Quantum key system and quantum key method

Abstract

A quantum key system and a quantum key method are provided. The quantum key method includes the following steps: an initiating quantum key distribution module and a receiving quantum key distribution module use qubits and quantum logic gates to obtain negotiated information, wherein the quantum logic gates correspond to quantum superposition or quantum entanglement.

Claims

1. A quantum key system, comprising: The first terminal device includes the initiating quantum key distribution module; The system also includes a second terminal device, comprising a receiving quantum key distribution module, which is communicatively connected to the first terminal device. The initiating quantum key distribution module and the receiving quantum key distribution module each include qubits. The initiating and receiving quantum key distribution modules utilize the qubits and quantum logic gates to obtain negotiated messages. The quantum logic gates correspond to either a quantum uniform superposition state or a quantum entangled state. The initiating quantum key distribution module generates original messages and an initiating control signal. Based on the original messages, the initiating quantum key distribution module determines whether to operate a NOT gate on the qubit of its own qubit. Based on the initiating control signal, the initiating quantum key distribution module determines whether to operate one or more quantum logic gates on the qubit of its own qubit to generate the quantum uniform superposition state. The system then transmits the qubit of its own qubit to the receiving quantum key distribution module via quantum communication. The receiving-end quantum key distribution module generates a receiving-end control signal. It receives the qubit via quantum communication and, based on the receiving-end control signal, decides whether to operate one or more quantum logic gates on the qubit to generate the quantum uniform superposition state. It also measures the qubit to obtain a classical bit value as measurement information. The receiving-end quantum key distribution module transmits the receiving-end control signal to the initiating-end quantum key distribution module via classical communication. The initiating-end quantum key distribution module compares the initiating-end control signal and the receiving-end control signal to obtain a control signal comparison result, and transmits the control signal comparison result to the receiving-end quantum key distribution module via classical communication. The initiating-end quantum key distribution module decides whether to adopt the original message based on the control signal comparison result. The receiving-end quantum key distribution module decides whether to adopt the measurement message based on the control signal comparison result.

2. The quantum key system as described in claim 1, wherein the number of qubits is 1, and wherein the initiating quantum key distribution module and the receiving quantum key distribution module repeatedly execute 2N times to obtain the negotiated message.

3. The quantum key system as claimed in claim 1, wherein the number of qubits is 2N.

4. The quantum key system as claimed in claim 1, wherein the quantum logic gate includes a Hadamard gate, wherein the initiating quantum key distribution module determines, according to the initiating control signal, whether to operate the Hadamard gate on the qubit of the initiating quantum key distribution module to generate the quantum uniform superposition state; and the receiving quantum key distribution module determines, according to the receiving control signal, whether to operate the Hadamard gate on the qubit of the receiving quantum key distribution module to generate the quantum uniform superposition state.

5. The quantum key system as claimed in claim 1, wherein the quantum logic gate includes an SX gate, wherein the initiating quantum key distribution module determines, according to the initiating control signal, whether to operate the SX gate on the qubit of the initiating quantum key distribution module to generate the quantum uniform superposition state; and the receiving quantum key distribution module determines, according to the receiving control signal, whether to operate the SX gate on the qubit of the receiving quantum key distribution module to generate the quantum uniform superposition state.

6. The quantum key system as claimed in claim 1, wherein the quantum logic gate includes an RX gate, wherein the initiating quantum key distribution module determines, based on the initiating control signal, whether to operate the RX gate on the qubit of the initiating quantum key distribution module to generate the quantum uniform superposition state; and the receiving quantum key distribution module determines, based on the receiving control signal, whether to operate the RX gate on the qubit of the receiving quantum key distribution module to generate the quantum uniform superposition state; wherein... The rotation radius of the RX gate is 0.5π or its equivalent radius.

7. The quantum key system as claimed in claim 1, wherein the quantum logic gate includes an RY gate, wherein the initiating quantum key distribution module determines, based on the initiating control signal, whether to operate the RY gate on the qubit of the initiating quantum key distribution module to generate the quantum uniform superposition state; and the receiving quantum key distribution module determines, based on the receiving control signal, whether to operate the RY gate on the qubit of the receiving quantum key distribution module to generate the quantum uniform superposition state; wherein... The rotation radius of the RY gate is 0.5π or its equivalent radius.

8. The quantum key distribution system as claimed in claim 1, wherein the quantum logic gate includes a Phase gate and a Hadamard gate, wherein the initiating quantum key distribution module determines, based on the initiating control signal, whether to operate the Phase gate and the Hadamard gate on the qubit of the initiating quantum key distribution module to generate the quantum uniform superposition state; the receiving quantum key distribution module determines, based on the receiving control signal, whether to operate the Phase gate and the Hadamard gate on the qubit of the receiving quantum key distribution module to generate the quantum uniform superposition state; wherein... The rotation radius of the Phase gate is 0.5π or its equivalent radius.

