CN113961952A - Quantum digital signature method and system based on rare earth quantum storage - Google Patents
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Abstract
The invention discloses a quantum digital signature method and a system based on rare earth quantum storage, which avoid the disadvantage that entanglement cannot be generated deterministically in the system by selecting a definite entangled photon pair as an entanglement source, have high quantum relay efficiency and realize long-distance quantum communication; moreover, the rare earth doped quantum storage module has long service life, large bandwidth, high fidelity, high multi-mode working capability, capability of realizing multiplexing operation, higher efficiency in quantum relay application and strong practicability; the key distribution is realized on the quantum network through the quantum relay, and then the hash function based on the linear feedback shift register is generated by using the key and the random number, so that the hash value can be generated for the message with any length, and the method has high efficiency and good practicability.
Description
Technical Field
The invention relates to the field of quantum security, in particular to a quantum digital signature method and system based on rare earth quantum storage.
Background
In classical cryptography, symmetric ciphers can protect the privacy of data, asymmetric ciphers can protect the integrity, and authentication and denial prevention are realized. However, the basis for the classical cryptography to satisfy these information security requirements is the complexity of mathematical problem solution, and with the improvement of computer computing power and the development of quantum computing technology, the security of the cryptosystem based on the computational complexity will be threatened.
The development of quantum information technology has given revolutionary solutions to the cryptographic task. In 2016, Yin et al proposed that a secret key is generated by two methods, namely a two-photon six-state method and a decoy state method, so as to realize quantum digital signature, and theoretically, the implementation distance can reach 100 km; in 2021, Lu et al designed an efficient quantum digital signature scheme, which adopts a post-matching processing method, and the signature efficiency and the detection efficiency showed a linear relationship. These protocols ensure the integrity of data and prevent tampering and repudiation, but these protocols can only carry out digital signature on data of one bit in each round of signature, the signature efficiency is low, and the practicability is lacked under the condition that the message is long.
The main challenge facing quantum secure communication at present is the realization of long-distance quantum communication, and quantum networks can provide perfect solutions for the two problems. On a quantum network, long-distance entanglement distribution can be realized by means of quantum relay, so that long-distance quantum communication is realized, and various cryptology tasks are completed under the condition of long distance. Therefore, the realization of quantum networks is an important core problem of the current quantum information scientific development. In 2001, Duan et al proposed to create quantum relays, and to create remote quantum entanglement through entanglement swapping and quantum storage. Subsequently, quantum memories, which are important components of quantum relays, have been demonstrated experimentally for many times. In 2020, Yu et al achieved entanglement at distances of 20km and 50km using quantum memory based on cold atomic ensembles, but here the atom-light entanglement was derived from collective excitation and raman scattered photons of random atomic ensembles, i.e. entanglement could not be generated deterministically, the efficiency of achieving quantum relaying was low, and the practicality of deployment on quantum networks was weak. To this end, we propose a quantum digital signature method and system based on rare earth quantum storage to address the above-mentioned deficiencies of the prior art.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a quantum digital signature method and a system based on rare earth quantum storage, which solve the problems that the prior entanglement source can not generate entanglement deterministically, the efficiency of quantum relay is low, and long-distance quantum communication can not be realized; and the existing quantum digital signature has low efficiency, each round of signature can only carry out signature on one bit of data, and the generation of the signature needs to consume a large amount of communication resources.
The technical scheme is as follows: the invention discloses a quantum digital signature method based on rare earth quantum storage, which comprises the following steps:
(1) shared GHZ entangled state: a pair of photons in the maximum entangled state is shared between the sending end and the receiving end, and a pair of photons in the maximum entangled state is shared between the receiving end and the verification end; the method comprises the steps that a receiving end firstly carries out controlled NOT gate operation on two photons in a hand of the receiving end, after the controlled NOT gate operation is completed, the receiving end measures photons entangled with an authentication end in the hand of the receiving end under a first basis vector, and judges whether the authentication end needs to carry out bit reversal or not according to a measurement display result, so that a sending end, the receiving end and the authentication end share a GHZ entangled state;
(2) the classical bit is obtained: after sharing of the GHZ entangled state is completed, the transmitting end, the receiving end and the verifying end respectively measure photons in hands under a second basis vector, the measured "+" corresponds to the classical bit being 0, the measured "-" corresponds to the classical bit being 1, the obtained classical bit result is used as a final secret key, and the transmitting end, the receiving end and the verifying end respectively measure the obtained classical bit b as the GHZ entangled state is shared by the transmitting end, the receiving end and the verifying enda，bbAnd bcSatisfy
(3) Obtaining a key string: repeating the steps (1) and (2) for multiple times, so that the sending end, the receiving end and the verifying end obtain the key string Ba，BbAnd BcAnd satisfy
(4) Generation of digital signature: after completing the generation of the key string, the transmitting end follows its own key string BaRandomly selecting a first group of n-bit keys and acquiring n-bit random numbers from a random number generator of a sending end, wherein the n-bit random numbers are used for generating an irreducible polynomial, the irreducible polynomial and the first group of n-bit keys serving as input random numbers generate a hash function based on a linear feedback shift register, then inputting a message needing to be signed into the hash function to obtain a first hash value, and the first hash value and a character string consisting of coefficients of each item except the highest item in the irreducible polynomial form a first abstract; sending end slave key string BaTaking a second group of 2 n-bit keys from the rest keys to carry out exclusive-or encryption operation on the first abstract so as to generate a final digital signature;
(5) and (3) verification of the digital signature: the sending end sends the message to be signed and the digital signature to the receiving end, and the receiving end receives the digital signature and the message to be signed and then sends the digital signature, the message to be signed and the key string B of the receiving endbSending to a verification end, wherein the verification end receives the digital signature, the message needing to be signed and a key string BbThen the key string BcSending the data to a receiving end;
at this time, the receiving end and the verifying end both contain the key string BbAnd BcTwo key strings BbAnd BcPerforming XOR operation to obtain the key string B identical to the sending endaThe receiving end and the verifying end are respectively at the key string BaThe key which is the same as the key used by the sending end to encrypt the first abstract is selected to decrypt the digital signature to obtain a second abstract; each bit of the character string in the second abstract corresponds to the coefficient of each item except the highest item in the irreducible polynomial, an irreducible polynomial with the highest item coefficient being 1 is generated, the generated irreducible polynomial and a first group of n-bit keys which are selected from the key string and are the same as those generated by the sending end based on the linear feedback shift register hash function generate the hash function, and then the received message which needs to be signed is input to generateGenerating a third hash value by the hash function; comparing the obtained third hash value with a second hash value in the second abstract by the receiving end and the verifying end, and receiving the signature if the second hash value is the same as the third hash value; otherwise, the signature is not accepted.
