Quantum digital signature method and system based on rare earth quantum storage

Abstract

The invention discloses a quantum digital signature method and system based on rare earth quantum storage. By selecting a deterministic entangled photon pair as an entanglement source, the disadvantage that entanglement cannot be generated deterministically in the system is avoided, the efficiency of quantum relay is high, and long-distance quantum communication is realized. In addition, a rare earth-doped quantum storage module is used, which has a long life, a large bandwidth, high fidelity, a high degree of multi-mode working ability, and can realize multiplexing operation. It has high efficiency and strong practicality in quantum relay applications. The key distribution is realized on the quantum network through quantum relay, and then the key and random number are used to generate a hash function based on a linear feedback shift register, which can generate a hash value for a message of any length, and has high efficiency and good practicality.

Description

Technical Field

[0001] The present invention relates to the field of quantum security, and in particular to a quantum digital signature method and system based on rare earth quantum storage. Background Art

[0002] In classical cryptography, symmetric cryptography can protect the privacy of data, and asymmetric cryptography can protect integrity, achieve authentication, and prevent repudiation. However, the basis for classical cryptography to meet these information security needs is the complexity of solving mathematical problems. With the improvement of computer computing power and the development of quantum computing technology, the security of this cryptographic system based on computational complexity will be threatened.

[0003] The development of quantum information technology has provided a revolutionary solution to cryptographic tasks. In 2016, Yin et al. proposed to use two methods, namely, two-photon six-state and decoy state, to generate keys to implement quantum digital signatures, which can theoretically reach an implementation distance of 100 km. In 2021, Lu et al. designed an efficient quantum digital signature scheme, which uses a post-matching processing method, and the signature efficiency and detection efficiency show a linear relationship. These protocols ensure the integrity of the data and prevent tampering and denial, but these protocols can only digitally sign one bit of data in each round of signatures, which has low signature efficiency and lacks practicality when the message is long.

[0004] At present, the main challenge facing quantum secure communication is the realization of long-distance quantum communication. Quantum networks can provide perfect solutions to these two problems. On quantum networks, quantum relays can be used to achieve long-distance entanglement distribution, thereby realizing long-distance quantum communication and completing various cryptographic tasks over long distances. It can be seen that the realization of quantum networks is an important core issue in the current development of quantum information science. In 2001, Duan et al. proposed to establish quantum relays to establish remote quantum entanglement through entanglement exchange and quantum storage. Subsequently, quantum memory, as an important component of quantum relays, has been demonstrated many times in experiments. In 2020, Yu et al. used quantum memory based on cold atomic ensembles to achieve entanglement at distances of 20km and 50km, but the atom-light entanglement here originated from the collective excitation of random atomic ensembles and Raman scattered photons, that is, entanglement cannot be generated deterministically, the efficiency of quantum relays is low, and the practicality of deployment on quantum networks is weak. To this end, we propose a quantum digital signature method and system based on rare earth quantum storage to address the shortcomings of the existing technology mentioned above. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a quantum digital signature method and system based on rare earth quantum storage, which solves the problems that the existing entanglement source cannot generate entanglement deterministically, the efficiency of quantum relay is low, and long-distance quantum communication cannot be realized; and the existing quantum digital signature efficiency is very low, each round of signature can only sign one bit of data, and generating signatures requires a large amount of communication resources.

[0006] Technical solution: The present invention provides a quantum digital signature method based on rare earth quantum storage, comprising the following steps:

[0007] (1) Sharing GHZ entangled state: A pair of photons in the maximum entangled state is shared between the transmitter and the receiver, and a pair of photons in the maximum entangled state is shared between the receiver and the verifier. The receiver first performs a controlled NOT gate operation on the two photons in its hand. After completing the controlled NOT gate operation, the receiver measures the photon entangled with the verifier in its hand under the first basis vector, and determines whether the verifier needs to perform a bit flip based on the measurement display result, so that the transmitter, receiver and verifier share the GHZ entangled state.

[0008] (2) Obtaining the classical bit: After completing the sharing of the GHZ entangled state, the sender, receiver, and verifier measure the photons in their hands under the second basis vector respectively. The measured “+” corresponds to the classical bit 0, and the measured “-” corresponds to the classical bit 1. The obtained classical bit result is used as the final key. Since the sender, receiver, and verifier share the GHZ entangled state, the classical bits b measured by the sender, receiver, and verifier are a , b b and b c Satisfaction between

[0009] (3) Obtaining the key string: Repeat steps (1) and (2) multiple times, so that the sender, receiver, and verifier obtain the key string B a , B b and B c And meet

[0010] (4) Generation of digital signature: After completing the generation of the key string, the sender generates a digital signature from its own key string B. a A first group of n-bit keys is randomly selected from the random number generator of the sending end, and an n-bit random number is obtained from the random number generator of the sending end. The n-bit random number is used to generate an irreducible polynomial. The irreducible polynomial and the first group of n-bit keys as the input random number are used together to generate a hash function based on a linear feedback shift register. Then, the message to be signed is input into the hash function to obtain a first hash value. The first hash value and the character string composed of each coefficient of the irreducible polynomial except the highest term constitute the first summary. The sending end selects a first group of n-bit keys from the random number generator of the sending end, and the first group of n-bit keys as the input random number are used to generate a hash function based on a linear feedback shift register. Then, the message to be signed is input into the hash function to obtain a first hash value. The first hash value and the character string composed of each coefficient of the irreducible polynomial except the highest term constitute the first summary. aThe second 2n-bit key is taken from the remaining keys to perform XOR encryption operation on the first summary to generate the final digital signature;