9. The quantum key distribution system as claimed in claim 1, wherein the quantum logic gate includes a first RZ gate, an RY gate, and a second RZ gate, wherein the initiating quantum key distribution module determines, based on the initiating control signal, whether to operate the first RZ gate, the RY gate, and the second RZ gate on the qubit of the initiating quantum key distribution module to generate the quantum uniform superposition state; the receiving quantum key distribution module determines, based on the receiving control signal, whether to operate the first RZ gate, the RY gate, and the second RZ gate on the qubit of the receiving quantum key distribution module to generate the quantum uniform superposition state; wherein... The rotation radius of each of the first RZ gate, the RY gate, and the second RZ gate is 0.5π or its equivalent radius.

10. The quantum key system as claimed in claim 1, wherein the initiating quantum key distribution module and the receiving quantum key distribution module perform a hash algorithm on the negotiated message to obtain N bit values.

11. A quantum key system, comprising: The first terminal device includes the initiating quantum key distribution module; The system also includes a second terminal device, comprising a receiving quantum key distribution module, which is communicatively connected to the first terminal device. The initiating quantum key distribution module and the receiving quantum key distribution module each include qubits. The initiating and receiving quantum key distribution modules utilize the qubits and quantum logic gates to obtain negotiated information. The quantum logic gates correspond to either a quantum uniform superposition state or a quantum entangled state. A quantum entangled state exists between the qubits of the initiating and receiving quantum key distribution modules. The number of qubits is 1. During the quantum entanglement state establishment phase, the qubits of the initiating quantum key distribution module operate the quantum logic gate to generate the quantum uniform superposition state and operate the CNOT gate. The qubits of the initiating quantum key distribution module are the control bits of the CNOT gate, and the qubits of the receiving quantum key distribution module are the target bits of the CNOT gate. During the message transmission phase, the initiating quantum key distribution module generates an initiating control signal. Based on the initiating control signal, the initiating quantum key distribution module decides whether to operate one or more quantum logic gates on the qubit of the initiating quantum key distribution module. Similarly, the receiving quantum key distribution module generates a receiving control signal. Based on the receiving control signal, the initiating quantum key distribution module decides whether to operate one or more quantum logic gates on the qubit of the initiating quantum key distribution module. During the message measurement phase, the initiating quantum key distribution module measures the qubit of its own qubit to obtain a measurement message. The receiving quantum key distribution module measures the qubit of its own qubit to obtain the measurement message. The receiving quantum key distribution module then transmits the receiving control signal to the initiating quantum key distribution module via classical communication. The initiating quantum key distribution module compares the initiating control signal and the receiving control signal to obtain a control signal comparison result, and transmits the control signal comparison result to the receiving quantum key distribution module via classical communication. During the message production stage, the initiating quantum key distribution module decides whether to adopt the measurement message based on the control signal comparison result, and the receiving quantum key distribution module also decides whether to adopt the measurement message based on the control signal comparison result. The initiating control signal and the receiving control signal contain one of T types of signals. The initiating quantum key distribution module and the receiving quantum key distribution module repeatedly execute this process TN times to obtain the negotiated message.

12. The quantum key system as claimed in claim 11, wherein the initiator control signal and the receiver control signal comprise one of the following three signals: not operating the quantum logic gate, operating the Hadamard gate, and operating the S gate and operating the Hadamard gate.

13. The quantum key system as claimed in claim 11, wherein during the quantum entanglement state establishment phase, the qubit operation of the Hadamard gate of the initiating quantum key distribution module generates the quantum uniform superposition state.

14. The quantum key system as claimed in claim 11, wherein during the quantum entanglement state establishment phase, the qubit of the initiating quantum key distribution module operates the RY gate, sets the rotation radian of the RY gate to 0.5π or its equivalent radian, and generates the quantum uniform superposition state.

15. The quantum key system as claimed in claim 11, wherein during the quantum entanglement state establishment phase, the qubit of the initiating quantum key distribution module operates the RX gate, sets the rotation radian of the RX gate to 0.5π or its equivalent radian, generates the quantum uniform superposition state, and operates the S gate.

16. The quantum key system as claimed in claim 11, wherein during the quantum entanglement state establishment phase, the qubit of the initiating quantum key distribution module operates the SX gate to generate the quantum uniform superposition state, and operates the S gate.

