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CN-122001570-A - Verifiable multiparty geometric area calculation method based on quantum homomorphic encryption

CN122001570ACN 122001570 ACN122001570 ACN 122001570ACN-122001570-A

Abstract

The invention discloses a verifiable multiparty geometric area calculation method based on quantum homomorphic encryption, which relates to the technical field of multiparty cooperative calculation, and the method obtains polygonal area through a calculation center, a key center and based on quantum homomorphic encryption calculation; the invention can safely and reliably complete the cooperative calculation of the polygonal area in the state of encrypting the whole course of the self-selected position of the client, and simultaneously gives consideration to the attack resistance and the data privacy protection strength in the quantum computing environment.

Inventors

  • LI ZHENZHEN
  • LIU MINGKUI
  • GAO BO

Assignees

  • 北京印刷学院

Dates

Publication Date
20260508
Application Date
20260126

Claims (8)

  1. 1. The verifiable multiparty geometric area calculating method based on quantum homomorphic encryption is characterized by comprising the following steps of: s1, client Acquiring decimal coordinates of a discretionary position And converts it into binary coordinates Wherein, the method comprises the steps of, ; ; Representing the number of customers; ; representing binary abscissa A corresponding binary digit number; Representing binary ordinate A corresponding binary digit number; Sequentially represent The first digit from right to left Binary number of bits, the first A1 st bit binary number; Sequentially represent The first digit from right to left Binary number of bits, the first A1 st bit binary number; S2, client Using the binary coordinates Preparing the customer Is of the initial quantum state of (a) Wherein, the method comprises the steps of, ; Q represents quantum information; S3 customer For the initial quantum state Supplement to the left For initialized qubits until the abscissa is supplemented to Bit, ordinate to supplement Bit, obtain quantum plaintext state Wherein, the method comprises the steps of, ; ; Representation of In (a) Supplementary data of bits; Representation of In (a) Bit raw data; Representation of In (a) Supplementary data of bits; Representation of In (a) Bit raw data; S4, randomly generating a first group of encryption keys by the key center And a second set of encryption keys Wherein i=1, 2, M; j=1, 2,. -%, N; S5, client Using the first set of encryption keys And said second set of encryption keys For the quantum plaintext state Encrypting to obtain initial quantum ciphertext state ; S6, client For the initial quantum ciphertext state Inserting the decoy particles to obtain the final quantum ciphertext state ; S7, the computing center is based on the final quantum ciphertext state Performing security check on the quantum channel, and executing S8 if the security check passes, and executing S1 if the security check fails; s8, removing the decoy particles by a computing center to obtain the initial quantum ciphertext state ; S9, the computing center is based on the initial quantum ciphertext state And clients Calculates the cumulative result related to the polygon area Wherein when Time of day The polygonal area is the area of a polygonal area surrounded by n client self-selected positions; S10, the key center encrypts the first group of encryption keys And said second set of encryption keys Updating to obtain the first group of encryption keys Corresponding first group of decryption keys And said second set of encryption keys Corresponding second group decryption key ; S11, the key center is based on the first group decryption key And said second set of decryption keys For the accumulated result Decrypting to obtain a decryption result ; S12, the key center is based on the decryption result Performing reliability verification, and if the reliability verification is passed, the key center is based on the decryption result If the reliability verification is not passed, executing S1 or selecting other computing centers to execute S1 again; S13, client The polygonal area is obtained based on 2 times the polygonal area.
  2. 2. The verifiable multiparty geometric area calculation method based on quantum homomorphic encryption according to claim 1, wherein M and N in S3 satisfy the following conditions: , And When (1) Time of day 。
  3. 3. The verifiable multiparty geometric area calculation method based on quantum homomorphic encryption, according to claim 2, wherein the steps of: The initial quantum ciphertext state Is the abscissa of (2) ; The initial quantum ciphertext state Is the ordinate of (2) ; Wherein X and Z represent the X gate and Z gate in the universal quantum gate.