[0011] (5) Verification of digital signature: The sender sends the message to be signed and the digital signature to the receiver. After receiving the digital signature and the message to be signed, the receiver sends the digital signature, the message to be signed, and its own key string B b Sent to the verification end, the verification end receives the digital signature, the message to be signed and the key string B b Then key string B c Send to the receiving end;

[0012] At this time, both the receiving end and the verification end have key string B b and B c , the two key strings B b and B c Perform an XOR operation to obtain the same key string B as the sender. a , the receiving end and the verification end are in their respective key strings B a The same key as that used by the sender to encrypt the first summary is selected from the key string to decrypt the digital signature to obtain a second summary; each bit of the string in the second summary corresponds to the coefficient of each term except the highest term in the irreducible polynomial, and an irreducible polynomial with the highest term coefficient of 1 is generated. The generated irreducible polynomial is used to generate a hash function with the first group of n-bit keys selected from the key string that is the same as that used by the sender to generate a hash function based on a linear feedback shift register, and then the received message to be signed is input into the generated hash function to generate a third hash value; the receiving end and the verification end both compare the obtained third hash value with the second hash value in the second summary, and if the second hash value and the third hash value are the same, the signature is accepted; otherwise, the signature is not accepted.

[0013] Furthermore, in the step (1), it is determined whether the verification end needs to perform bit flipping according to the measurement display result. The specific process is: if the measurement display result is horizontal polarization, then the transmitting end, the receiving end and the verification end share the GHZ entangled state; if the measurement result shows vertical polarization, then the verification end needs to perform bit flipping, and the transmitting end, the receiving end and the verification end share the GHZ entangled state.

[0014] Furthermore, in step (1), the operator expression of the controlled NOT gate operation is Where B and B′ represent two photons at the receiving end that are entangled with the sending end and the verification end respectively, id represents the unit mapping, represents a bit flip operation, H represents horizontal polarization, and V represents vertical polarization;

[0015] In step (1), the first basis vector is {|V>B′ ,|H> B′}; In step (2), the second basis vector is

[0016] Furthermore, the specific process of using the n-bit random number to generate an irreducible polynomial is as follows:

[0017] 1) First, use each bit of the n-bit random number to correspond to the coefficient of each term in the polynomial except the highest term, and generate an n-order polynomial in the GF(2) field, where the coefficient of the highest term is 1;

[0018] 2) Then, use the FMC algorithm to verify whether this polynomial is an irreducible polynomial. If the verification result is "no", directly generate another set of n-bit random numbers from the random number generator at the sender, and return to step 1) as new n-bit random numbers to regenerate the polynomial and verify it; if the verification result is "yes", stop the verification and obtain an irreducible polynomial.

[0019] Furthermore, before step 1), if the last bit of the n-bit random number is 0, the last bit of the random number is set to 1, and an n-order irreducible polynomial in the GF(2) field is generated; or if the last bit of the n-bit random number is 0, n-bit random numbers are regenerated until the last bit of the generated n-bit random number is 1, and an n-order irreducible polynomial in the GF(2) field is generated.

[0020] Furthermore, in step (4), the hash function based on the linear feedback shift register is a Toeplitz matrix of dimension n×m, where n is the number of bytes of the key string B from the sender. a Select the length of the first set of keys, where m is the length of the message to be signed.

[0021] The present invention also includes a quantum digital signature system based on rare earth quantum storage, including a transmitting end, a receiving end and a verifying end, wherein the transmitting end, the receiving end and the verifying end all include a photon generating unit, the photon generating unit of the transmitting end and the photon generating unit of the receiving end are connected to a first measuring end through a quantum channel, and the photon generating unit of the verifying end and the photon generating unit of the receiving end are connected to a second measuring end through a quantum channel;

[0022] The photon generating unit comprises a rare earth doped quantum storage module and an entangled photon pair source module connected to each other, wherein the rare earth doped quantum storage module is used to store photons generated by the entangled photon pair source module, and the entangled photon pair source module is used to generate entangled photon pairs, wherein one photon of the photon pair enters the measuring end through the quantum channel, and the other photon is stored in the rare earth doped quantum storage module;

[0023] The first measuring end and the second measuring end are both used to realize the photon entanglement prediction function, so that a maximum entangled state is established between the two photon generating units connected to the measuring ends.

[0024] Further, the entangled photon pair source module includes a pump submodule, a spontaneous parametric down-conversion submodule, a filtering submodule and an entanglement generation submodule which are interconnected;

[0025] The pump submodule is used to generate pump laser that enters the spontaneous parametric down-conversion submodule;

[0026] The spontaneous parametric down-conversion submodule is used to generate two photons with different polarizations;

[0027] The filtering submodule is used to filter the photons generated by the spontaneous parametric down-conversion submodule;

[0028] The entanglement generation submodule is used to interfere the photon pair and combine the post-selection method to make the photon pair in Bell state.

[0029] Further, the entanglement generation submodule includes a first polarization beam splitting element, two output ends of the first polarization beam splitting element are respectively connected to the input end of the first polarization rotation element and the input end of the second polarization rotation element, the output end of the first polarization rotation element and the output end of the second polarization rotation element are respectively connected to the two input ends of the second polarization beam splitting element, and the two output ends of the second polarization beam splitting element are respectively connected to the input end of the first phase compensation element and the input end of the second phase compensation element; the output end of the first phase compensation element is connected to the measurement end, and the output end of the second phase compensation element is connected to the rare earth doped quantum storage module;

[0030] The first polarization beam splitting element and the second polarization beam splitting element are both used to perform a beam splitting operation on the photon pair;

[0031] The first polarization rotation element and the second polarization rotation element are both used to rotate the polarization of the photon;

[0032] The first phase compensation element and the second phase compensation element are both used to compensate for phase drift.