17. The quantum key system as claimed in claim 11, wherein during the quantum entanglement state establishment phase, the qubit of the initiating quantum key distribution module operates a first RZ gate, an RY gate, and a second RZ gate, sets the rotation radian of each of the first RZ gate, the RY gate, and the second RZ gate to 0.5π or its equivalent radian, generates the quantum uniform superposition state, and operates an S gate.

18. A quantum key system, comprising: The first terminal device includes the initiating quantum key distribution module; The system also includes a second terminal device, comprising a receiving quantum key distribution module, wherein the second terminal device is communicatively connected to the first terminal device. The initiating quantum key distribution module and the receiving quantum key distribution module each include qubits. The initiating quantum key distribution module and the receiving quantum key distribution module utilize the qubits and quantum logic gates to obtain negotiated messages. The quantum logic gates correspond to a quantum uniform superposition state or a quantum entangled state. The first terminal device further includes a post-quantum cryptographic digital signature module, and the second terminal device further includes a post-quantum cryptographic digital signature module. The second terminal device uses the post-quantum cryptographic digital signature module to execute a post-quantum cryptographic digital signature algorithm, inputting the private key of the second terminal device and the message M, to generate an L-bit signature value (Signature), and to generate a K-bit random number R1 as the pseudo-random number seed R1 for the first signature reconstruction value. Only the pseudo-random number seed R1 for the first signature reconstruction value is publicly disclosed. The initiating quantum key distribution module of the first terminal device and the receiving quantum key distribution module of the second terminal device use the negotiated message to execute a hash algorithm to obtain a K-bit random number R2 as the pseudo-random number seed R2 for the second signature reconstruction value. The second terminal device and the first terminal device each substitute the pseudo-random number seed R1 for the first signature reconstruction value into a pseudo-random number function to obtain an L-bit first signature reconstruction value R1', and substitute the pseudo-random number seed R2 for the second signature reconstruction value into the pseudo-random number function to obtain an L-bit second signature reconstruction value R2'. The second terminal device calculates a third signature reconstruction value R3' = Signature ⨁ R1' ⨁ R2', and transmits the third signature reconstruction value R3' to the first terminal device. The first terminal device calculates Signature = R1' ⨁ R2' ⨁ R3' obtains the L-bit signature value. The first terminal device uses the post-quantum cryptography digital signature module to execute the post-quantum cryptography digital signature algorithm, and substitutes the public key of the second terminal device, the message M, and the L-bit signature value to verify the signature value.

19. The quantum key system as claimed in claim 18, wherein the post-quantum cryptographic digital signature algorithm is an ML-DSA signature algorithm, and wherein the post-quantum cryptographic digital verification algorithm is an ML-DSA verification algorithm.

20. The quantum key system as claimed in claim 18, wherein the post-quantum cryptographic digital signature algorithm is the SLH-DSA signature algorithm, and wherein the post-quantum cryptographic digital verification algorithm is the SLH-DSA verification algorithm.

21. The quantum key system as claimed in claim 18, wherein the post-quantum cryptographic digital signature algorithm is the Falcon signature algorithm or a derivative thereof, and wherein the post-quantum cryptographic digital verification algorithm is the Falcon verification algorithm or a derivative thereof.

22. The quantum key system as claimed in claim 18, wherein the initiating quantum key distribution module and the receiving quantum key distribution module correspond to BB84 quantum key distribution.

23. The quantum key system as claimed in claim 18, wherein the initiating quantum key distribution module and the receiving quantum key distribution module correspond to E91 quantum key distribution.

24. The quantum key system as described in claim 18, wherein the pseudo-random number function is the SHAKE algorithm, and the output length of the pseudo-random number function is L bits.

25. A quantum key system, comprising: The first terminal device includes the initiating quantum key distribution module; The first terminal device includes a receiving quantum key distribution module, which is communicatively connected to the first terminal device. The initiating and receiving quantum key distribution modules each include qubits. These modules utilize the qubits and quantum logic gates to obtain negotiated messages. The quantum logic gates correspond to a quantum uniform superposition state or a quantum entangled state. The first terminal device further includes a post-quantum cryptography key encapsulation mechanism encryption module, and the second terminal device further includes a post-quantum cryptography key encapsulation mechanism decryption module. The first terminal device uses its post-quantum cryptography key encapsulation mechanism encryption module to execute a post-quantum cryptography key encapsulation mechanism encryption algorithm, inputting the second terminal device's public key and a first random number R1 to generate a ciphertext value (Ciphertext), and then transmits the ciphertext value (Ciphertext) to the second terminal device. The initiating quantum key distribution module of the first terminal device and the receiving quantum key distribution module of the second terminal device substitute the negotiated message into a hash algorithm to obtain a second random number R2; the second terminal device uses its post-quantum cryptographic key encapsulation mechanism decryption module to execute a post-quantum cryptographic key encapsulation mechanism decryption algorithm, substituting the private key of the second terminal device and the ciphertext value Ciphertext to obtain the first random number R1; the first terminal device and the second terminal device respectively substitute the first random number R1 and the second random number R2 into a pseudo-random number function to obtain an L-bit negotiated key value.

