CN114793157B - Quantum digital signature system and method based on orbital angular momentum - Google Patents
Quantum digital signature system and method based on orbital angular momentum Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0852—Quantum cryptography
- H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/70—Photonic quantum communication
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
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- H—ELECTRICITY
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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- H—ELECTRICITY
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/34—Encoding or coding, e.g. Huffman coding or error correction
Abstract
The invention discloses a quantum digital signature system and a quantum digital signature method based on orbital angular momentum, wherein the quantum digital signature method comprises the following steps: step S1, a sender generates two parts of signal light loaded with orbital angular momentum and sends the signal light to two receivers respectively; step S2, generating signal light loaded with orbital angular momentum by two receivers, performing interference detection on the signal light and the received signal light, and acquiring respective initial quantum digital signatures based on detection results and the opposite base of the transmitter; step S3, the two receivers exchange the signatures to obtain a final quantum digital signature; s4, the sender signs the information by using the quantum digital signature, and then sends the information to the receiver for signature verification; the method has the advantages of easy encoding-decoding process, small calculation amount and high signature acquisition efficiency.
Description
Technical Field
The invention belongs to the technical field of quantum digital signature, and particularly relates to a quantum digital signature system and method based on orbital angular momentum.
Background
Digital signatures are widely applied to financial transactions and emails, and the authenticity and transmissibility of information are effectively guaranteed, however, the security of traditional digital signatures generally depends on complex mathematical problems, such as discrete logarithm and large number decomposition, and with the rapid development of quantum computing, the security of digital signatures is severely challenged, in contrast, quantum Digital Signatures (QDS) provide theoretical information security under the guarantee of quantum mechanics law.
Gottesmann and Chuang in 2007 first proposed the concept of classical information quantum dot scheme based on quantum one-way function, which requires long-term quantum memory and quantum mechanical exchange testing, making it difficult to realize practically; the scheme described above was improved by Clarke et al in 2011, which has been validated in experiments without the need for quantum mechanical exchange testing; the 2016 Roberts et al describes a measurement device independent QDS based scheme that is safe against side channel attacks by all probes; thorntonet et al 2019 proposed a new Continuous Variable (CV) based QDS protocol based on coherent phase measurements.
However, the quantum digital signature protocol is mostly developed in a fiber channel, and the following disadvantages exist in the fiber transmission: 1. the optical fiber has crisp texture and poor mechanical strength; 2. the cutting and splicing of the optical fiber need to use certain tools, equipment and technology, and the operation process is complicated; 3. before two communication parties communicate, an actual link is paved, which is not beneficial to realizing the integration of the world and the sky; in order to solve the above problems, the free space is used in the art for communication, and the free space system uses the atmosphere as a transmission medium for transmitting optical signals, so long as there is an unobstructed line-of-sight path and enough optical emission power between the two transceiver terminals, the communication can be performed; free space communication may play an important role in: 1) Interconnection between mobile communication base stations and data return of wireless base stations; 2) Building a metropolitan area network and accessing the last kilometer; 3) In areas where it is technically or economically undesirable to lay fiber optic cables, where it is undesirable or limited to use wireless communications; 4) And carrying out network interconnection and data transmission inside the enterprise.
In free space terms, wallden et al, by introducing a classical post-processing step, eliminates the requirement for optical multiport so that the free space signature protocol can run in urban environments above 1.6km, which proposes a QDS scheme using heterodyne measurements, which by practice demonstrates that it can work on fluctuating free space channels, the first free space experiment of quantum signatures, heterodyne detection is used to eliminate ambiguities and give the result of each transmitted state; however, the method is used for distributing the discrete variable quantum key in the technical aspect, single photon detection equipment is needed in the implementation, the equipment cost is high, the single photon detection difficulty is high, and the encryption and decryption process is complex.
Disclosure of Invention
The embodiment of the invention aims to provide a quantum digital signature system and a quantum digital signature method based on orbital angular momentum, which use a continuous variable quantum key distribution technology, are compatible with classical optical communication and are easy to realize.