Further, in the step (1), it is determined whether the verification end needs to perform bit flipping according to the measurement display result, and the specific process is as follows: if the measurement display result is horizontal polarization, the sending end, the receiving end and the verification end share the GHZ entangled state at this moment; if the measurement result shows vertical polarization, the sending end, the receiving end and the verifying end share the GHZ entangled state after the verifying end needs to perform bit flipping.
Further, in the step (1), the operator expression of the controlled not gate operation is as follows
Wherein B and B' represent two photons of the receiving end respectively entangled with the transmitting end and the verifying end, id represents unit mapping,
represents a bit flipping operation, H represents horizontal polarization, and V represents vertical polarization;
in the step (1), the first basis vector is { | V>B′,|H>B′}; in step (2), the second basis vector is
Further, the specific process of the n-bit random number for generating the irreducible polynomial is as follows:
1) firstly, sequentially using each bit of n-bit random numbers to correspond to the coefficient of each term except the highest term in the polynomial to generate an n-order polynomial in a GF (2) domain, wherein the coefficient of the highest term is 1;
2) then, verifying whether the polynomial is irreducible polynomial by using FMC algorithm, if the verification result is 'no', directly generating another group of n-bit random numbers from a random number generator at the sending end, and returning to the step 1) for regenerating the polynomial as a new n-bit random number and verifying; if the verification result is 'yes', the verification is stopped, and the irreducible polynomial is obtained.
Further, before step 1), if the last bit of the n-bit random number is 0, the last bit of the random number is 1, and an irreducible polynomial of order n in a GF (2) field is generated; or if the last bit of the n-bit random number is 0, regenerating the n-bit random number until the last bit of the generated n-bit random number is 1, and regenerating an n-order irreducible polynomial in a GF (2) field.
Further, in the step (4), the hash function based on the linear feedback shift register is a Toeplitz matrix with dimension n × m, where n is the slave key string B of the sending endaThe length of the first group key is selected, and m is the length of the message to be signed.
The invention also comprises a quantum digital signature system based on rare earth quantum storage, which comprises a sending end, a receiving end and a verification end, wherein the sending end, the receiving end and the verification end respectively comprise a photon generation unit;
the photon generation unit comprises a rare earth doped quantum storage module and an entangled photon pair source module which are connected with each other, the rare earth doped quantum storage module is used for storing photons generated by the entangled photon pair source module, the entangled photon pair source module is used for generating entangled photon pairs, one photon in each photon pair enters the measurement end through a 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 used for achieving a photon entanglement forecasting function, and therefore the maximum entangled state is established between the two photon generating units connected with the measuring ends.
Further, the entangled photon pair source module comprises a pumping sub-module, a spontaneous parameter down-conversion sub-module, a filtering sub-module and an entangled generation sub-module which are connected with each other;
the pumping sub-module is used for generating pumping laser entering the spontaneous parameter down-conversion sub-module;
the spontaneous parameter down-conversion sub-module is used for generating two photons with different polarizations;
the filtering submodule is used for filtering photons generated by the spontaneous parameter down-conversion submodule;
the entanglement generation submodule is used for enabling the photon pairs to be in a Bell state by means of interference and selection after combination.
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 with an input end of a first polarization rotation element and an input end of a second polarization rotation element, an output end of the first polarization rotation element and an output end of the second polarization rotation element are respectively connected with two input ends of the second polarization beam splitting element, and two output ends of the second polarization beam splitting element are respectively connected with an input end of a first phase compensation element and an input end of a second phase compensation element; the output end of the first phase compensation element is connected with the measuring end, and the output end of the second phase compensation element is connected with the rare earth doped quantum storage module;
the first polarization beam splitting element and the second polarization beam splitting element are used for splitting the photon pair;
the first polarization rotating element and the second polarization rotating element are used for rotating the polarization of the photons;
the first phase compensation element and the second phase compensation element are used for compensating phase drift.