26. The quantum key system as claimed in claim 25, wherein the post-quantum cryptographic key encapsulation mechanism encryption algorithm is the ML-KEM encryption algorithm, and wherein the post-quantum cryptographic key encapsulation mechanism decryption algorithm is the ML-KEM decryption algorithm.

27. The quantum key system as claimed in claim 25, wherein the post-quantum cryptographic key encapsulation mechanism encryption algorithm is the HQC encryption algorithm or a derivative thereof, and wherein the post-quantum cryptographic key encapsulation mechanism decryption algorithm is the HQC decryption algorithm or a derivative thereof.

28. The quantum key system as claimed in claim 25, wherein the pseudo-random number function is an HMAC algorithm and the output length of the pseudo-random number function is L bits.

29. The quantum key system as claimed in claim 25, wherein the pseudo-random number function is a CMAC algorithm and the output length of the pseudo-random number function is L bits.

30. The quantum key system as claimed in claim 25, wherein the pseudo-random number function is the KMAC algorithm, and the output length of the pseudo-random number function is L bits.

31. A quantum key system, comprising: The first terminal device includes the initiating quantum key distribution module; The first terminal device includes a receiving quantum key distribution module, which is communicatively connected to the first terminal device. The initiating and receiving quantum key distribution modules each include qubits. The initiating and receiving quantum key distribution modules utilize the qubits and quantum logic gates to obtain negotiated information. The quantum logic gates correspond to a quantum uniform superposition state or a quantum entangled state. The first terminal device further includes a quantum random number generator, and the second terminal device further includes the quantum random number generator.

32. The quantum key system as claimed in claim 31, wherein the quantum random number generator includes at least the qubit and the classical bit, wherein the quantum random number generator operates on the qubit by one or more of the quantum logic gates to generate the quantum uniform superposition state, and measures the qubit; the quantum random number generator stores the measurement result of the qubit in the classical bit, and outputs the value of the classical bit.

33. The quantum key system as claimed in claim 32, wherein the quantum logic gate includes at least a Hadamard gate, and the qubit operates the Hadamard gate to produce the quantum uniform superposition state.

34. The quantum key system as claimed in claim 32, wherein the quantum logic gate includes at least an SX gate, and the qubit operates the SX gate to generate the quantum uniform superposition state.

35. The quantum key system of claim 32, wherein the quantum logic gate includes at least an RX gate, the qubit operates the RX gate, and the rotation radian of the RX gate is set to 0.5π or its equivalent radian to generate the quantum uniform superposition state.

36. The quantum key system of claim 32, wherein the quantum logic gate includes at least an RY gate, the qubit operates the RY gate, and the rotation radian of the RY gate is set to 0.5π or its equivalent radian to generate the quantum uniform superposition state.

37. The quantum key system of claim 32, wherein the quantum logic gate includes at least a Phase gate and a Hadamard gate, the qubit operates the Phase gate and the Hadamard gate, and the rotation angle of the Phase gate is set to an arbitrary angle to generate the quantum uniform superposition state.

38. The quantum key system as claimed in claim 32, wherein the quantum logic gate includes at least a first RZ gate, an RY gate, and a second RZ gate, the qubit sequentially operates the first RZ gate, the RY gate, and the second RZ gate, and sets the rotation radian of each of the first RZ gate, the RY gate, and the second RZ gate to 0.5π or its equivalent radian to generate the quantum uniform superposition state.

39. The quantum key system as claimed in claim 32, wherein the number of qubits is 1, the number of classical bits is 1, and the quantum random number generator is repeatedly executed N times to obtain the values ​​of the N classical bits.

40. The quantum key system as claimed in claim 32, wherein the number of qubits is N, the number of classical bits is N, and the quantum random number generator stores the measurement result of the qubit into the corresponding classical bit to obtain the value of N classical bits.

41. The quantum key system as claimed in claim 31, wherein the quantum random number generator comprises at least 2N qubits and N classical bits, wherein the quantum random number generator establishes the quantum entangled state of the i-th qubit and the (N+i)-th qubit, wherein the i values ​​are the result of traversing from 0 to N–1; the quantum random number generator operates a Hadamard gate on the i-th qubit and a CNOT gate on the i-th qubit and the (N+i)-th qubit, setting the i-th qubit as the control bit and the (N+i)-th qubit as the target bit, wherein the i values ​​are the result of traversing from 0 to N–1; the quantum random number generator measures the (N+i)-th qubit and stores the measurement result in the i-th classical bit, wherein the i values ​​are the result of traversing from 0 to N–1; the quantum random number generator outputs the values ​​of the N classical bits.