  4. 4. The method for calculating the verifiable multiparty geometric area based on quantum homomorphic encryption according to claim 3, wherein S7 comprises the following steps: The computing center is customer-based A measurement base corresponding to the position and the particle state of the inserted decoy particles is inserted, the decoy particles are measured at the corresponding positions by using the corresponding measurement base, and then the measurement result is transmitted to the client Wherein the corresponding measuring group is an X group or a Z group; Client and method for providing a customer with a service Calculating the error rate of the decoy particles according to the measurement result and sending the error rate to a calculation center; If the error rates of the n clients are lower than the noise error rate of the quantum channel/are lower than a preset threshold value, the quantum channel is proved to be safe, namely the pass of the safety check is indicated; if the error rates of the n clients are not all lower than the noise error rate of the quantum channel/are not all lower than the preset threshold value, the quantum channel is proved to be unsafe, namely the quantum channel is proved to pass the security check.
  5. 5. The method for calculating the verifiable multiparty geometric area based on quantum homomorphic encryption according to claim 4, wherein S9 comprises the following steps: S91, the computing center calls 2n times of quantum multipliers to respectively divide As a multiplicand, will Is input into a quantum multiplier as a multiplier to obtain a multiplication result ; S92, the computing center calls n times of quantum subtractors to respectively divide As a subtracted number, will Is input into a quantum subtracter as a subtraction number to obtain a subtraction result ; S93 from the subtraction result A non-negative number is arbitrarily selected as an added number or a subtracted number; S94 if the subtraction result If the second selected number is a non-negative number, inputting the non-negative number arbitrarily selected in S93 as an added number and the second selected number as an added number into a quantum adder to obtain a1 st accumulation result; If the subtraction result If the second selected number is not the non-negative number, inputting the non-negative number arbitrarily selected in S93 as the subtracted number and the second selected number as the subtracted number into the quantum subtracter to obtain the 1 st accumulation result; S95 if the subtraction result The method comprises the steps of inputting an r-2 th accumulated result as an added number and the r-1 th selected number as an added number to a quantum adder to obtain an r-1 th accumulated result, wherein r=3, 4, n; If the subtraction result The r-2 accumulation results are not non-negative numbers, the r-2 accumulation results are taken as the number to be subtracted, and the r-1 accumulation results are input to a quantum subtracter as the number to be subtracted, so that the r-1 accumulation results are obtained; If the subtraction result The r-2 accumulation result is taken as a subtracted number, and the r-1 accumulation result is obtained by taking the r-2 selected number as a subtracted number and inputting the r-2 selected number into a quantum subtracter; If the subtraction result If the r selected number is not a non-negative number and the r-2 accumulated result is not a non-negative number, taking the r-2 accumulated result as an added number, and inputting the r selected number as an added number to a quantum adder to obtain the r-1 accumulated result; S96, repeating S95 continuously until the n-1 accumulated result is obtained, wherein the n-1 accumulated result is the accumulated result 。
  6. 6. The method for calculating the verifiable multiparty geometric area based on quantum homomorphic encryption according to claim 5, wherein the first set of decryption keys And said second set of decryption keys The acquisition method of the (2) is consistent; the first set of decryption keys Obtained based on any one of the following formulas: ; ; ; ; ; ; Wherein X, Z, H, P, T, CONT represents a general quantum gate, r and T are intermediate values when T gate operation is performed by using a rotating Bell base method; And A key representing the second qubit of the CNOT gate.
  7. 7. The method for calculating the verifiable multiparty geometric area based on quantum homomorphic encryption according to claim 2, wherein S12 comprises the following steps: Sequentially picking out the decryption results from left to right by the key center A kind of electronic device Qubit, then measuring it by Z base to obtain measurement result, if the measurement result is all And the key center measures the rest quantum bits to obtain the polygonal area which is 2 times as large as the polygonal area, wherein the reliability verification is passed.
  8. 8. The method for calculating the verifiable multiparty geometric area based on quantum homomorphic encryption according to claim 1, wherein the client Dividing the polygonal area by 2 times to obtain the polygonal area.