[0033] Further, the first measuring end and the second measuring end both include a third polarization rotation element and a fourth polarization rotation element, the output end of the third polarization rotation element and the output end of the fourth polarization rotation element are respectively connected to two input ends of the third polarization beam splitting element, the two output ends of the third polarization beam splitting element are respectively connected to the input end of the fifth polarization rotation element and the input end of the sixth polarization rotation element, the output end of the fifth polarization rotation element is connected to the input end of the fourth polarization beam splitting element, the two output ends of the fourth polarization beam splitting element are respectively connected to the first and second input ends of the single photon detection element; the output end of the sixth polarization rotation element is connected to the input end of the fifth polarization beam splitting element, and the two output ends of the fifth polarization beam splitting element are respectively connected to the third and fourth input ends of the single photon detection element.

[0034] Furthermore, the working process of establishing the maximum entangled state between the two photon generating units is:

[0035] The pump submodules in the entangled photon pair source modules of the photon generating units in the transmitting and receiving ends both generate pump lasers. The pump lasers generate two types of photons, horizontally polarized and vertically polarized, through the spontaneous parametric down-conversion submodule. The two photons are filtered through the filtering submodule and then enter the first polarization beam splitting element of the entanglement generating submodule. The first polarization beam splitting element performs a beam splitting operation on the two photons so that the two types of photons, horizontally polarized and vertically polarized, are divided into two paths. The photons on both paths are rotated in polarization through the polarization rotation element. The polarization-rotated photons then reach the second polarization beam splitting element to cause two-photon interference. Through the post-selection method, the two photons are in the maximum entangled state. The two photons are split again and pass through phase compensation elements to compensate for the phase shift that occurs during the propagation process. After the compensation is completed, one photon enters the rare earth doped quantum storage module, and the other photon is sent to the first measurement end through the quantum channel;

[0036] After the above process, a photon in the maximum entangled state is stored in the rare earth doped quantum storage module at both the transmitter and the receiver, while the other two photons reach the first measurement end. At this time, the quantum state of the joint system composed of the transmitter and the receiver is

[0037] The first measurement end adjusts the time delay of photon propagation so that the photons generated by the photon generating units in the transmitting end and the receiving end can arrive at the first measurement end synchronously, and two photons cause two-photon interference at the first measurement end; when the first input end and the third input end or the second input end and the fourth input end of the single-photon detection element respond at the same time, it indicates that the two photons that arrive at the first measurement end at the same time are in the maximum entangled state |φ +>, indicating that the quantum states of photons stored in the rare-earth-doped quantum storage modules at the transmitter and receiver are also in the maximum entangled state |φ + >, thus a maximum entangled state is established between the transmitter and the receiver; similarly, a maximum entangled state is also established between the verifier and the receiver.

[0038] Furthermore, the sending end, the receiving end and the verification end also include classical processing units, and the classical processing units of the sending end and the receiving end, the classical processing units of the sending end and the verification end, and the classical processing units of the receiving end and the verification end are all connected through classical channels; the classical processing units are computers, and are all used to process the measurement results to obtain the final key; wherein, the classical processing unit of the sending end is also used to generate a digital signature, and the classical processing unit of the receiving end and the classical processing unit of the verification end are also used to complete the verification process of the digital signature.

[0039] Beneficial effects of the present invention:

[0040] (1) The present invention selects deterministic entangled photon pairs as entanglement sources, thus avoiding the disadvantage that entanglement cannot be generated deterministically in the ensemble. The efficiency of quantum relay is high, and long-distance quantum communication is realized.

[0041] (2) The present invention utilizes rare earth doped quantum storage modules, which have long life, large bandwidth, high fidelity, high multi-mode working capability, can realize multiplexing operation, have high efficiency in quantum relay applications, and are highly practical;

[0042] (3) The present invention realizes the distribution of keys on a quantum network through quantum relays, and then uses the keys and random numbers to generate a hash function based on a linear feedback shift register, which can generate hash values ​​for messages of any length, and has high efficiency and good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the system structure of the present invention;

[0044] Figure 2 Schematic diagram of the system for establishing entanglement between the sender and the receiver;

[0045] Figure 3 This is a schematic diagram of the structure of the entangled photon pair source module;

[0046] Figure 4 is a schematic diagram of the structure of the first measuring end;

[0047] Figure 5 It is a schematic diagram of the process of generating GHZ entangled state after three parties share Bell state in pairs;

[0048] Figure 6 Schematic diagram of how the limit of signature efficiency changes with channel length. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0050] like Figure 1 As shown, the present invention is a quantum digital signature system based on rare earth quantum storage, including a sending end 1, a receiving end 2 and a verification end 3, wherein the sending end 1, the receiving end 2 and the verification end 3 all include a photon generating unit 11, the photon generating unit 11 of the sending end 1 and the photon generating unit 11 of the receiving end 2 are connected to a first measuring end 4 through a quantum channel, and the photon generating unit 11 of the verification end 3 and the photon generating unit 11 of the receiving end 2 are connected to a second measuring end 5 through a quantum channel;

[0051] like Figure 2 As shown, the photon generating unit 11 includes a rare earth doped quantum storage module 111 and an entangled photon pair source module 112 connected to each other. The rare earth doped quantum storage module 111 is used to store the photons generated by the entangled photon pair source module 112. The stored photons can be further transmitted to other locations through a quantum channel. The module uses a rare earth doped crystal quantum memory combined with an atomic frequency comb pump laser to realize quantum storage;