42. The quantum key system as claimed in claim 31, wherein the quantum random number generator comprises at least two qubits and one classical bit, wherein the quantum random number generator establishes the quantum entangled state of the 0th qubit and the 1st qubit; the quantum random number generator operates a Hadamard gate on the 0th qubit and a CNOT gate on the 0th qubit and the 1st qubit, setting the 0th qubit as the control bit and the 1st qubit as the target bit; the quantum random number generator measures the 1st qubit and stores the measurement result in the classical bit; the quantum random number generator outputs the value of the classical bit; the quantum random number generator cycles N times, outputting the values ​​of the N classical bits.

43. The quantum key system as claimed in claim 31, wherein the quantum random number generator comprises at least a first circuit and a second circuit, wherein the first circuit comprises at least N qubits and N classical bits, wherein the second circuit comprises at least N qubits and N classical bits, wherein the quantum random number generator operates on a quantum logic gate, which is an RX gate or an RY gate, for each qubit of the first circuit, the quantum random number generator sets the rotation radian of the quantum logic gate to a value or its equivalent radian, generates the quantum uniform superposition state, and measures each qubit of the first circuit, stores the measurement result of each qubit of the first circuit in the corresponding classical bit of the first circuit, and outputs the value of each classical bit of the first circuit, wherein the value of the i-th classical bit of the first circuit is represented by c1,i; The quantum random number generator operates on a quantum logic gate, which is either an RX gate or an RY gate, for each qubit of the second circuit. The quantum random number generator sets the rotation radian of the quantum logic gate to a value or its equivalent radian to generate the quantum uniform superposition state. It also measures each qubit of the second circuit and stores the measurement result of each qubit of the second circuit into the corresponding classical bit of the second circuit. The quantum random number generator outputs the value of each classical bit of the second circuit, and the value of the i-th classical bit of the second circuit is represented by c2,i. The quantum random number generator compares the value of the i-th classical bit c1,i of the first circuit with the value of the i-th classical bit c2,i of the second circuit; if both c1,i and c2,i are 0, the quantum random number generator sets the i-th output bit ci to 1; if either c1,i or c2,i is not 0, the quantum random number generator sets the i-th output bit ci to c1,i; the quantum random number generator outputs these output bits ci, where the values ​​of i range from 0 to N–1.

44. The quantum key system as claimed in claim 31, wherein the quantum random number generator includes at least a first circuit and a second circuit, wherein the first circuit includes at least one qubit and one classical bit, wherein the second circuit includes at least one qubit and one classical bit, wherein the quantum random number generator operates on a quantum logic gate, which is an RX gate or an RY gate, for each qubit of the first circuit, the quantum random number generator sets the rotation radian of the quantum logic gate to a value or its equivalent radian to generate the quantum uniform superposition state, and measures the qubit of the first circuit, stores the measurement result of the qubit of the first circuit in the corresponding classical bit of the first circuit, and outputs the value of the classical bit of the first circuit, wherein the value of the classical bit of the first circuit is represented by c1; The quantum random number generator operates a quantum logic gate (either an RX gate or an RY gate) on each qubit of the second circuit. The generator sets the rotation radian of the gate to a value or its equivalent radian to generate a quantum uniform superposition state. The generator also measures the qubit of the second circuit and stores the measurement result in the corresponding classical bit of the second circuit. The generator outputs the value of the classical bit of the second circuit, denoted as c2. The generator compares the value c1 of the classical bit of the first circuit with the value c2 of the classical bit of the second circuit. If both c1 and c2 are 0, the generator sets the output bit c to 1. If either c1 or c2 is not 0, the generator sets the output bit c to c1. The output bit c is then output. This process is repeated N times, outputting a total of N output bit values.

45. The quantum key system as claimed in claim 31, wherein the first terminal device further includes a post-quantum cryptography key pair generation module, wherein the second terminal device further includes the post-quantum cryptography key pair generation module, wherein the quantum random number generator generates one or a plurality of random numbers according to the length and number of random number parameters required by the post-quantum cryptography key pair generation module to generate the key pair; the post-quantum cryptography key pair generation module substitutes the random numbers to generate the key pair, wherein the key pair includes a post-quantum cryptography public key and a post-quantum cryptography private key.