Description

Verifiable multiparty geometric area calculation method based on quantum homomorphic encryption Technical Field The invention relates to the technical field of multiparty collaborative computing, in particular to a verifiable multiparty geometric area computing method based on quantum homomorphic encryption. Background At present, in the technical scene of multiparty collaborative computing geometric attributes, each client usually needs to share the selected position coordinates in a plaintext form so as to jointly calculate the area of a polygon formed by the position points, but the method has obvious safety and privacy defects, the client needs to expose the position information selected by the client, so that sensitive data has leakage risk, and the application requirement of the position privacy with high requirements cannot be met, therefore, how to provide a method for calculating the polygon area, which can safely and reliably complete the collaborative calculation of the polygon area in the state that the client is fully encrypted at the selected position, and simultaneously consider the anti-attack capability and the data privacy protection strength in the quantum computing environment, is a problem to be solved by a person in the field. Disclosure of Invention In view of the above, the present invention aims to provide a verifiable multiparty geometric area calculation method based on quantum homomorphic encryption. In order to achieve the above purpose, the present invention adopts the following technical scheme: A verifiable multiparty geometric area calculation method based on quantum homomorphic encryption comprises the following steps: s1, client Acquiring decimal coordinates of a discretionary positionAnd converts it into binary coordinatesWherein, the method comprises the steps of,;;Representing the number of customers;; representing binary abscissa A corresponding binary digit number; Representing binary ordinate A corresponding binary digit number; Sequentially represent The first digit from right to leftBinary number of bits, the firstA1 st bit binary number; Sequentially represent The first digit from right to leftBinary number of bits, the firstA1 st bit binary number; S2, client Using the binary coordinatesPreparing the customerIs of the initial quantum state of (a)Wherein, the method comprises the steps of,;Q represents quantum information; S3 customer For the initial quantum stateSupplement to the leftFor initialized qubits until the abscissa is supplemented toBit, ordinate to supplementBit, obtain quantum plaintext stateWherein, the method comprises the steps of,;;Representation ofIn (a)Supplementary data of bits; Representation of In (a)Bit raw data; Representation of In (a)Supplementary data of bits; Representation of In (a)Bit raw data; S4, randomly generating a first group of encryption keys by the key center And a second set of encryption keysWherein i=1, 2, M; j=1, 2,. -%, N; S5, client Using the first set of encryption keysAnd said second set of encryption keysFor the quantum plaintext stateEncrypting to obtain initial quantum ciphertext state; S6, clientFor the initial quantum ciphertext stateInserting the decoy particles to obtain the final quantum ciphertext state; S7, the computing center is based on the final quantum ciphertext statePerforming security check on the quantum channel, and executing S8 if the security check passes, and executing S1 if the security check fails; s8, removing the decoy particles by a computing center to obtain the initial quantum ciphertext state ; S9, the computing center is based on the initial quantum ciphertext stateAnd clientsCalculates the cumulative result related to the polygon areaWherein whenTime of dayThe polygonal area is the area of a polygonal area surrounded by n client self-selected positions; S10, the key center encrypts the first group of encryption keys And said second set of encryption keysUpdating to obtain the first group of encryption keysCorresponding first group of decryption keysAnd said second set of encryption keysCorresponding second group decryption key; S11, the key center is based on the first group decryption keyAnd said second set of decryption keysFor the accumulated resultDecrypting to obtain a decryption result; S12, the key center is based on the decryption resultPerforming reliability verification, and if the reliability verification is passed, the key center is based on the decryption resultIf the reliability verification is not passed, executing S1 or selecting other computing centers to execute S1 again; S13, client The polygonal area is obtained based on 2 times the polygonal area. Preferably, M and N in S3 satisfy the following conditions:, And When (1)Time of day。 Preferably, the method comprises the steps of, The initial quantum ciphertext stateIs the abscissa of (2); The initial quantum ciphertext stateIs the ordinate of (2); Wherein X and Z represent the X gate and Z gate in the universal quant