[0052] like Figure 3 As shown, the entangled photon pair source module 112 is used to generate entangled photon pairs, one photon in the photon pair enters the measurement end through the quantum channel, and the other is stored in the rare earth doped crystal quantum memory of the rare earth doped quantum storage module 111; wherein the entangled photon pair source module 112 includes a pump submodule 1121, a spontaneous parametric down conversion submodule 1122, a filtering submodule 1123 and an entanglement generation submodule 1124 which are interconnected;

[0053] The pump submodule 1121 is used to generate pump laser light that enters the spontaneous parametric down-conversion submodule 1122. A sapphire laser with a central wavelength of 880 nm, a lens with a focal length of 100 mm, a periodically polarized potassium titanyl phosphate (hereinafter referred to as PPKTP) bulk crystal, and a dichroic filter can be selected as this module; the sapphire laser generates a laser with a wavelength of 880 nm, which is focused on the PPKTP bulk crystal through a lens. With the help of the second harmonic generation effect, the 880 nm light is converted into 440 nm light. After being emitted from the lens, it passes through the dichroic filter so that only the 440 nm component is transmitted;

[0054] The spontaneous parametric down-conversion submodule 1122 is used to generate two photons with different polarizations. Two aspheric lenses and a PPKTP crystal waveguide chip can be selected to form this module. The pump laser from the pump submodule 1121 is focused on the waveguide chip through the aspheric lens, and two photons with different polarizations are generated through a type II spontaneous parametric down-conversion process.

[0055] The filtering submodule 1123 is used to filter the photons generated by the spontaneous parametric down-conversion submodule 1122; an interference filter and two calibrators can be selected as this module;

[0056] The entanglement generation submodule 1124 is used to interfere the photon pair and combine the photon pair to make the photon pair in Bell state by a post-selection method; wherein the entanglement generation submodule 1124 comprises a first polarization beam splitting element 11241, two output ends of the first polarization beam splitting element 11241 are respectively connected to the input end of the first polarization rotation element 11242 and the input end of the second polarization rotation element 11243, the output end of the first polarization rotation element 11242 and the output end of the second polarization rotation element 11243 are respectively connected to the two input ends of the second polarization beam splitting element 11244, and the two output ends of the second polarization beam splitting element 11244 are respectively connected to the input end of the first phase compensation element 11245 and the input end of the second phase compensation element 11246; the output end of the first phase compensation element 11245 is connected to the measurement end, and the output end of the second phase compensation element 11246 is connected to the rare earth doped quantum storage module 111;

[0057] The first polarization beam splitter element 11241 and the second polarization beam splitter element 11244 are both used to perform a beam splitting operation on a photon pair, and a polarization beam splitter can be selected as this module; the first polarization rotation element 11242 and the second polarization rotation element 11243 are both used to rotate the polarization of photons, and a half-wave plate can be selected as this module; the first phase compensation element 11245 and the second phase compensation element 11246 are both used to compensate for phase drift, and a wedge plate can be selected as this module;

[0058] like Figure 4 As shown, the first measuring end 4 and the second measuring end 5 are both used to realize the photon entanglement prediction function, so that the maximum entangled state is established between the two photon generating units 11 connected to the measuring ends, that is, the maximum entangled state is established between the transmitting end and the receiving end, and between the verification end and the receiving end;

[0059] The first measuring end 4 and the second measuring end 5 both include a third polarization rotation element 41 and a fourth polarization rotation element 42. The output end of the third polarization rotation element 41 and the output end of the fourth polarization rotation element 42 are respectively connected to the two input ends of the third polarization beam splitting element 43. The two output ends of the third polarization beam splitting element 43 are respectively connected to the input end of the fifth polarization rotation element 44 and the input end of the sixth polarization rotation element 45. The output end of the fifth polarization rotation element 44 is connected to the input end of the fourth polarization beam splitting element 46. The two output ends of the fourth polarization beam splitting element 46 are respectively connected to the first and second input ends of the single photon detection element 47. The output end of the sixth polarization rotation element 45 is connected to the input end of the fifth polarization beam splitting element 48. The two output ends of the fifth polarization beam splitting element 48 are respectively connected to the third and fourth input ends of the single photon detection element 47.

[0060] The single-photon detection element 47 is used to detect the photons emitted from the fourth polarization beam splitting element 46 and the fifth polarization beam splitting element 48 respectively, and a superconducting nanowire single-photon detector can be selected to form this module; the third polarization rotation element 41, the fourth polarization rotation element 42, the fifth polarization rotation element 44 and the sixth polarization rotation element 45 are used to rotate the polarization of the photons, and a half-wave plate can be selected as this module; the third polarization beam splitting element 43, the fourth polarization beam splitting element 46 and the fifth polarization beam splitting element 48 are used to perform a beam splitting operation on the photon pair, and a polarization beam splitter can be selected as this module; the quantum channel is used to transmit the emitted photons, and a single-mode optical fiber can be selected as this channel;

[0061] Based on the above system, it is possible to share a pair of photons in the maximum entangled state between the transmitter 1 and the receiver 2, and between the verification end 3 and the receiver 2. Where H represents horizontal polarization, V represents vertical polarization, and the system used to establish the maximum entangled state is as follows Figure 2 As shown; taking the establishment of the maximum entangled state between the transmitter 1 and the receiver 2 as an example, the process of establishing the maximum entangled state is described in detail:

[0062] The pump submodule 1121 in the entangled photon pair source module 112 of the photon generating unit 11 in the transmitting end 1 and the receiving end 2 both generate pump lasers. The pump lasers generate two types of photons, horizontally polarized and vertically polarized, through the spontaneous parametric down-conversion submodule 1122. The two photons are filtered through the filtering submodule 1123 and then enter the first polarization beam splitter element 11241 of the entanglement generating submodule 1124. The first polarization beam splitter element 11241 performs a beam splitting operation on the two photons so that the two types of photons, horizontally polarized and vertically polarized, are divided into two paths. The photons on both paths are rotated in polarization through the polarization rotation element. The polarization-rotated photons then reach the second polarization beam splitter element 11244 to cause two-photon interference. Through the post-selection method, the two photons are in a maximum entangled state. The two photons are split again and pass through the phase compensation element to compensate for the phase shift that occurs during the propagation process. After the compensation is completed, one photon enters the rare earth doped quantum storage module 111, and the other photon is sent to the first measurement end 4 through the single mode optical fiber;

[0063] After the above process, the rare earth doped quantum storage modules 111 of the transmitting end 1 and the receiving end 2 store a photon in the maximum entangled state, and the other two photons reach the first measuring end 4. At this time, the quantum state of the joint system composed of the transmitting end 1 and the receiving end 2 is

[0064] The first measuring end 4 regulates the time delay of photon propagation so that the photons generated by the photon generating units 11 in the transmitting end 1 and the receiving end 2 can arrive at the first measuring end 4 synchronously, and two photons cause two-photon interference at the first measuring end 4 (in order to arrive at the first measuring end 4 synchronously, an optical delay device, such as an optical delay line, can be used); when the first input end and the third input end or the second input end and the fourth input end of the single-photon detection element 47 respond simultaneously, it indicates that the two photons that arrive at the first measuring end 4 simultaneously are in the maximum entangled state |φ + >, indicating that the quantum state of the photons stored in the rare-earth doped quantum storage module 111 at the transmitting end 1 and the receiving end 2 is also in the maximum entangled state |φ + >, thus a maximum entangled state is established between the transmitter 1 and the receiver 2; similarly, the process of establishing a maximum entangled state between the verification terminal 3 and the receiver 2 is exactly the same as above, and a maximum entangled state is also established between the verification terminal 3 and the receiver 2.

[0065] The sending end 1, the receiving end 2 and the verification end 3 also include a classical processing unit 6. The classical processing units of the sending end 1 and the receiving end 2, the sending end 1 and the verification end 3, and the receiving end 2 and the verification end 3 are all connected through classical channels; the classical processing unit 6 is a computer, which is used to process the measurement result to obtain the final key; among them, the classical processing unit of the sending end 1 is also used to generate a digital signature, and the classical processing unit of the receiving end 2 and the classical processing unit of the verification end 3 are also used to complete the verification process of the digital signature.

[0066] The present invention also includes a quantum digital signature method based on rare earth quantum storage, comprising the following steps:

[0067] like Figure 5 As shown, (1) Sharing GHZ entangled state: After completing the above process steps to establish the maximum entangled state, a pair of photons in the maximum entangled state are shared between the transmitter 1 and the receiver 2. A pair of photons in a maximum entangled state is shared between the receiving end 2 and the verification end 3 At this time, the receiving end 2 has two photons, which are entangled with the photons of the sending end 1 and the photons of the verification end 3. The receiving end 2 first performs a controlled NOT gate operation on the two photons in its hand. The operator expression of the controlled NOT gate operation is Where B and B′ represent two photons at the receiving end 2 that are entangled with the sending end 1 and the verification end 3 respectively, id represents the unit mapping, represents the bit flip operation, H represents horizontal polarization, and V represents vertical polarization; after completing the controlled NOT gate operation, the receiving end 2 has the first basis vector {|V> B′ ,|H> B′}, measure the photon in its hand that is entangled with the verification end 3, and determine whether the verification end 3 needs to perform a bit flip based on the measurement display result, so that the sending end 1, the receiving end 2 and the verification end 3 share the GHZ entangled state;

[0068] Among them, it is determined whether the verification end 3 needs to perform bit flipping according to the measurement display result. The specific process is: if the measurement display result is horizontal polarization, then the transmitting end 1, the receiving end 2 and the verification end 3 share the GHZ entangled state; if the measurement result shows vertical polarization, then the verification end 3 needs to perform bit flipping, and the transmitting end 1, the receiving end 2 and the verification end 3 share the GHZ entangled state.

[0069] (2) Obtaining the classical bit: After completing the sharing of the GHZ entangled state, the transmitter 1, the receiver 2, and the verification end 3 are respectively Next, the photon in his hand is measured, and the classical bit corresponding to the measured "+" is 0, and the classical bit corresponding to the measured "-" is 1. The classical bit result is used as the final key. Since the transmitter 1, the receiver 2 and the verification end 3 share the GHZ entangled state, the classical bits b measured by the transmitter 1, the receiver 2 and the verification end 3 are a , b b and b c Satisfaction between

[0070] (3) Obtaining the key string: Repeat steps (1) and (2) multiple times, so that the sender, receiver, and verifier obtain the key string B a , B b and B c And meet

[0071] (4) Generation of digital signature: After completing the generation of the key string, the sender, as the sender of the information, generates a digital signature from its own key string B. aA first group of n-bit keys is randomly selected from the random number generator of the sending end, and an n-bit random number is obtained from the random number generator of the sending end. The n-bit random number is used to generate an irreducible polynomial. The irreducible polynomial and the first group of n-bit keys as the input random number are used together to generate a hash function based on a linear feedback shift register. Then, the message to be signed is input into the hash function to obtain a first hash value. The first hash value and the character string composed of each coefficient of the irreducible polynomial except the highest term constitute the first summary. The sending end selects a first group of n-bit keys from the random number generator of the sending end, and the first group of n-bit keys as the input random number are used to generate a hash function based on a linear feedback shift register. Then, the message to be signed is input into the hash function to obtain a first hash value. The first hash value and the character string composed of each coefficient of the irreducible polynomial except the highest term constitute the first summary. a The second 2n-bit key is taken from the remaining keys to perform XOR encryption operation on the first summary to generate the final digital signature;