In order to solve the technical problems, the invention adopts the technical scheme that the quantum digital signature system based on orbital angular momentum comprises a sender Alice, a receiver Bob and a receiver Charlie;
the sender Alice is configured to generate two parts of signal light loaded with orbital angular momentum, and send the two parts of signal light to the receiver Bob and the receiver Charlie respectively;
the structure of the receiver Bob is the same as that of the receiver Charlie, and the receiver Bob and the receiver Charlie both comprise:
a polarization beam splitter for interfering the signal light loaded with orbital angular momentum generated by itself with the received signal light;
the charge coupler is used for carrying out imaging detection on the interference result, and carrying out pairing with the sender Alice based on the detection result to obtain quantum digital signatures of the sender Alice, the receiver Bob and the receiver Charlie;
the sender Alice is respectively connected with the receiver Bob and the receiver Charlie through free space links, and the receiver Bob is connected with the receiver Charlie through classical encryption channels.
Further, the sender Alice includes:
a continuous wave pulse laser for generating a continuous wave laser beam;
the amplitude modulator and the phase modulator are used for modulating the amplitude and the phase of the continuous wave laser beam to prepare signal light containing four discrete quantum states;
a variable optical attenuator for attenuating the power of the signal light to a quantum level;
the beam splitter is used for equally dividing the signal light of the quantum level into two parts and respectively sending the two parts to the spatial light modulator;
a random number generator for generating a random number;
and the spatial light modulator is used for modulating the signal light according to the random number to obtain the signal light loaded with orbital angular momentum.
Further, the receiving party Bob and the receiving party Charlie further include:
a continuous wave pulse laser for generating a continuous wave laser beam;
the amplitude modulator and the phase modulator are used for modulating the amplitude and the phase of the continuous wave laser beam to prepare four discrete quantum states;
a variable optical attenuator for attenuating the power of the discrete quantum state to a quantum level to obtain signal light;
a random number generator for generating a random number;
and the spatial light modulator is used for modulating the signal light according to the random number to obtain the signal light loaded with orbital angular momentum.
The quantum digital signature method based on the orbital angular momentum comprises the following steps:
step S1, a sender Alice generates two parts of signal light loaded with orbital angular momentum and sends the signal light to a receiver Bob and a receiver Charlie respectively;
step S2, the receiving party Bob carries out interference detection on the signal light which is generated by itself and loaded with orbital angular momentum and the received signal light, and carries out pairing with the sending party Alice based on the detection result, and after the pairing is finished, the sending party Alice obtains a quantum digital signatureThe receiver Bob obtains the initial quantum digital signature +.>
The receiving party Charlie carries out interference detection on the signal light which is generated by the receiving party Charlie and loaded with orbital angular momentum and the received signal light, performs pairing with the sending party Alice based on the detection result, and the sending party Alice obtains a quantum digital signature after the pairing is completedThe receiver Charlie obtains the initial quantum digital signature +.>
Where j represents the number variable of the string encoded after the base, ζl represents the total number of strings encoded after the base,representing the effective coding rate, L representing the classical string length, QA Bj Representing the character string, QA, encoded after the sender Alice and the receiver Bob pair base Cj Character string and QS for representing base pair post coding of sender Alice and receiver Charlie Bj Character string representing base pair post-coding of receiver Bob and sender Alice, QS Cj A character string which represents the base pair post-coding of the receiving party Charlie and the sending party Alice;
step S3, the receiver Bob and the receiver Charlie perform signature exchange to obtain a final quantum digital signature;
and S4, after signing the single-bit information by utilizing the quantum digital signature, the sender Alice sends the single-bit information to the receiver Bob, after successful signature verification of the receiver Bob, the sender Alice sends the single-bit information to the receiver Charlie, after successful signature verification of the receiver Charlie, the receiver Bob or the receiver Charlie receives the information, and after failed signature verification of the receiver Charlie, the information transmission fails.
Further, the preparation process of the signal light loaded with orbital angular momentum is as follows:
the continuous wave laser beam prepared by the continuous wave pulse laser is sequentially input into an amplitude modulator and a phase modulator, and the amplitude and the phase of the continuous wave laser beam are respectively modulated to prepare discrete quantum state |alpha k >＝|αe i(2k+1)π/4 >The power of the signal light is attenuated to the quantum level by using a variable optical attenuator;
where α represents the amplitude of the discrete quantum states, i represents the complex variable, k ε {0,1,2,3}, (2k+1) pi/4 represents the phase of each discrete quantum state;
based on the random number generated by the random number generator, the spatial light modulator modulates the attenuated signal light to obtain the signal light loaded with orbital angular momentum, wherein the discrete quantum state isWherein R (R, z) represents discrete quantum states +.>R represents radial radius, z represents transmission distance, l represents topological charge of orbital angular momentum, phi represents angular coordinates, ++>Representing elements in a classical string, +.>j A Variable j representing the number of elements in a classical string A ＝1,2,…,L，l 1 Orbital angular momentum modulus, l, representing a topological charge number of 1 4 Representing the orbital angular momentum mode with a topological charge number of 4.