Furthermore, the first measuring end and the second measuring end both comprise a third polarization rotating element and a fourth polarization rotating element, an output end of the third polarization rotating element and an output end of the fourth polarization rotating element are respectively connected with two input ends of a third polarization beam splitting element, two output ends of the third polarization beam splitting element are respectively connected with an input end of a fifth polarization rotating element and an input end of a sixth polarization rotating element, an output end of the fifth polarization rotating element is connected with an input end of the fourth polarization beam splitting element, and two output ends of the fourth polarization beam splitting element are respectively connected with a first input end and a second input end of the single photon detecting element; the output end of the sixth polarization rotating element is connected with the input end of a fifth polarization beam splitting element, and the two output ends of the fifth polarization beam splitting element are respectively connected with the third input end and the fourth input end of the single photon detection element.
Further, the working process of establishing the maximum entangled state between the two photon generating units is as follows:
entangled photons of photon generation units in a sending end and a receiving end generate pump laser for a pump submodule in a source module, the pump laser generates two photons of horizontal polarization and vertical polarization through a spontaneous parameter down-conversion submodule, the two photons enter a first polarization beam splitting element of an entanglement generation submodule after being filtered by a filtering submodule, the first polarization beam splitting element splits the two photons so that the two photons of the horizontal polarization and the vertical polarization are divided into two paths, the photons on the two paths rotate polarization through a polarization rotating element, the photons after polarization rotation reach a second polarization beam splitting element to generate two-photon interference, and the two photons are in the maximum entangled state through a post-selection method
The two photons are split again and respectively pass through a phase compensation element to compensate phase shift generated in the transmission process, after compensation is completed, one photon enters a rare earth doped quantum storage module, and the other photon is sent to a first measuring end through a quantum channel;
after the processes, photons in the maximum entangled state are stored in the rare earth doped quantum storage modules of the sending end and the receiving end, the other two photons reach the first measuring end, and the quantum state of a combined system formed by the sending end and the receiving end is the quantum state
The first measuring end regulates and controls the time delay of photon propagation, so that photons generated by photon generating units in the transmitting end and the receiving end can synchronously reach the first measuring end, and two photons generate two-photon interference at the first measuring 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 simultaneously, two photons arriving at the first measurement end at the same time are predicted to be in the maximum entanglement state | phi |+>It is indicated that the quantum states of the photons stored in the rare earth doped quantum storage modules of the transmitting end and the receiving end are also in the maximum entangled state | phi+>Thus, the maximum entanglement state is established between the sending end and the receiving end; similarly, the maximum entanglement state is also established between the verification end and the receiving end.
Further, the transmitting end, the receiving end and the verifying end also comprise classical processing units, and the classical processing units of the transmitting end and the receiving end, the classical processing units of the transmitting end and the verifying end and the classical processing units of the receiving end and the verifying end are all connected through classical channels; the classical processing units are computers and are used for processing the measurement result to obtain a final key; the classical processing unit of the sending end is also used for generating the digital signature, and the classical processing unit of the receiving end and the classical processing unit of the verifying end are also used for finishing the verification process of the digital signature.
The invention has the beneficial effects that:
(1) the method selects the determined entangled photon pair as an entanglement source, avoids the disadvantage that entanglement cannot be generated by determinacy in an ensemble, has high quantum relay efficiency, and realizes long-distance quantum communication;
(2) the invention utilizes the rare earth doped quantum storage module, has long service life, large bandwidth, high fidelity, high multi-mode working capability, can realize multiplexing operation, has higher efficiency in quantum relay application and strong practicability;
(3) the invention realizes the distribution of the key on the quantum network through the quantum relay, further utilizes the key and the random number to generate the hash function based on the linear feedback shift register, can generate the hash value for the message with any length, and has high efficiency and good practicability.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention;
FIG. 2 is a schematic diagram of a system for establishing entanglement between a transmitting end and a receiving end;
FIG. 3 is a schematic structural diagram of an entangled photon pair source module;
FIG. 4 is a schematic view of a first measuring end structure;
FIG. 5 is a schematic flow diagram of three parties generating a GHZ entangled state after sharing a Bell state two by two;
fig. 6 is a graph showing the variation of the signature efficiency limit with the channel length.