[0072] The hash function based on the linear feedback shift register is a Toeplitz matrix of dimension n×m, where n is the number of bytes from the key string B at the sender. a Select the length of the first group of keys, where m is the length of the message to be signed;

[0073] The specific process of using n-bit random numbers to generate irreducible polynomials is as follows:

[0074] First, use each bit of the n-bit random number to correspond to the coefficient of each term in the polynomial except the highest term, and generate an n-order polynomial in the GF(2) field, where the coefficient of the highest term is 1; for example, the random number is (a n-1 ,a n-2 ,…,a1,a0), then the generated polynomial is p1(x)=x n +a n-1 x n-1 +…+a1x+a0; Preferably, only when a0=1, the generated polynomial is likely to be an irreducible polynomial. Therefore, in order to reduce the amount of calculation in the later verification of irreducible polynomials, the n-bit random number can be judged first: if the last bit of the n-bit random number is 0, then the last bit of the random number is set to 1, and then an n-order irreducible polynomial in the GF(2) field is generated; or if the last bit of the n-bit random number is 0, then regenerate n-bit random numbers until the last bit of the generated n-bit random number is 1, and then generate an n-order irreducible polynomial in the GF(2) field; this can reduce the amount of calculation in the later verification of irreducible polynomials, and finally make a0=1, and the generated polynomial is p1(x)=x n +a n-1 x n-1 +…+a1x+1;

[0075] Then, the FMC algorithm, i.e., Fast modular composition, is used to verify whether the polynomial is an irreducible polynomial. If the verification result is "no", another set of n-bit random numbers is directly generated from the random number generator at the sending end, and the new n-bit random numbers are returned to step 1) to regenerate the polynomial and verify it; if the verification result is "yes", the verification is stopped and an irreducible polynomial is obtained.

[0076] The sending end then uses the irreducible polynomial and the first group of n-bit keys as the input random number to generate a hash function based on a linear feedback shift register. For this embodiment, an n×m Toeplitz matrix based on a linear feedback shift register is used as the hash function, where m is the length of the message to be signed; the generated hash function is matrix multiplied with the column vector corresponding to the message to obtain a first hash value corresponding to the message, the first hash value is a column vector with a length of n, and the first hash value and the character string composed of each coefficient of the irreducible polynomial except the highest term constitute a first summary; the sending end takes a second group of 2n-bit keys from the remaining key string to perform an XOR encryption operation on the first summary to generate a final digital signature with a length of 2n;

[0077] For example, the sender selects a key and a random number to generate a Toeplitz matrix based on a linear feedback shift register (hereinafter referred to as LFSR) as a hash function; the Toeplitz matrix based on the LFSR is an n×m matrix, where m is the length of the message vector corresponding to the message to be signed, which is a variable value, and n is a fixed value, representing the length of the hash value vector generated after the matrix acts on the message; that is, the Toeplitz matrix based on the LFSR can convert a vector of any length m as the message to be signed into a vector of a fixed length of n, i.e., the first hash value. Such an operation has no requirements for the length of the received message, i.e., each round of signature can sign a message of any length, and the signature efficiency is higher than the existing quantum digital signature technology;

[0078] (5) Verification of digital signature: The sender sends the message to be signed and the digital signature to the receiver. After receiving the digital signature and the message to be signed, the receiver sends the digital signature, the message to be signed, and its own key string B b Sent to the verification end, the verification end receives the digital signature, the message to be signed and the key string B b Then key string B c Send to receiving end 2;

[0079] At this time, both the receiving end and the verification end have key string B b and B c , the two key strings B b and B cPerform an XOR operation to obtain the same key string B as the sender. a , the receiving end and the verification end are in their respective key strings B a The same key as that used by the sender to encrypt the first digest is selected from the key string to decrypt the digital signature to obtain a second digest, wherein the second digest is composed of a character string consisting of the second hash value and the coefficients of each term except the highest term in the irreducible polynomial; each bit of the character string in the second digest corresponds to the coefficient of each term except the highest term in the irreducible polynomial, and an irreducible polynomial with the highest term coefficient of 1 is generated, and the generated irreducible polynomial is used to generate a hash function with the first group of n-bit keys selected from the key string that is the same as that used by the sender to generate a hash function based on a linear feedback shift register, and then the received message to be signed is input into the generated hash function to generate a third hash value; the receiving end and the verification end both compare the obtained third hash value with the second hash value in the second digest, and if the second hash value and the third hash value are the same, the signature is accepted; otherwise, the signature is not accepted.

[0080] like Figure 6 To further demonstrate the performance of the system provided by the present invention, we show in the figure how the signature efficiency (the number of messages of any length that can be signed by each optical pulse) of the quantum network with relays changes with the channel length. It can be seen that at a distance of 300 km, the signature efficiency remains at 10 -6 Such efficiency is of very high practicality.