Further, the pairing process is as follows:
checking whether the detection result is bright spots or not, and if so, discarding the signal light under the time window;
if the light spot is present, detecting the quantum state of the signal light under the time window, if the quantum state is |l 1 >And I-l 1 >The signature is encoded as 1 if the quantum state is |l 4 >And I-l 4 >The signature is encoded as 0.
Further, the signature exchange process is as follows:
receiver Bob's digital signature from initial quantaIs selected at random->Element, send to receiver Charlie, charlie is from initial quantum digital signature +.>Middle followMachine selection->The element is sent to the receiver Bob, and the final quantum digital signature of the receiver Bob is +.>The final quantum digital signature of the receiver Charlie is +.>
Representing the character string element reserved by recipient Bob, < >>Character string element representing that receiver Charlie is sent to receiver Bob, < ->Character string element representing the reservation of the receiver Charlie, < >>A string element representing the character string that the recipient Bob sends to the recipient Charlie.
Further, the signature verification process is as follows:
receiver Bob detects own quantum digital signatureQuantum digital signature with sender Alice +.>If the mismatch of the two partial signatures is smaller than + ->Signature verificationSuccessfully receiving the information and sending the information to a receiver Charlie; otherwise, the signature verification fails, the receiver Bob refuses to receive the information and stops the protocol;
receiver Charlie detects own quantum digital signatureQuantum digital signature with sender Alice +.>If the mismatch of the two partial signatures is smaller than + ->The signature verification is successful and the information is received; otherwise, the signature verification fails, the receiving party Charlie refuses to receive the information, and stops the protocol.
The beneficial effects of the invention are as follows: the quantum digital signature is loaded with orbital angular momentum when being generated, the orbital angular momentum is used as a new additional degree of freedom, the orbital angular momentum is completely irrelevant to wavelength, frequency, polarization and the like, an infinite-dimension Hilbert space can be constructed by the optical orbital angular momentum, quantum coding can be realized on a standard orthogonal basis formed by the orbital angular momentum state, a receiver only needs to detect light spots formed by discrete quantum states after interference when decoding, and the orbital angular momentum modes of a sender and a receiver are estimated based on the light spots, so that the basis is realized, the quantum digital signature of each protocol three is obtained, the whole process is easy to encode and decode, the calculated amount is small, and the signature acquisition efficiency is high; finally, the two receivers of the invention also randomly exchange the quantum digital signatures, respectively detect the mismatch rate of the two parts of quantum digital signatures, and verify the signatures according to the detection result, thereby ensuring the safety of quantum communication.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic diagram of an embodiment of the present invention.
Fig. 2 is an optical path diagram of an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
A quantum digital signature protocol involves three parties, namely a sender Alice and two receivers Bob and Charlie, for a classical single-bit message m to be transmitted, the sender Alice firstly transmits the classical single-bit message m to the receiver Bob, and the receiver Bob forwards the classical single-bit message m to the receiver Charlie; line (2) represents the message delivery phase, where the sender Alice sends a message and an additional quantum digital signature to the receiver Bob and receiver Charlie.
The quantum digital signature system based on orbital angular momentum has the structure shown in fig. 2 and comprises a sender Alice, a receiver Bob and a receiver Charlie, wherein the sender Alice comprises a continuous wave Laser for generating a continuous wave Laser beam; an amplitude modulator AM and a phase modulator PM for modulating the amplitude and phase of the continuous wave laser beam to obtain signal light containing four discrete quantum states; a variable optical attenuator VOA for attenuating the power of the signal light to a quantum level; a beam splitter for splitting the signal light of quantum level equally into two parts to be input to the spatial light modulator SLM; a random number generator RNG for generating a random number; the spatial light modulator SLM is configured to modulate the input signal light according to a random number, prepare a signal light loaded with orbital angular momentum, and send the signal light to the receiver Bob and the receiver Charlie through a free space link.