Detailed Description
The invention is further described below with reference to the following figures and examples:
as shown in fig. 1, the quantum digital signature system based on rare earth quantum storage of the present invention includes a sending end 1, a receiving end 2 and a verification end 3, where the sending end 1, the receiving end 2 and the verification end 3 all include a photon generation unit 11, the photon generation unit 11 of the sending end 1 and the photon generation unit 11 of the receiving end 2 are connected to a first measurement end 4 through a quantum channel, and the photon generation unit 11 of the verification end 3 and the photon generation unit 11 of the receiving end 2 are connected to a second measurement end 5 through a quantum channel;
as shown in fig. 2, the photon generation unit 11 includes a rare earth doped quantum storage module 111 and an entangled photon pair source module 112, which are connected to each other, the rare earth doped quantum storage module 111 is configured to store photons generated by the entangled photon pair source module 112, the stored photons can be further transmitted to other positions through a quantum channel, and the module implements quantum storage by using a rare earth doped crystal quantum memory in combination with an atomic frequency comb pump laser;
as shown in fig. 3, the entangled photon pair source module 112 is used to generate entangled photon pairs, one photon of a photon pair entering the measurement end through the quantum channel and one being stored in the rare earth doped crystal quantum memory of the rare earth doped quantum memory module 111; the entangled photon pair source module 112 includes a pumping sub-module 1121, a spontaneous parameter down-conversion sub-module 1122, a filtering sub-module 1123, and an entanglement generation sub-module 1124 which are connected to each other;
the pumping sub-module 1121 is configured to generate pumping laser light entering the spontaneous parametric down-conversion sub-module 1122, and may select a sapphire laser having a center wavelength of 880nm, a lens having a focal length of 100mm, a periodically polarized potassium titanyl phosphate (hereinafter referred to as PPKTP) bulk crystal, and a dichroic filter as the module; the sapphire laser generates laser with the wavelength of 880nm, the laser is focused on the PPKTP bulk crystal through a lens, 880nm light is converted into 440nm light by means of a second harmonic generation effect, and only 440nm components are transmitted through a dichroic filter after the light is emitted from the lens;
the spontaneous parametric down-conversion submodule 1122 is used to generate two photons of different polarizations; two aspheric lenses and a PPKTP crystal waveguide chip can be selected to form the module, pump laser from the pump sub-module 1121 is focused on the waveguide chip through the aspheric lenses, and two photons with different polarizations are generated through a II-type spontaneous parameter down-conversion process;
the filtering submodule 1123 is configured to filter photons generated by the spontaneous parametric down-conversion submodule 1122; it can select an interference filter and two calibrators as the module;
the entanglement generation sub-module 1124 is configured to interfere and combine the photon pairs to make the photon pairs in a bell state; the entanglement generation submodule 1124 includes a first polarization beam splitting element 11241, two output ends of the first polarization beam splitting element 11241 are respectively connected to an input end of a first polarization rotation element 11242 and an input end of a second polarization rotation element 11243, an output end of the first polarization rotation element 11242 and an output end of the second polarization rotation element 11243 are respectively connected to two input ends of a second polarization beam splitting element 11244, and two output ends of the second polarization beam splitting element 11244 are respectively connected to an input end of a first phase compensation element 11245 and an input end of a second phase compensation element 11246; the output end of the first phase compensation element 11245 is connected with the measuring end, and the output end of the second phase compensation element 11246 is connected with the rare earth doped quantum memory module 111;
the first and second polarizing beam splitting elements 11241 and 11244 are used to split the photon pair, and a polarizing beam splitter may be selected as this module; the first polarization rotating element 11242 and the second polarization rotating element 11243 are both used to rotate the polarization of the photons, and a half-wave plate may be selected as this module; a first phase compensation element 11245 and a second phase compensation element 11246, both for compensating for phase drift, a wedge plate may be chosen as this module;
as shown in fig. 4, the first measuring end 4 and the second measuring end 5 are both used for implementing a photon entanglement prediction function, so that a maximum entangled state is established between two photon generating units 11 connected to the measuring ends, that is, a maximum entangled state is established between the transmitting end and the receiving end, and between the verifying end and the receiving end;
the first measuring end 4 and the second measuring end 5 both comprise a third polarization rotating element 41 and a fourth polarization rotating element 42, an output end of the third polarization rotating element 41 and an output end of the fourth polarization rotating element 42 are respectively connected with two input ends of a third polarization beam splitting element 43, two output ends of the third polarization beam splitting element 43 are respectively connected with an input end of a fifth polarization rotating element 44 and an input end of a sixth polarization rotating element 45, an output end of the fifth polarization rotating element 44 is connected with an input end of a fourth polarization beam splitting element 46, and two output ends of the fourth polarization beam splitting element 46 are respectively connected with a first input end and a second input end of a fourth polarization beam splitting element 47; the output end of the sixth polarization rotating element 45 is connected with the input end of the fifth polarization beam splitting element 48, and two output ends of the fifth polarization beam splitting element 48 are respectively connected with the third and fourth input ends of the single photon detecting element 47;
the single photon detection element 47 is used for detecting photons respectively emitted from the fourth polarization beam splitting element 46 and the fifth polarization beam splitting element 48, and can select a superconducting nanowire single photon detector to form the module; the third polarization rotating element 41, the fourth polarization rotating element 42, the fifth polarization rotating element 44 and the sixth polarization rotating element 45 are used for rotating the polarization of the photons, and a half-wave plate can be selected as the 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 for splitting the photon pair, and a polarization beam splitter can be selected as the module; the quantum channel is used for transmitting emitted photons, and a single-mode optical fiber can be selected as the channel;
based on the system, the transmitting end 1 and the receiving end 2 and the verifying end 3 and the receiving end 2 can share a pair of photons in the maximum entangled state respectively
Where H denotes horizontal polarization and V denotes vertical polarization, the system used to establish the maximum entanglement state is shown in fig. 2; the process of establishing the maximum entangled state is described in detail by taking the example of establishing the maximum entangled state between the transmitting end 1 and the receiving end 2:
the entangled photons of the photon generation unit 11 in the transmitting end 1 and the receiving end 2 both generate pump laser to the pump sub-module 1121 of the source module 112, the pump laser generates two photons of horizontal polarization and vertical polarization through the spontaneous parameter down-conversion sub-module 1122, the two photons are filtered by the filtering sub-module 1123 and then enter the first polarization beam splitting element 11241 of the entanglement generation sub-module 1124, the first polarization beam splitting element 11241 splits the two photons so that the two photons of horizontal polarization and vertical polarization are divided into two paths, the photons of the two paths are rotated by the polarization rotating element, the photons rotated by polarization then reach the second polarization beam splitting element 11244 to generate two-photon interference, and the two photons are in the maximum entangled state by the post-selection method
The two photons are split again and respectively pass through a phase compensation element to compensate phase shift generated in the transmission process, after compensation is completed, one photon enters the rare earth doped quantum storage module 111, and the other photon is sent to the first measuring end 4 through a single mode fiber;
after the above processes, the rare earth doped quantum memory modules 111 of the transmitting terminal 1 and the receiving terminal 2 both store photons in a maximum entangled state, and the other two photons reach the first measuring terminal 4, at this time, the transmitting terminal 1 and the receiving terminal 12 has a quantum state of
The first measuring end 4 regulates and controls the time delay of photon propagation, so that photons generated by the photon generating unit 11 from the transmitting end 1 and the receiving end 2 can synchronously reach the first measuring end 4, and two photons generate two-photon interference at the first measuring end 4 (in order to synchronously reach the first measuring end 4, an optical delay device such as an optical delay line and the like can be used); when the first input terminal and the third input terminal or the second input terminal and the fourth input terminal of the single photon detecting element 47 respond simultaneously, it is predicted that two photons arriving at the first measuring terminal 4 at the same time are in the maximum entanglement state | φ+>It is shown that the quantum states of the photons stored in the rare earth doped quantum storage modules 111 of the transmitting end 1 and the receiving end 2 are also in the maximum entangled state | phi |+>Thus, the maximum entanglement state is established between the sending end 1 and the receiving end 2; similarly, the process of establishing the maximum entanglement state between the verifying end 3 and the receiving end 2 is completely consistent with the above, and the maximum entanglement state is also established between the verifying end 3 and the receiving end 2.