46. ​​The quantum key system as described in claim 45, wherein the post-quantum cryptographic key pair generation module is a Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) module, wherein the post-quantum cryptographic key pair generation module executes the quantum random number generator to generate two different random numbers, each with a length of 256-bit, takes one of the random numbers as the random number parameter d, takes the other random number as the random number parameter z, substitutes them into ML-KEM.KeyGen_internal(d, z), and generates the ML-KEM public key and the ML-KEM private key.

47. The quantum key system as described in claim 45, wherein the post-quantum cryptographic key pair generation module is a Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) module, wherein the post-quantum cryptographic key pair generation module executes the quantum random number generator to generate a 512-bit random number, takes the first 256 bits of the random number as a first random number, and takes the last 256 bits of the random number as a second random number; the post-quantum cryptographic key pair generation module sets the first random number as a random number parameter d, sets the second random number as a random number parameter z, and substitutes them into ML-KEM.KeyGen_internal(d, z) to generate an ML-KEM public key and an ML-KEM private key.

48. The quantum key system as described in claim 45, wherein the post-quantum cryptographic key pair generation module is a Module-Lattice-Based Digital Signature Algorithm (ML-DSA) module, wherein the post-quantum cryptographic key pair generation module executes the quantum random number generator to generate a 256-bit random number; the post-quantum cryptographic key pair generation module sets the random number as a random number parameter 𝜉, substitutes it into ML-DSA.KeyGen_internal (𝜉), and generates an ML-DSA public key and an ML-DSA private key.

49. The quantum key system as described in claim 45, wherein the post-quantum cryptographic key pair generation module is a Stateless Hash-Based Digital Signature Algorithm (SLH-DSA) module, wherein the post-quantum cryptographic key pair generation module executes the quantum random number generator to generate three different random numbers of different bit lengths; the post-quantum cryptographic key pair generation module sets the random numbers as random number parameters SK.seed, SK.prf, and PK.seed respectively, and substitutes them into slh_keygen_internal(SK.seed, SK.prf, PK.seed) to generate the SLH-DSA public key and SLH-DSA private key; wherein n is one of 16, 24, and 32.

50. The quantum key system as described in claim 45, wherein the post-quantum cryptographic key pair generation module is a Stateless Hash-Based Digital Signature Algorithm (SLH-DSA) module, wherein the post-quantum cryptographic key pair generation module executes the quantum random number generator to generate a random number of 1-bit length; the post-quantum cryptographic key pair generation module takes the 0th to 8n-1th bits of the random number as a first random number; the post-quantum cryptographic key pair generation module takes the 8nth to 16n-1th bits of the random number as a second random number; the post-quantum cryptographic key pair generation module takes the 16nth to 24n-1th bits of the random number as a third random number; The post-quantum cryptography key generation module sets the first random number as the random number parameter SK.seed, the second random number as the random number parameter SK.prf, and the third random number as the random number parameter PK.seed, and substitutes them into slh_keygen_internal(SK.seed, SK.prf, PK.seed) to generate the SLH-DSA public key and SLH-DSA private key; where n is one of 16, 24, or 32.

51. The quantum key system as claimed in claim 45, wherein the post-quantum cryptographic key generation module executes the quantum random number generator to generate two different random numbers, each 256-bit in length, taking one of the random numbers as random number parameter d and the other random number as random number parameter z; the post-quantum cryptographic key generation module generates parameters k, q, and N1, and substitutes the random number parameters d and k into a pseudo-random number generator of a pseudo-random number seed to generate pseudo-random number seed A and pseudo-random number seed N1, wherein the pseudo-random number seed A is used to generate a matrix, and the pseudo-random number seed N1 is used to generate noise; The post-quantum cryptography key pair generation module generates an n×n matrix 𝐀, where each element of matrix 𝐀 is a multinomial equation with m coefficients. The value of each coefficient is an integer obtained by modulo the parameter 𝑞 of a pseudo-random number generated by the post-quantum cryptography key pair generation module based on the pseudo-random number seed 𝜌 and the matrix index value. The post-quantum cryptography key pair generation module also generates a vector 𝐬, which contains n elements. Each element of vector 𝐬 is a multinomial equation with m coefficients. The value of each coefficient is an integer obtained by modulo the parameter 𝑞 of a pseudo-random number generated by the key derivation module based on the pseudo-random number seed 𝜎 and the parameter N1. The post-quantum cryptography key pair generation module generates a vector 𝐞, which contains 𝑘 elements. Each element of the vector 𝐞 is a polynomial equation with m coefficients. The value of each coefficient is an integer obtained by modulo the parameter 𝑞 of a pseudo-random number generated by the key derivation module based on the pseudo-random number seed 𝜎 and the parameter N1. The post-quantum cryptography key pair generation module generates a core public key value 𝐭, which is 𝐭 = 𝐀 ⨯ 𝐬 + 𝐞. The post-quantum cryptography key pair generation module generates a post-quantum cryptography public key ek, which contains at least the core public key value 𝐭 and the pseudo-random number seed 𝜌. The post-quantum cryptography key pair generation module generates a post-quantum cryptography private key dk, which at least includes the vector 𝐬, the post-quantum cryptography public key ek, the hash value of the post-quantum cryptography public key ek, and the random number parameter z.

