators  118  and  120  oriented at 90° degrees with respect to each other. The purpose of these phase modulators  118  and  120  is to remove the encryption signal that was applied to the optical signal at the transmitter. The need for a pair of modulators rather than just one stems from the polarization sensitivity of the modulators used in this demonstration (Lithium niobate phase modulators). The polarization maintaining fiber  122  is used to flip the polarization modes of the optical signal before the optical signal enters the second phase modulator  120 . By connecting the modulators with polarization-maintaining fiber and orienting the modulators with a 90° rotation, the two polarization-modes of the optical signal receive the same amount of optical phase-modulation thereby making the process of decryption (the process of removing the optical encryption signal) insensitive to the polarization-state of the incoming light. The uncertainty of the polarization-state of the light entering Bob is due to the fact that the all-optical channel may apply an arbitrary polarization-state rotation unknown to either user (Alice or Bob). The optical phase of the light is changed by the phase modulator by the voltage applied to the phase modulators  118  and  120 .  
      The electrical drive signal, consisting of differential-phase-shift-keyed data-bit information as well as an encryption signals, driving the modulator pair  118  and  120  are identical. The electronic voltage signal that drives the concatenated phase modulators is the same signal where an electronic delay equal to the optical path-length delay (between the modulators) is required. The voltage signal is the output of a digital-to-analog converter that this then amplified and split into two equal parts (for each modulator). The digital-to-analog converter is driven by the output of a micro-processor/micro-controller  
      The optical signal then passes through the optical circulator  124  and into the fiber Michelson interferometer. The path length difference in the arms of the interferometer corresponds to the period of an optical symbol (bit). The demodulated light leaves the interferometer where it is detected by the photodiodes  132  and  133 .  
      After optical decryption, the optical signal passes through the optical circulator  124  and is decoded by the dither-lock-stabilized interferometer into their original un-encoded form. The arms of the interferometer are  {fraction (1/2)} bit-period off from one another in length ( 1 bit-period round trip), so that the differentially encoded optical signal as demodulated results in two outputs from the interferometer. The light from these outputs is directed onto the photodiodes  132  and  133 , generating a photocurrent. Because the interferometer is polarization-state independent, the interferometer performance is not a function of the polarization-state of the light entering the interferometer.  
      The photocurrent then enters the trans-impedance amplifier  185  before the electronic high-frequency (bit information) is separated from the low frequency (dither-lock information). The low frequency signal enters a dither-locking circuit which locks the phase of the interferometer. This is achieved with the use of the piezo-electric stretcher  187 , including the PZT  189  connected in one of the optical-fiber arms of the interferometer, controlled by the PZT controller  190 . The high frequency electronic signal (data bits) enters the clock/data recovery circuit  188  which electronically “recovers” the data and clock signals. These signals are fed back into the micro-processor/micro-controller  181  for the purpose of maintaining cryptographic synchronization between the two users Alice and Bob.  
      As is stated above, the micro-processor/micro-controller  210  in the transmitter  108  is driven with the data bits to be encrypted, a clock signal, and a secret-key. The micro-processor/micro-controller  181  in the receiver  110  is driven by the secret-key as well as synchronizing signals produced by the clock/data recovery circuit  188  in response to with the arriving encrypted data stream for synchronization purposes.  
      Unlike the schemes presented in FIGS. 6, 22, 23, 24 of U.S. application, Ser. No. 10/674,241, the scheme of the system shown in  FIG. 14  performs exactly the same cryptographic objective but without the use of difficult to maintain polarization-states of light. The scheme shown in FIGS. 18 and 27 of U.S. application Ser. No. 10/674,241, approximate a polarization-insensitive version of the systems shown in FIGS. 6, 22, 23, 24 of the referenced application by encrypting the data bits in phase-states of light rather than polarization-states of light. However, the receiver (Bob) used in this scheme is sensitive to polarization. In contrast, the scheme illustrated in FIG. X 1 , provided by the present invention, not only encrypts the data bits in phase-states of light rather than polarization-states of light, but also utilizes a carefully designed receiver (Bob) that is internally polarization-state insensitive.  
      It may therefore be appreciated from the above detailed description of the preferred embodiment of the present invention that it provides quantum-noise protected data encryption in a polarization-state insensitive manner. The present invention provides a data encryption/decryption system that transmits encrypted data over WDM links that is compatible with standard NRZ and RZ communication formats being used with WDM communications today.  
      Although an exemplary embodiment of the present invention has been shown and described with reference to particular embodiments and applications thereof, it will be apparent to those having ordinary skill in the art that a number of changes, modifications, or alterations to the invention as described herein may be made, none of which depart from the spirit or scope of the present invention. All such changes, modifications, and alterations should therefore be seen as being within the scope of the present invention.