The transmitting end 1, the receiving end 2 and the verifying end 3 further comprise classical processing units 6, and the transmitting end 1 and the receiving end 2, the transmitting end 1 and the verifying end 3, and the receiving end 2 and the verifying end 3 are connected through classical channels; the classical processing unit 6 is a computer and is used for processing the measurement result to obtain a final key; the classical processing unit of the sending end 1 is further configured to generate a digital signature, and the classical processing unit of the receiving end 2 and the classical processing unit of the verifying end 3 are further configured to complete a verification process of the digital signature.
The invention also comprises a quantum digital signature method based on rare earth quantum storage, which comprises the following steps:
as shown in fig. 5, (1) share the GHZ entangled state: after the above process steps of establishing the maximum entangled state are completed, the transmitting end 1 and the receiving end 2 share a pair of photons of the maximum entangled state
A pair of photons with maximum entanglement states is shared between the receiving end 2 and the verifying end 3
At the moment, the receiving end 2 masters two photons, the two photons are respectively entangled with the transmitting end 1 and the verifying end 3, the receiving end 2 firstly carries out controlled NOT gate operation on the two photons in the hands of the receiving end, and the operator expression of the controlled NOT gate operation is
Where B and B' represent two photons of the receiving end 2 that are entangled with the transmitting end 1 and the verifying end 3, respectively, id represents a unit mapping,
represents a bit flipping operation, H represents horizontal polarization, and V represents vertical polarization; after the controlled not gate operation is completed, the receiving end 2 has a first basis vector of { | V>B′,|H>B′Measuring photons entangled with the verification end 3 in hands of the user, and judging whether the verification end 3 needs to perform bit inversion according to a measurement display result, so that the sending end 1, the receiving end 2 and the verification end 3 share a GHZ entangled state;
wherein, whether the verification terminal 3 needs to perform bit flipping is judged according to the measurement display result, and the specific process is as follows: if the measurement display result is horizontal polarization, the sending terminal 1, the receiving terminal 2 and the verification terminal 3 share the GHZ entangled state at this time; if the measurement result shows vertical polarization, the sending end 1, the receiving end 2 and the verifying end 3 share the GHZ entangled state after the verifying end 3 needs to perform bit flipping.
(2) The classical bit is obtained: after the sharing of the GHZ entangled state is completed, the sending terminal 1, the receiving terminal 2 and the verifying terminal 3 respectively have second basis vectors as
Measuring photons in hands of the user, wherein measured "+" corresponds to the classical bit being 0, measured "-" corresponds to the classical bit being 1, the obtained classical bit result is used as a final secret key, and since the sending end 1, the receiving end 2 and the verifying end 3 share the GHZ entangled state, the sending end 1, the receiving end 2 and the verifying end 3 respectively measure the obtained classical bit ba，bbAnd bcSatisfy
(3) Obtaining a key string: repeating the steps (1) and (2) for multiple times, so that the sending end, the receiving end and the verifying end obtain the key string Ba，BbAnd BcAnd satisfy
(4) Generation of digital signature: after the generation of the key string is completed, the sending end is used as the sender of the information, and the sending end receives the key string B of the sending end from the sending endaRandomly selecting a first group of n-bit keys and acquiring n-bit random numbers from a random number generator of a sending end, wherein the n-bit random numbers are used for generating an irreducible polynomial, the irreducible polynomial and the first group of n-bit keys serving as input random numbers generate a hash function based on a linear feedback shift register, then inputting a message needing to be signed into the hash function to obtain a first hash value, and the first hash value and a character string consisting of coefficients of each item except the highest item in the irreducible polynomial form a first abstract; sending end slave key string BaTaking a second group of 2 n-bit keys from the rest keys to carry out exclusive-or encryption operation on the first abstract so as to generate a final digital signature;
the hash function based on the linear feedback shift register is a Toeplitz matrix with dimension n multiplied by m, wherein n is a slave key string B of a sending endaIs selected to be the firstThe length of the group key, m is the length of the message needing to be signed;
the specific process of using the n-bit random number to generate the irreducible polynomial is as follows:
firstly, sequentially using each bit of n-bit random numbers to correspond to the coefficient of each term except the highest term in the polynomial to generate an n-order polynomial in a GF (2) domain, wherein the coefficient of the highest term is 1; for example, the random number is (a)n-1,an-2,…,a1,a0) Then the polynomial generated is p1(x)＝xn+an-1xn-1+…+a1x+a0(ii) a Preferably, only when a0Since the generated polynomial may be an irreducible polynomial when the irreducible polynomial is 1, the n-bit random number may be determined first in order to reduce the calculation amount in the later verification of the irreducible polynomial: if the last bit of the n-bit random number is 0, the last bit of the random number is 1, and an n-order irreducible polynomial in a GF (2) field is generated; or if the last bit of the n-bit random number is 0, regenerating the n-bit random number until the last bit of the generated n-bit random number is 1, and regenerating an n-order irreducible polynomial in a GF (2) domain; this reduces the amount of computation required to verify the irreducible polynomial at a later stage, and finally makes a0The polynomial generated is p ═ 11(x)＝xn+an-1xn-1+…+a1x+1；
Then, verifying whether the polynomial is an irreducible polynomial by utilizing an FMC (Fast modular composition), if the verification result is 'no', directly generating another group of n-bit random numbers from a random number generator at a transmitting end, returning to the step 1) as new n-bit random numbers to regenerate the polynomial and verifying; if the verification result is 'yes', the verification is stopped, and the irreducible polynomial is obtained.