52. The quantum key system as claimed in claim 50, wherein the quantum random number generator generates a 256-bit random number SQ; the post-quantum cryptographic key pair generation module updates the pseudo-random number seed SQ to the random number SQ, and the post-quantum cryptographic key pair generation module uses the random number SQ to generate the vectors A and B.

53. The quantum key system as claimed in claim 45, wherein the post-quantum cryptographic key generation module executes the quantum random number generator to generate a 256-bit random number as a random number parameter φ; the post-quantum cryptographic key generation module generates parameters k, ℓ, d, and φ, and substitutes the random number parameter φ, the parameter k, and the parameter ℓ into a pseudo-random number generator to generate pseudo-random number seeds φ, φ', and φ, wherein the pseudo-random number seed φ is used to generate a matrix, and the pseudo-random number seed φ' is used to generate a polynomial; The post-quantum cryptography key pair generation module generates an ℓ matrix ᵀ, where each element of ᵀ is a multinomial equation with m coefficients. The value of each coefficient is an integer obtained by modulo the parameter ᵀ with a pseudo-random number generated by the post-quantum cryptography key pair generation module based on the pseudo-random number seed ᵌ and the matrix index value. The post-quantum cryptography key pair generation module generates a vector ᵬ1, which contains ℓ elements. Each element of ᵬ1 is a multinomial equation with m coefficients. The value of each coefficient is a pseudo-random number between [–ᵂ, ᵂ] generated by the key derivation module based on the pseudo-random number seed ᵌ'. The post-quantum cryptography key pair generation module generates a vector 𝐬2, which contains k elements. Each element of vector 𝐬2 is a multinomial equation with m coefficients. The values ​​of these coefficients are pseudo-random numbers between [-𝜂, 𝜂] generated by the key derivation module based on the pseudo-random number seed 𝜌'. The post-quantum cryptography key pair generation module generates a core key value 𝐭, which is 𝐭 = 𝐀𝐬1 + 𝐬2. The post-quantum cryptography key pair generation module performs a coefficient slicing operation, slicing the value of each coefficient of the core public key value 𝐭 according to the parameter d, to generate the core public key value 𝐭1 and the core private key value 𝐭0. The post-quantum cryptography key pair generation module generates a post-quantum cryptography public key 𝑝𝑘, which at least contains the pseudo-random number seed 𝜌 and the core public key value 𝐭1; the post-quantum cryptography key pair generation module generates a post-quantum cryptography public key hash value 𝑡𝑟 and a post-quantum cryptography private key 𝑠𝑘, wherein the post-quantum cryptography private key 𝑠𝑘 at ​​least contains the pseudo-random number seed 𝜌, the pseudo-random number 𝐾, the post-quantum cryptography public key hash value 𝑡𝑟, the vector 𝐬1, the vector 𝐬2, and the core private key value 𝐭0.

54. The quantum key system as claimed in claim 53, wherein the quantum random number generator generates a 512-bit random number SQ1; the post-quantum cryptographic key pair generation module updates the pseudo-random number seed ' to the random number SQ1, and the post-quantum cryptographic key pair generation module uses the random number SQ1 to generate the vectors 𝐬1 and 𝐬2.

55. The quantum key system as claimed in claim 53, wherein the quantum random number generator generates a 256-bit random number SQ2; the post-quantum cryptographic key pair generation module updates the random number SQ2 to the random number SQ2, and the post-quantum cryptographic key pair generation module uses the random number SQ2 to generate the post-quantum cryptographic private key K.

56. The quantum key system as claimed in claim 31, wherein the first terminal device further includes a uniformly distributed floating-point conversion module, wherein the second terminal device further includes the uniformly distributed floating-point conversion module, wherein the quantum random number generator generates a 1-bit first random number and a 52-bit second random number; the uniformly distributed floating-point conversion module generates a 64-bit temporary floating-point number, wherein the first to 12th bits of the temporary floating-point number are 001111111110, and the 13th to 64th bits of the temporary floating-point number are the second random number; if the first random number is 0, then the output value u of the quantum random number generator is the 64-bit floating-point value 1 minus the temporary floating-point number; if the first random number is 1, then the output value u of the quantum random number generator is the temporary floating-point number.