The receiver Bob and the receiver Charlie have the same structure and both comprise a continuous wave Laser for generating a continuous wave Laser beam; an amplitude modulator AM and a phase modulator PM for modulating the amplitude and phase of the continuous wave laser beam to obtain signal light containing four discrete quantum states; a variable optical attenuator VOA for attenuating the power of the signal light to a quantum level and inputting it to the spatial light modulator SLM; a random number generator RNG for generating a random number; the spatial light modulator SLM is used for modulating input signal light according to random numbers, preparing signal light loaded with orbital angular momentum, sending the signal light to the polarization beam splitter PBS, the polarization beam splitter PBS interferes the signal light prepared by a receiver with the signal light sent by a sender, sending an interference result to the charge coupler CCD, the charge coupler CCD carries out imaging detection on the interference result, and discloses a detection result, the receiver and the sender carry out base pairing based on the detection result to obtain an initial quantum digital signature, and the receiver Bob and the receiver Charlie are connected through a classical encryption channel and are used for signature exchange to obtain a final quantum digital signature.
The sender Alice signs classical information by using the quantum digital signature, and after the signature verification is successful, the sender Alice sends the classical information to the receiver Bob through a free space link, and the receiver Bob sends the classical information to the receiver Charlie through a classical encryption channel for signature verification, so that the classical information is transmitted.
The quantum digital signature method based on the orbital angular momentum specifically comprises the following steps:
step 1, a sender Alice, a receiver Bob and a receiver Charlie respectively use continuous wave pulse lasers to generate continuous wave laser beams, then the amplitude modulator and the phase modulator sequentially modulate the amplitude and the phase of the continuous wave laser beams to obtain signal lights, the modulated signal lights are input into a variable optical attenuator VOA, and the power of the modulated signal lights is attenuated to a quantum level;
the signal light comprises four discrete quantum states |alpha k >＝|αe i(2k+1)π/4 >Modulation variance V M ＝2α 2 Alpha represents a discrete quantum state |alpha k >I represents complex variables, k e {0,1,2,3}, (2k+1) pi/4 represents the phase of each discrete quantum state, and when k=0, discrete quantum state |α 0 >＝|αe iπ/4 >When k=1, discrete quantum state |α 1 >＝|αe i3π/4 >When k=2, discrete quantum state |α 2 >＝|αe i5π/4 >When k=3, discrete quantum state |α 3 >＝|αe i7π/4 >Pi/4 represents a discrete quantum state |alpha 0 >Is 3 pi/4 represents the discrete quantum state |alpha 1 >5 pi/4 represents the discrete quantum state |alpha 2 >Is 7 pi/4 represents the discrete quantum state |alpha 3 >Is a phase of (2);
step 2, a sender Alice loads orbital angular momentum on a discrete quantum state of quantum level signal light to form new signal light, and the specific process is as follows:
the sender Alice uses a beam splitter BS to divide the attenuated signal light into two parts, and inputs the two parts into a spatial light modulator SLM, and the spatial light modulator SLM modulates the input signal light based on random numbers generated by a random number generator RNG to prepare a Laguerre Gaussian (LG) beam loaded with orbital angular momentumWherein the discrete quantum state is->And respectively inputting the data into a receiver Bob and a receiver Charlie through a free space link;
expressed in discrete quantum state |alpha k >Discrete quantum state obtained after loading orbital angular momentum, < > on>The formula of (2) is as follows:
wherein R (R, z) represents a discrete quantum stateR represents radial radius, z represents transmission distance, l represents topological charge of orbital angular momentum, phi represents angular coordinates, ++>Representing elements in a classical string, the classical string being generated by a random number generator, the length of the classical string being agreed before communication,/->j A Variable j representing the number of elements in a classical string A ＝1,2,…,L，l 1 Orbital angular momentum modulus, l, representing a topological charge number of 1 4 An orbital angular momentum mode representing a topological charge number of 4;
step 3, the receiving party Bob and the receiving party Charlie respectively input the attenuated signal light into a spatial modulator SLM, and the spatial modulator SLM modulates the input signal light based on random numbers generated by a random number generator RNG to prepare laguerre-Gaussian (LG) light beams loaded with orbital angular momentumAnd->Then, the Laguerre-Gaussian beam is interfered with signal light sent by a sender Alice through a polarization beam splitter PBS;
wherein the method comprises the steps ofRepresenting classical string element generated by recipient Bob, < >>Representing classical string element, j generated by receiver Charlie B 、j C Respectively indicate->Number variable of>j B ＝j C ＝1,2,…,L；
Step 4, respectively using a charge-coupled device CCD to image and detect signal light interference results of a receiving party Bob and a receiving party Charlie, and disclosing detection results, wherein the detection results are as follows:
since sender Alice sends l 1 ＝1、l 4 =4, the receiver sends-l 1 ＝-1、-l 4 = -4, then l 1 ′＝-l 1 ＝-1、l 4 ′＝-l 4 The detection results of = -4 are as follows: (1) The center of the detection result presents a bright spot, namely, in a corresponding time window, the signal pulse sent by the sender Alice is a quantum state |l loaded with an orbital angular momentum mode 1 >The signal pulse sent by the receiver Bob is quantum state I-l loaded with orbital angular momentum mode 1 >The method comprises the steps of carrying out a first treatment on the surface of the (2) The center of the detection result presents a bright spot, namely, in a corresponding time window, the signal pulse sent by the sender Alice is a quantum state |l loaded with an orbital angular momentum mode 4 >The signal pulse sent by the receiver Bob is quantum state I-l loaded with orbital angular momentum mode 4 >The method comprises the steps of carrying out a first treatment on the surface of the (3) The center of the detection result presents a dark spot, and in the corresponding time window, the signal pulse sent by the sender Alice is a quantum state |l loaded with an orbital angular momentum mode 1 >The signal pulse sent by the receiver Bob is quantum state I-l loaded with orbital angular momentum mode 4 >Or the signal pulse sent by sender Alice is quantum state |l loaded with orbital angular momentum mode 4 >The signal pulse transmitted by the receiving party BobThe dashes are quantum states | -l loaded with orbital angular momentum modes 1 >；
Similarly, the receiving party Charlie interferes the incident signal light with the signal light generated by the receiving party Charlie and then images the signal light through the CCD, and the detection results also show the three conditions;
based on the detection result, the sender Alice respectively performs a base pairing with the receiver Bob and the receiver Charlie, and the base pairing process is as follows:
for each signal window, the receiver Bob discloses the detection result after interference, and the sender Alice and the receiver Bob perform pairing, so that the following three conditions exist: (1) In a time window, if the receiving party Bob discloses that the detection result center presents a bright spot, the sending party Alice and the receiving party Bob respectively send quantum states |l loaded with orbital angular momentum 1 >And I-l 1 >The time window is encoded as 1, and the signatures of the sender Alice and the receiver Bob are respectively recorded as QA Bj ＝1、QS Bj =1; (2) In a time window, if the receiving party Bob discloses that the detection result center presents a bright spot, the sending party Alice and the receiving party Bob respectively send quantum states |l loaded with orbital angular momentum 4 >And I-l 4 >The time window is encoded to 0, and the signatures of the sender Alice and the receiver Bob are respectively recorded as QA Bj ＝0、QS Bj =0; (3) In a time window, if the receiving party Bob discloses that the detection result center is a dark spot, the time window is abandoned and no coding is performed;
after the base pair is finished, sender Alice obtains quantum digital signatureThe receiver Bob obtains the initial quantum digital signature +.>The receiver Charlie obtains the initial quantum digital signature +.>
Wherein the method comprises the steps ofRepresenting the total number of strings encoded after the base, j representing the number variable of strings encoded after the base,representing the effective coding rate, L representing the classical string length, QA Bj Representing the character string, QA, encoded after the sender Alice and the receiver Bob pair base Cj Character string and QS for representing base pair post coding of sender Alice and receiver Charlie Bj Representing a string encoded by the post-base recipient Bob, QS Cj Representing a character string encoding the postbase receiver Charlie;
step 5, the receiver Bob and the receiver Charlie randomly select from the character strings encoded by the receiver Bob and the receiver Charlie respectivelyThe elements are sent to the other party through an encrypted classical channel to complete signature exchange, and a final quantum digital signature is obtained;
the final quantum digital signature of the receiving party Bob is at this timeThe final quantum digital signature of the receiver Charlie is +.> Representing the character string element reserved by recipient Bob, < >>Character string element representing that receiver Charlie is sent to receiver Bob, < ->Character string element representing the reservation of the receiver Charlie, < >>A character string element representing that the receiver Bob sends to the receiver Charlie;
the character string elements exchanged between the receiver Bob and the receiver Charlie and the positions thereof are kept secret to the sender Alice, and the exchanged character string elements can protect the protocol from denial of attack;
step 6, the sender Alice signs the single-bit information m by using the signature thereof to obtain classical information S,and sends it to the recipient Bob;
step 7, the receiving party Bob detects the quantum digital signature of itselfQuantum digital signature with sender->If the mismatch of the two partial signatures is smaller than + ->Then message m is received and classical message +.>Forwarding to receiver Charlie, otherwise signature verification fails, refusing to receive message, and asking for stopping protocol, wherein the security threshold s of receiver Bob b Satisfy->
Step S8, the receiving party Charlie detects the quantum digital signature of the receiving party CharlieQuantum digital signature with sender->If the mismatch rate is smaller than +.>The signature verification is successful, the single-bit message m is accepted, the protocol is regarded as successful, otherwise, the signature authentication fails, the message is refused to be received, and the protocol is required to be stopped;
wherein the safety threshold satisfiesCharacter string indicating that the receiver Charlie itself reserves,/->Character string s representing that receiver Bob sends to receiver Charlie c Representing the security threshold of the receiving party Charlie.