Claims

1. A quantum digital signature method based on rare earth quantum storage, characterized in that: The following steps are involved: (1) Sharing GHZ entangled state: A pair of photons in the maximum entangled state is shared between the transmitter and the receiver, and a pair of photons in the maximum entangled state is shared between the receiver and the verifier. The receiver first performs a controlled NOT gate operation on the two photons in its hand. After completing the controlled NOT gate operation, the receiver measures the photon entangled with the verifier in its hand under the first basis vector, and determines whether the verifier needs to perform a bit flip based on the measurement display result, so that the transmitter, receiver and verifier share the GHZ entangled state. (2) Obtaining the classical bit: After completing the sharing of the GHZ entangled state, the sender, receiver, and verifier measure the photons in their hands under the second basis vector respectively. The measured "+" corresponds to the classical bit 0, and the measured "-" corresponds to the classical bit 1. The obtained classical bit result is used as the final key. Since the sender, receiver, and verifier share the GHZ entangled state, the classical bits b measured by the sender, receiver, and verifier are a , b b and b c Satisfaction between (3) Obtaining the key string: Repeat steps (1) and (2) multiple times, so that the sender, receiver, and verifier obtain the key string B a , B b and B c And meet (4) Generation of digital signature: After completing the generation of the key string, the sender generates a digital signature from its own key string B. a A first group of n-bit keys is randomly selected and an n-bit random number is obtained from a random number generator at the sending end, the n-bit random number is used to generate an irreducible polynomial, the irreducible polynomial and the first group of n-bit keys as the input random number are used together to generate a hash function based on a linear feedback shift register, and then the message to be signed is input into the hash function to obtain a first hash value, and the first hash value and a character string composed of each coefficient of the irreducible polynomial except the highest term constitute a first summary; The sender uses key string B a The second 2n-bit key is taken from the remaining keys to perform XOR encryption operation on the first summary to generate the final digital signature; (5) Verification of digital signature: The sender sends the message to be signed and the digital signature to the receiver. After receiving the digital signature and the message to be signed, the receiver sends the digital signature, the message to be signed, and its own key string B b Sent to the verification end, the verification end receives the digital signature, the message to be signed and the key string B b Then key string B c Send to the receiving end; At this time, both the receiving end and the verification end have key string B b and B c , the two key strings B b and B c Perform an XOR operation to obtain the same key string B as the sender. a , the receiving end and the verification end are in their respective key strings B a The same key as that used by the sender to encrypt the first summary is selected from the key string to decrypt the digital signature to obtain a second summary; each bit of the string in the second summary corresponds to the coefficient of each term except the highest term in the irreducible polynomial, and an irreducible polynomial with the highest term coefficient of 1 is generated. The generated irreducible polynomial is used to generate a hash function with the first group of n-bit keys selected from the key string that is the same as that used by the sender to generate a hash function based on a linear feedback shift register, and then the received message to be signed is input into the generated hash function to generate a third hash value; the receiving end and the verification end both compare the obtained third hash value with the second hash value in the second summary, and if the second hash value and the third hash value are the same, the signature is accepted; otherwise, the signature is not accepted.

2. The quantum digital signature method based on rare earth quantum storage according to claim 1 is characterized in that: In the step (1), it is determined whether the verification end needs to perform bit flipping according to the measurement display result. The specific process is: if the measurement display result is horizontal polarization, then the transmitting end, the receiving end and the verification end share the GHZ entangled state; if the measurement result shows vertical polarization, then the verification end needs to perform bit flipping, and the transmitting end, the receiving end and the verification end share the GHZ entangled state.

3. The quantum digital signature method based on rare earth quantum storage according to claim 1 is characterized in that: In step (1), the operator expression of the controlled NOT gate operation is Where B and B′ represent two photons at the receiving end that are entangled with the sending end and the verification end respectively, id represents the unit mapping, represents a bit flip operation, H represents horizontal polarization, and V represents vertical polarization; In step (1), the first basis vector is {|V> B′ ,|H> B′ }; In step (2), the second basis vector is 4. The quantum digital signature method based on rare earth quantum storage according to claim 1 is characterized in that: The specific process of using the n-bit random number to generate an irreducible polynomial is as follows: 1) First, use each bit of the n-bit random number to correspond to the coefficient of each term in the polynomial except the highest term, and generate an n-order polynomial in the GF(2) field, where the coefficient of the highest term is 1; 2) Then, use the FMC algorithm to verify whether this polynomial is an irreducible polynomial. If the verification result is "no", directly generate another set of n-bit random numbers from the random number generator at the sender, and return to step 1) as new n-bit random numbers to regenerate the polynomial and verify it; if the verification result is "yes", stop the verification and obtain an irreducible polynomial.

5. The quantum digital signature method based on rare earth quantum storage according to claim 4 is characterized in that: Before step 1), if the last bit of the n-bit random number is 0, then the last bit of the random number is set to 1, and then an irreducible polynomial of order n in the GF(2) field is generated; or if the last bit of the n-bit random number is 0, then n-bit random numbers are regenerated until the last bit of the generated n-bit random number is 1, and then an irreducible polynomial of order n in the GF(2) field is generated.

6. The quantum digital signature method based on rare earth quantum storage according to claim 1 is characterized in that: In step (4), the hash function based on the linear feedback shift register is a Toeplitz matrix of dimension n×m, where n is the number of bytes from the key string B at the sender. a Select the length of the first set of keys, where m is the length of the message to be signed.