57. The quantum key system as claimed in claim 56, wherein the uniformly distributed floating-point conversion module calculates a standard normal distribution random number z from the output value u using a Box-Muller conversion.

58. The quantum key system as claimed in claim 57, wherein the uniformly distributed floating-point conversion module linearly transforms the standard normal distribution random number z to calculate the normal distribution random number x based on the mean and standard deviation.

59. The quantum key system as claimed in claim 57, wherein the uniformly distributed floating-point conversion module performs an exponential transformation on the standard normal distribution random number z to calculate the standard log-normal distribution random number x.

60. The quantum key system as claimed in claim 56, wherein the uniformly distributed floating-point conversion module performs a logarithmic transformation on the output value u to calculate an exponentially distributed random number x based on the mean 1 / λ.

61. The quantum key system as claimed in claim 56, wherein the uniformly distributed floating-point conversion module calculates the output value u to obtain a standard normal distribution random number.

62. The quantum key system as claimed in claim 57, wherein the uniformly distributed floating-point conversion module calculates a normal distribution random number z from the standard normal distribution random number z based on the mean μ and the standard deviation σ.

63. The quantum key system as claimed in claim 57, wherein the uniformly distributed floating-point conversion module calculates a standard logarithmic normal distribution random number z from the standard normal distribution random number z.

64. The quantum key system as claimed in claim 57, wherein the uniformly distributed floating-point conversion module calculates a log-normally distributed random number z from the standard normally distributed random number z based on the mean μ and the standard deviation σ.

65. The quantum key system as claimed in claim 56, wherein the uniformly distributed floating-point conversion module calculates an exponentially distributed random number from the output value u based on the average 1 / λ.

66. The quantum key system as claimed in claim 31, wherein the first terminal device further includes a post-quantum cryptographic key encapsulation module, wherein the second terminal device further includes the post-quantum cryptographic key encapsulation module, wherein the quantum random number generator generates random numbers based on the post-quantum cryptographic key encapsulation module, wherein the random numbers are designed to achieve indistinguishability under Chosen-Ciphertext Attack (IND-CCA) security level; and the post-quantum cryptographic key encapsulation module substitutes the random numbers to generate a post-quantum cryptographic key encapsulation value.

67. The quantum key system as described in claim 66, wherein the post-quantum cryptographic key encapsulation module is a Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) module, wherein the post-quantum cryptographic key encapsulation module executes the quantum random number generator to generate a 256-bit random number as the random number parameter m, and generates a public key ek, which is then substituted into ML-KEM.Encaps_internal(ek, m) to generate the post-quantum cryptographic key encapsulation value.

68. The quantum key system as claimed in claim 31, wherein the second terminal device further includes a post-quantum cryptographic digital signature module, wherein the quantum random number generator generates a random number based on the post-quantum cryptographic digital signature module, wherein the random number is intended to achieve an Existential Unforgeability under Chosen Message Attack (EUF-CMA) security level; the post-quantum cryptographic digital signature module inputs the random number to generate a post-quantum cryptographic digital signature value.

69. The quantum key system as described in claim 68, wherein the post-quantum cryptographic digital signature module is a Module-Lattice-Based Digital Signature Algorithm (ML-DSA) module, wherein the post-quantum cryptographic digital signature module executes the quantum random number generator to generate a 256-bit random number as a random number parameter rnd, and substitutes the random number parameter rnd, the private key sk, and the message to be signed M' into ML-DSA.Sign_internal(sk, M', rnd) to generate the post-quantum cryptographic digital signature value.

70. The quantum key system as described in claim 58, wherein the post-quantum cryptographic digital signature module is a Stateless Hash-Based Digital Signature Algorithm (SLH-DSA) module; the post-quantum cryptographic digital signature module executes the quantum random number generator to generate a random number of length -bit as a random number parameter addrnd, and substitutes the random number parameter addrnd, the message to be signed M', and the private key SK into slh_sign_internal(M', SK, addrnd) to generate the post-quantum cryptographic digital signature value; wherein n is one of 16, 24, and 32.

71. A quantum key method, suitable for a system including a first terminal device and a second terminal device, wherein the first terminal device includes an initiating quantum key distribution module, and the second terminal device includes a receiving quantum key distribution module, wherein the initiating quantum key distribution module and the receiving quantum key distribution module each include qubits, wherein the quantum key method includes the following steps: the initiating quantum key distribution module and the receiving quantum key distribution module use the qubits and quantum logic gates to obtain negotiated messages, wherein the quantum logic gates correspond to a quantum uniform superposition state or a quantum entangled state.

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