The continuous variable quantum key distribution technology is used, the continuous variable quantum key distribution technology is compatible with a classical optical channel, the implementation is easy, the cost is low, the detection is convenient, the communication between a sender and a receiver is realized by using a free space link, no optical fiber is required to be laid, the quantum digital signature system is simple to erect, the discrete quantum state is loaded with the orbital angular momentum, the orbital angular momentum mode of the discrete quantum state is detected at a receiving end, the base pairing between the receiver and the sender is realized, the quantum digital signature is obtained, the encoding-decoding of the process is simpler, the implementation is convenient, the two receivers also exchange random quantum digital signatures for the decoded result, and the safety of quantum communication is ensured.
In this specification, each embodiment is described in a related manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, as relevant to see a section of the description of method embodiments.
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims (6)
1. The quantum digital signature system based on the orbital angular momentum is characterized by comprising a sender Alice, a receiver Bob and a receiver Charlie;
the sender Alice is configured to generate two parts of signal light loaded with orbital angular momentum, and send the two parts of signal light to the receiver Bob and the receiver Charlie respectively;
the structure of the receiver Bob is the same as that of the receiver Charlie, and the receiver Bob and the receiver Charlie both comprise:
a polarization beam splitter for interfering the signal light loaded with orbital angular momentum generated by itself with the received signal light;
the charge coupler is used for carrying out imaging detection on the interference result, and carrying out pairing with the sender Alice based on the detection result to obtain quantum digital signatures of the sender Alice, the receiver Bob and the receiver Charlie;
the sender Alice is connected with the receiver Bob and the receiver Charlie through free space links respectively, and the receiver Bob is connected with the receiver Charlie through classical encryption channels;
then comprises the following steps:
step S1, a sender Alice generates two parts of signal light loaded with orbital angular momentum and sends the signal light to a receiver Bob and a receiver Charlie respectively;
step S2, the receiving party Bob carries out interference detection on the signal light which is generated by itself and loaded with orbital angular momentum and the received signal light, and carries out pairing with the sending party Alice based on the detection result, and after the pairing is finished, the sending party Alice obtains a quantum digital signatureThe receiver Bob obtains the initial quantum digital signature +.>
The receiving party Charlie carries out interference detection on the signal light which is generated by the receiving party Charlie and loaded with orbital angular momentum and the received signal light, performs pairing with the sending party Alice based on the detection result, and the sending party Alice obtains a quantum digital signature after the pairing is completedThe receiver Charlie obtains the initial quantum digital signature +.>
Where j represents a variable number of character strings encoded after the base,representing the total number of character strings encoded after the base, representing the effective coding rate, L representing the classical string length, QA Bj Representing the character string, QA, encoded after the sender Alice and the receiver Bob pair base Cj Character string and QS for representing base pair post coding of sender Alice and receiver Charlie Bj Character string representing base pair post-coding of receiver Bob and sender Alice, QS Cj A character string which represents the base pair post-coding of the receiving party Charlie and the sending party Alice;
step S3, the receiver Bob and the receiver Charlie perform signature exchange to obtain a final quantum digital signature;
step S4, after signing the single-bit information by utilizing the quantum digital signature, the sender Alice sends the single-bit information to the receiver Bob, after successful signature verification of the receiver Bob, the sender Alice sends the single-bit information to the receiver Charlie, after successful signature verification of the receiver Charlie, the receiver Bob or the receiver Charlie receives the information, and when the signature verification of the receiver Bob or the receiver Charlie fails, the information transmission fails;
the signature exchange process is as follows:
receiver Bob's digital signature from initial quantaIs selected at random->Element, send to receiver Charlie, charlie is from initial quantum digital signature +.>Is selected at random->The element is sent to the receiver Bob, and the final quantum digital signature of the receiver Bob is +.>The final quantum digital signature of the receiver Charlie is +.>
Representing the character string element reserved by recipient Bob, < >>Character string element representing that receiver Charlie is sent to receiver Bob, < ->Character string element representing the reservation of the receiver Charlie, < >>A string element representing the character string that the recipient Bob sends to the recipient Charlie.