7. A digital signature system according to any one of claims 1 to 6, characterized in that: The method comprises a transmitting end, a receiving end and a verifying end, wherein the transmitting end, the receiving end and the verifying end all comprise a photon generating unit, the photon generating unit of the transmitting end and the photon generating unit of the receiving end are connected to a first measuring end via a quantum channel, and the photon generating unit of the verifying end and the photon generating unit of the receiving end are connected to a second measuring end via a quantum channel; The photon generating unit comprises a rare earth doped quantum storage module and an entangled photon pair source module connected to each other, wherein the rare earth doped quantum storage module is used to store photons generated by the entangled photon pair source module, and the entangled photon pair source module is used to generate entangled photon pairs, wherein one photon of the photon pair enters the measuring end through the quantum channel, and the other photon is stored in the rare earth doped quantum storage module; The first measuring end and the second measuring end are both used to realize the photon entanglement prediction function, so that a maximum entangled state is established between the two photon generating units connected to the measuring ends.

8. The digital signature system of the quantum digital signature method based on rare earth quantum storage according to claim 7 is characterized in that: The entangled photon pair source module includes a pump submodule, a spontaneous parametric down-conversion submodule, a filtering submodule and an entanglement generation submodule which are interconnected; The pump submodule is used to generate pump laser that enters the spontaneous parametric down-conversion submodule; The spontaneous parametric down-conversion submodule is used to generate two photons with different polarizations; The filtering submodule is used to filter the photons generated by the spontaneous parametric down-conversion submodule; The entanglement generation submodule is used to interfere the photon pair and combine the post-selection method to make the photon pair in Bell state.

9. The digital signature system of the quantum digital signature method based on rare earth quantum storage according to claim 8 is characterized in that: The entanglement generation submodule comprises a first polarization beam splitting element, two output ends of the first polarization beam splitting element are respectively connected to the input end of the first polarization rotation element and the input end of the second polarization rotation element, the output end of the first polarization rotation element and the output end of the second polarization rotation element are respectively connected to the two input ends of the second polarization beam splitting element, and the two output ends of the second polarization beam splitting element are respectively connected to the input end of the first phase compensation element and the input end of the second phase compensation element; The output end of the first phase compensation element is connected to the measurement end, and the output end of the second phase compensation element is connected to the rare earth doped quantum storage module; The first polarization beam splitting element and the second polarization beam splitting element are both used to perform a beam splitting operation on the photon pair; The first polarization rotation element and the second polarization rotation element are both used to rotate the polarization of the photon; The first phase compensation element and the second phase compensation element are both used to compensate for phase drift.

10. The digital signature system of the quantum digital signature method based on rare earth quantum storage according to claim 7, characterized in that: The first measuring end and the second measuring end both include a third polarization rotation element and a fourth polarization rotation element, the output end of the third polarization rotation element and the output end of the fourth polarization rotation element are respectively connected to the two input ends of the third polarization beam splitting element, the two output ends of the third polarization beam splitting element are respectively connected to the input end of the fifth polarization rotation element and the input end of the sixth polarization rotation element, the output end of the fifth polarization rotation element is connected to the input end of the fourth polarization beam splitting element, the two output ends of the fourth polarization beam splitting element are respectively connected to the first and second input ends of the single photon detection element; the output end of the sixth polarization rotation element is connected to the input end of the fifth polarization beam splitting element, and the two output ends of the fifth polarization beam splitting element are respectively connected to the third and fourth input ends of the single photon detection element.

11. The digital signature system of the quantum digital signature method based on rare earth quantum storage according to claim 7, characterized in that: The working process of establishing the maximum entangled state between two photon generating units is: The pump submodules in the entangled photon pair source modules of the photon generating units in the transmitting and receiving ends both generate pump lasers. The pump lasers generate two types of photons, horizontally polarized and vertically polarized, through the spontaneous parametric down-conversion submodule. The two photons are filtered through the filtering submodule and then enter the first polarization beam splitting element of the entanglement generating submodule. The first polarization beam splitting element performs a beam splitting operation on the two photons so that the two types of photons, horizontally polarized and vertically polarized, are divided into two paths. The photons on both paths are rotated in polarization through the polarization rotation element. The polarization-rotated photons then reach the second polarization beam splitting element to cause two-photon interference. Through the post-selection method, the two photons are in the maximum entangled state. The two photons are split again and pass through phase compensation elements to compensate for the phase shift that occurs during the propagation process. After the compensation is completed, one photon enters the rare earth doped quantum storage module, and the other photon is sent to the first measurement end through the quantum channel; After the above process, a photon in the maximum entangled state is stored in the rare earth doped quantum storage module at both the transmitter and the receiver, while the other two photons reach the first measurement end. At this time, the quantum state of the joint system composed of the transmitter and the receiver is The first measurement end adjusts the time delay of photon propagation so that the photons generated by the photon generating units in the transmitting end and the receiving end can arrive at the first measurement end synchronously, and two photons cause two-photon interference at the first measurement end; when the first input end and the third input end or the second input end and the fourth input end of the single-photon detection element respond at the same time, it indicates that the two photons that arrive at the first measurement end at the same time are in the maximum entangled state |φ + >, indicating that the quantum states of photons stored in the rare-earth-doped quantum storage modules at the transmitter and receiver are also in the maximum entangled state |φ + >, thus a maximum entangled state is established between the transmitter and the receiver; similarly, a maximum entangled state is also established between the verifier and the receiver.

12. The digital signature system of the quantum digital signature method based on rare earth quantum storage according to claim 7, characterized in that: The sending end, the receiving end and the verification end also include classical processing units, and the classical processing units of the sending end and the receiving end, the classical processing units of the sending end and the verification end, and the classical processing units of the receiving end and the verification end are all connected through classical channels; the classical processing units are computers, and are all used to process the measurement results to obtain the final key; wherein the classical processing unit of the sending end is also used to generate a digital signature, and the classical processing unit of the receiving end and the classical processing unit of the verification end are also used to complete the verification process of the digital signature.

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