The sending end then uses the irreducible polynomial and a first group of n-bit keys as input random numbers to generate a hash function based on a linear feedback shift register, namely, an n × m Toeplitz matrix based on the linear feedback shift register is used as the hash function for the embodiment, wherein m is the length of the message needing to be signed; performing matrix multiplication on the generated hash function and a column vector corresponding to the message to obtain a first hash value corresponding to the message, wherein the first hash value is a column vector with the length of n, and a character string consisting of the first hash value and each coefficient except the highest term in the irreducible polynomial forms a first abstract; the sending end takes a second group of keys with the length of 2n bits from the rest key strings to carry out XOR encryption operation on the first abstract, and a final digital signature with the length of 2n is generated;
for example, the sender selects a key and a random number to generate a toeplitz matrix based on a linear feedback shift register (hereinafter, LFSR) as a hash function; the Toeplitz matrix based on the LFSR is an n multiplied by m matrix, wherein m is the length of a message vector corresponding to a signature, and is a variable value, and n is a fixed value and represents the length of a hash value vector generated after the matrix acts on the message; that is, the LFSR-based toeplitz matrix can convert a vector of arbitrary length m, which is a message to be signed, into a vector of fixed length n, i.e. a first hash value, and such operation has no requirement on the length of the received message, i.e. each round of signature can sign a message of arbitrary length, and the signature efficiency is higher than that of the existing quantum digital signature technology;
(5) and (3) verification of the digital signature: the sending end sends the message to be signed and the digital signature to the receiving end, and the receiving end receives the digital signature and the message to be signed and then sends the digital signature, the message to be signed and the key string B of the receiving endbSending to a verification end, wherein the verification end receives the digital signature, the message needing to be signed and a key string BbThen the key string BcSending to the receiving end 2;
at this time, the receiving end and the verifying end both contain the key string BbAnd BcTwo key strings BbAnd BcPerforming XOR operation to obtain the key string B identical to the sending endaThe receiving end and the verifying end are respectively at the key string BaThe method comprises the steps of selecting a key which is the same as that used when a sending end encrypts a first digest to decrypt a digital signature to obtain a second digest, wherein the second digest is composed of a second hash value and each item except the highest item in an irreducible polynomialA character string composed of coefficients; each bit of the character string in the second abstract corresponds to the coefficient of each item except the highest item in the irreducible polynomial, an irreducible polynomial with the highest item coefficient being 1 is generated, the generated irreducible polynomial and a first group of n-bit keys which are selected from the key string and are the same as those generated by the sending end based on the hash function of the linear feedback shift register are used for generating the hash function, and then the received message needing to be signed is input into the generated hash function to generate a third hash value; comparing the obtained third hash value with a second hash value in the second abstract by the receiving end and the verifying end, and receiving the signature if the second hash value is the same as the third hash value; otherwise, the signature is not accepted.
To further illustrate the behavior of the system provided by the present invention, we show the variation of the signature efficiency (number of messages of any length that can be signed per optical pulse) bound of the network with relaying quanta as a function of the channel length, as shown in fig. 6. It can be seen that at a distance of 300km, the signature efficiency remains at 10-6In order of magnitude, such efficiency has very high utility.