2. The orbital angular momentum based quantum digital signature system according to claim 1, wherein the sender Alice comprises:
a continuous wave pulse laser for generating a continuous wave laser beam;
the amplitude modulator and the phase modulator are used for modulating the amplitude and the phase of the continuous wave laser beam to prepare signal light containing four discrete quantum states;
a variable optical attenuator for attenuating the power of the signal light to a quantum level;
the beam splitter is used for equally dividing the signal light of the quantum level into two parts and respectively sending the two parts to the spatial light modulator;
a random number generator for generating a random number;
and the spatial light modulator is used for modulating the signal light according to the random number to obtain the signal light loaded with orbital angular momentum.
3. The orbital angular momentum based quantum digital signature system of claim 1, wherein the receiver Bob and receiver Charlie further comprise:
a continuous wave pulse laser for generating a continuous wave laser beam;
the amplitude modulator and the phase modulator are used for modulating the amplitude and the phase of the continuous wave laser beam to prepare four discrete quantum states;
a variable optical attenuator for attenuating the power of the discrete quantum state to a quantum level to obtain signal light;
a random number generator for generating a random number;
and the spatial light modulator is used for modulating the signal light according to the random number to obtain the signal light loaded with orbital angular momentum.
4. The quantum digital signature system based on orbital angular momentum according to claim 1, wherein the preparation process of the signal light loaded with orbital angular momentum is as follows:
the continuous wave laser beam prepared by the continuous wave pulse laser is sequentially input into an amplitude modulator and a phase modulator, and the amplitude and the phase of the continuous wave laser beam are respectively modulated to prepare discrete quantum state |alpha k >＝|αe i(2k+1)π/4 >The power of the signal light is attenuated to the quantum level by using a variable optical attenuator;
where α represents the amplitude of the discrete quantum states, i represents the complex variable, k ε {0,1,2,3}, (2k+1) pi/4 represents the phase of each discrete quantum state;
based on the random number generated by the random number generator, the spatial light modulator modulates the attenuated signal light to obtain the signal light loaded with orbital angular momentum, wherein the discrete quantum state is Wherein R (R, z) represents discrete quantum states +.>R represents radial radius, z represents transmission distance, l represents topological charge of orbital angular momentum, phi represents angular coordinates, ++>Representing elements in a classical string, +.>j A Variable j representing the number of elements in a classical string A ＝1,2,…,L，l 1 Orbital angular momentum modulus, l, representing a topological charge number of 1 4 Representing the orbital angular momentum mode with a topological charge number of 4.
5. The orbital angular momentum based quantum digital signature system according to claim 1, wherein the pairing process is as follows:
checking whether the detection result is bright spots or not, and if so, discarding the signal light under the time window;
if the light spot is present, detecting the quantum state of the signal light under the time window, if the quantum state is |l 1 >And I-l 1 >The signature is encoded as 1 if the quantum state is |l 4 >And I-l 4 >The signature is encoded as 0.
6. The orbital angular momentum based quantum digital signature system according to claim 1, wherein the signature verification process is as follows:
receiver Bob detects own quantum digital signatureQuantum digital signature with sender Alice +.>If the mismatch of the two partial signatures is smaller than + ->The signature verification is successful, the information is received, and the information is sent to a receiver Charlie; otherwise, the signature verification fails, the receiver Bob refuses to receive the information and stops the protocol;
receiver Charlie detects own quantum digital signatureQuantum digital signature with sender Alice +.>If the mismatch of the two partial signatures is smaller than + ->The signature verification is successful and the information is received; otherwise, the signature verification fails, the receiving party Charlie refuses to receive the information, and stops the protocol.
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