Claims (12)
1. A quantum digital signature method based on rare earth quantum storage is characterized by comprising the following steps:
(1) shared GHZ entangled state: a pair of photons in the maximum entangled state is shared between the sending end and the receiving end, and a pair of photons in the maximum entangled state is shared between the receiving end and the verification end; the method comprises the steps that a receiving end firstly carries out controlled NOT gate operation on two photons in a hand of the receiving end, after the controlled NOT gate operation is completed, the receiving end measures photons entangled with an authentication end in the hand of the receiving end under a first basis vector, and judges whether the authentication end needs to carry out bit reversal or not according to a measurement display result, so that a sending end, the receiving end and the authentication end share a GHZ entangled state;
(2) the classical bit is obtained: after sharing of the GHZ entangled state is completed, the transmitting end, the receiving end and the verifying end respectively measure photons in hands under a second basis vector, the measured "+" corresponds to the classical bit being 0, the measured "-" corresponds to the classical bit being 1, and the obtained classical bit result is used as the classical bit resultAnd as the sending end, the receiving end and the verifying end share the GHZ entangled state, the sending end, the receiving end and the verifying end respectively measure the obtained classical bit ba，bbAnd bcSatisfy
(3) Obtaining a key string: repeating the steps (1) and (2) for multiple times, so that the sending end, the receiving end and the verifying end obtain the key string Ba，BbAnd BcAnd satisfy
(4) Generation of digital signature: after completing the generation of the key string, the transmitting end follows its own key string BaRandomly selecting a first group of n-bit keys and acquiring n-bit random numbers from a random number generator of a sending end, wherein the n-bit random numbers are used for generating an irreducible polynomial, the irreducible polynomial and the first group of n-bit keys serving as input random numbers generate a hash function based on a linear feedback shift register, then inputting a message needing to be signed into the hash function to obtain a first hash value, and the first hash value and a character string consisting of coefficients of each item except the highest item in the irreducible polynomial form a first abstract; sending end slave key string BaTaking a second group of 2 n-bit keys from the rest keys to carry out exclusive-or encryption operation on the first abstract so as to generate a final digital signature;
(5) and (3) verification of the digital signature: the sending end sends the message to be signed and the digital signature to the receiving end, and the receiving end receives the digital signature and the message to be signed and then sends the digital signature, the message to be signed and the key string B of the receiving endbSending to a verification end, wherein the verification end receives the digital signature, the message needing to be signed and a key string BbThen the key string BcSending the data to a receiving end;
at this time, the receiving end and the verifying end both contain the key string BbAnd BcTwo key strings BbAnd BcPerform an XOR operation, i.e.The same key string B as the sending end can be obtainedaThe receiving end and the verifying end are respectively at the key string BaThe key which is the same as the key used by the sending end to encrypt the first abstract is selected to decrypt the digital signature to obtain a second abstract; each bit of the character string in the second abstract corresponds to the coefficient of each item except the highest item in the irreducible polynomial, an irreducible polynomial with the highest item coefficient being 1 is generated, the generated irreducible polynomial and a first group of n-bit keys which are selected from the key string and are the same as those generated by the sending end based on the hash function of the linear feedback shift register are used for generating the hash function, and then the received message needing to be signed is input into the generated hash function to generate a third hash value; comparing the obtained third hash value with a second hash value in the second abstract by the receiving end and the verifying end, and receiving the signature if the second hash value is the same as the third hash value; otherwise, the signature is not accepted.
2. A quantum digital signature method based on rare earth quantum storage as claimed in claim 1 wherein: in the step (1), whether the verification end needs to perform bit flipping is judged according to the measurement display result, and the specific process is as follows: if the measurement display result is horizontal polarization, the sending end, the receiving end and the verification end share the GHZ entangled state at this moment; if the measurement result shows vertical polarization, the sending end, the receiving end and the verifying end share the GHZ entangled state after the verifying end needs to perform bit flipping.
3. A quantum digital signature method based on rare earth quantum storage as claimed in claim 1 wherein: in the step (1), the operator expression of the controlled NOT gate operation is
Wherein B and B' represent two photons of the receiving end respectively entangled with the transmitting end and the verifying end, id represents unit mapping,
represents a bit flipping operation, H represents horizontal polarization, and V represents vertical polarization;
in the step (1), the first basis vector is { | V>B′,|H>B′}; in step (2), the second basis vector is
4. A quantum digital signature method based on rare earth quantum storage as claimed in claim 1 wherein: the specific process of the n-bit random number for generating the irreducible polynomial is as follows:
1) firstly, sequentially using each bit of n-bit random numbers to correspond to the coefficient of each term except the highest term in the polynomial to generate an n-order polynomial in a GF (2) domain, wherein the coefficient of the highest term is 1;
2) then, verifying whether the polynomial is irreducible polynomial by using FMC algorithm, if the verification result is 'no', directly generating another group of n-bit random numbers from a random number generator at the sending end, and returning to the step 1) for regenerating the polynomial as a new n-bit random number and verifying; if the verification result is 'yes', the verification is stopped, and the irreducible polynomial is obtained.
5. The quantum digital signature method based on rare earth quantum storage of claim 4, wherein: before step 1), if the last bit of the n-bit random number is 0, the last bit of the random number is 1, and an n-order irreducible polynomial in a GF (2) field is generated; or if the last bit of the n-bit random number is 0, regenerating the n-bit random number until the last bit of the generated n-bit random number is 1, and regenerating an n-order irreducible polynomial in a GF (2) field.
6. A quantum digital signature method based on rare earth quantum storage as claimed in claim 1 wherein: in the step (4), the signal is sent based on linear feedback shiftThe hash function of the memory is a Toeplitz matrix with dimension n multiplied by m, wherein n is a key string B of the sending end slaveaThe length of the first group key is selected, and m is the length of the message to be signed.
7. A digital signature system of a quantum digital signature method based on rare earth quantum storage according to any one of claims 1 to 6, characterized in that: the system comprises a sending end, a receiving end and a verification end, wherein the sending end, the receiving end and the verification end respectively comprise a photon generation unit, the photon generation unit of the sending end and the photon generation unit of the receiving end are connected with a first measuring end through a quantum channel, and the photon generation unit of the verification end and the photon generation unit of the receiving end are connected with a second measuring end through the quantum channel;
the photon generation unit comprises a rare earth doped quantum storage module and an entangled photon pair source module which are connected with each other, the rare earth doped quantum storage module is used for storing photons generated by the entangled photon pair source module, the entangled photon pair source module is used for generating entangled photon pairs, one photon in each photon pair enters the measurement end through a 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 used for achieving a photon entanglement forecasting function, and therefore the maximum entangled state is established between the two photon generating units connected with the measuring ends.
8. A quantum digital signature system based on rare earth quantum storage as claimed in claim 7 wherein: the entangled photon pair source module comprises a pumping sub-module, a spontaneous parameter down-conversion sub-module, a filtering sub-module and an entangled generation sub-module which are mutually connected;
the pumping sub-module is used for generating pumping laser entering the spontaneous parameter down-conversion sub-module;
the spontaneous parameter down-conversion sub-module is used for generating two photons with different polarizations;
the filtering submodule is used for filtering photons generated by the spontaneous parameter down-conversion submodule;
the entanglement generation submodule is used for enabling the photon pairs to be in a Bell state by means of interference and selection after combination.
9. A quantum digital signature system based on rare earth quantum storage as claimed in claim 8 wherein: the entanglement generation submodule comprises a first polarization beam splitting element, two output ends of the first polarization beam splitting element are respectively connected with an input end of a first polarization rotation element and an input end of a second polarization rotation element, an output end of the first polarization rotation element and an output end of the second polarization rotation element are respectively connected with two input ends of the second polarization beam splitting element, and two output ends of the second polarization beam splitting element are respectively connected with an input end of a first phase compensation element and an input end of a second phase compensation element; the output end of the first phase compensation element is connected with the measuring end, and the output end of the second phase compensation element is connected with the rare earth doped quantum storage module;
the first polarization beam splitting element and the second polarization beam splitting element are used for splitting the photon pair;
the first polarization rotating element and the second polarization rotating element are used for rotating the polarization of the photons;
the first phase compensation element and the second phase compensation element are used for compensating phase drift.
10. A quantum digital signature system based on rare earth quantum storage as claimed in claim 7 wherein: the first measuring end and the second measuring end respectively comprise a third polarization rotating element and a fourth polarization rotating element, the output end of the third polarization rotating element and the output end of the fourth polarization rotating element are respectively connected with the two input ends of a third polarization beam splitting element, the two output ends of the third polarization beam splitting element are respectively connected with the input end of a fifth polarization rotating element and the input end of a sixth polarization rotating element, the output end of the fifth polarization rotating element is connected with the input end of the fourth polarization beam splitting element, and the two output ends of the fourth polarization beam splitting single photon element are respectively connected with the first input end and the second input end of a fourth polarization beam splitting single photon detecting element; the output end of the sixth polarization rotating element is connected with the input end of a fifth polarization beam splitting element, and the two output ends of the fifth polarization beam splitting element are respectively connected with the third input end and the fourth input end of the single photon detection element.
11. A quantum digital signature system based on rare earth quantum storage as claimed in claim 7 wherein: the working process of establishing the maximum entanglement state between the two photon generating units is as follows:
entangled photons of photon generation units in a sending end and a receiving end generate pump laser for a pump submodule in a source module, the pump laser generates two photons of horizontal polarization and vertical polarization through a spontaneous parameter down-conversion submodule, the two photons enter a first polarization beam splitting element of an entanglement generation submodule after being filtered by a filtering submodule, the first polarization beam splitting element splits the two photons so that the two photons of the horizontal polarization and the vertical polarization are divided into two paths, the photons on the two paths rotate polarization through a polarization rotating element, the photons after polarization rotation reach a second polarization beam splitting element to generate two-photon interference, and the two photons are in the maximum entangled state through a post-selection method
The two photons are split again and respectively pass through a phase compensation element to compensate phase shift generated in the transmission process, after compensation is completed, one photon enters a rare earth doped quantum storage module, and the other photon is sent to a first measuring end through a quantum channel;
after the processes, photons in the maximum entangled state are stored in the rare earth doped quantum storage modules of the sending end and the receiving end, the other two photons reach the first measuring end, and the quantum state of a combined system formed by the sending end and the receiving end is the quantum state
The first measuring end regulates and controls the time delay of photon propagation, so that photons generated by photon generating units in the transmitting end and the receiving end can synchronously reach the first measuring end, and two photons generate two-photon interference at the first measuring 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 simultaneously, two photons arriving at the first measurement end at the same time are predicted to be in the maximum entanglement state | phi |+>It is indicated that the quantum states of the photons stored in the rare earth doped quantum storage modules of the transmitting end and the receiving end are also in the maximum entangled state | phi+>Thus, the maximum entanglement state is established between the sending end and the receiving end; similarly, the maximum entanglement state is also established between the verification end and the receiving end.
12. A quantum digital signature system based on rare earth quantum storage as claimed in claim 7 wherein: the transmitting end, the receiving end and the verifying end also comprise classical processing units, and the classical processing units of the transmitting end and the receiving end, the classical processing units of the transmitting end and the verifying end and the classical processing units of the receiving end and the verifying end are connected through classical channels; the classical processing units are computers and are used for processing the measurement result to obtain a final key; the classical processing unit of the sending end is also used for generating the digital signature, and the classical processing unit of the receiving end and the classical processing unit of the verifying end are also used for finishing the verification process of the digital signature.
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