Zero knowledge proof method based on quantum optimization integer decomposition algorithm

Abstract

The invention discloses a zero-knowledge proof method based on a quantum optimization integer decomposition algorithm, and the method comprises the steps: taking quantum calculation as a basis, and achieving the efficient calculation of candidate verification points through combining an elliptic curve point addition rule and a point doubling rule; a Grover algorithm is adopted to optimize candidate point search, so that verification efficiency is improved; according to the scheme, a three-stage process is taken as a core, the verification range is gradually reduced, a target value is dynamically generated or verified, and the accuracy and safety of the verification process are ensured; the proving party constructs zero-knowledge proof based on the complexity of integer decomposition, and provides smooth parameters, a calculation path and a verification point abscissa; the verification party verifies whether the candidate points meet the expected mathematical characteristics or not by reproducing the calculation path of the proving party, and original data does not need to be contacted; the scheme is widely applicable to block chain transaction verification, digital signature enhancement and data integrity protection, and has the characteristics of high efficiency, zero knowledge and high adaptability.

Description

Technical Field

[0001] The present invention relates to the technical field of cryptography and quantum computing, and in particular to a zero-knowledge proof method based on a quantum optimized integer factorization algorithm. Background Art

[0002] As an important branch of modern cryptography, zero-knowledge proof allows the prover to prove the authenticity of a statement to the verifier without revealing any actual information. This technology is widely used in blockchain transaction verification, privacy protection, identity authentication and other fields, and has high security and practicality. The integer factorization problem is an important mathematical problem and is widely used in modern cryptography. For example, the security of the RSA encryption algorithm is based on the difficulty of large integer factorization.

[0003] Existing research shows that the combination of quantum computing and zero-knowledge proof has broad application prospects, but there are still many challenges in actual implementation, including how to use quantum computing to improve verification efficiency while maintaining zero-knowledge characteristics, and how to ensure the security and adaptability of the solution. Therefore, combining quantum computing with zero-knowledge proof provides a new solution for data integrity verification and privacy protection. Summary of the invention

[0004] In order to solve the problems existing in the background technology, the present invention provides a zero-knowledge proof method based on a quantum optimized integer factorization algorithm, which aims to solve the problems of low verification efficiency, poor quantum computing compatibility and insufficient privacy protection in the existing zero-knowledge proof technology.

[0005] In order to achieve the above technical objectives, the present invention provides the following technical solutions:

[0006] A zero-knowledge proof method based on a quantum optimized integer factorization algorithm, comprising:

[0007] Prover: Receive the data block M to be verified, hash the data block M to get an integer n, n = H (M), set the expected value g, g is a positive integer less than n, set the smoothing parameters B1, B2 and B3; Optional curve E (A, B): By 2 =x 3 +Ax 2 +x(mod n) and a point P0(x0,z0) on it; define a quantum register, and introduce the quantized integer decomposition method based on the defined quantum register to find a solution that satisfies g=x Q mod n point Q, generate zero-knowledge proof π = {B1, B2, B3, E(A, B), P0(x0, z0), x Q}, x Q represents the horizontal coordinate of point Q;

[0008] Verifier: The verifier receives the zero-knowledge proof π and recomputes the path to verify whether it can find a solution that satisfies g = x. Q If the point Q of modn passes the verification, it proves that the data M is complete, otherwise it returns verification failure.

[0009] The present invention has at least the following beneficial effects

[0010] 1 Improve verification efficiency: This invention uses a quantum-optimized integer factorization algorithm, introduces elliptic curve point addition and point doubling rules, and combines the Grover algorithm to efficiently search for candidate points, greatly improving verification efficiency. Compared with traditional zero-knowledge proof solutions, this invention has significant computing performance advantages in big data scenarios and complex verification conditions.

[0011] 2 Enhanced data security: This invention uses the mathematical complexity of integer decomposition problems to construct a verification path, and dynamically adjusts the smoothing parameters and verification range to ensure the irreversibility and tamper resistance of the verification process. This solution provides a strong security guarantee for the mathematical derivation of the verification results and can effectively resist malicious attacks.

[0012] 3. Protecting data privacy: The zero-knowledge proof scheme of the present invention allows the verifier to verify the authenticity and integrity of the data without having to access or understand the original data content. By optimizing the verification conditions (such as performing a modular operation on the horizontal coordinates of the candidate points), the risk of exposing the original data is further reduced, thereby protecting data privacy to the greatest extent.

[0013] 4 Adaptable to multiple scenarios: The present invention has good flexibility and adaptability, and can be widely used in blockchain transaction verification, digital signature enhancement, data integrity verification and other fields, while meeting the needs of distributed systems, privacy protection and real-time verification. The solution supports dynamic generation of verification conditions and can cope with complex practical application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION

[0015] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0016] See also Figure 1 The present invention provides a zero-knowledge proof method based on a quantum optimized integer decomposition algorithm, comprising:

[0017] Prover: Receive the data block M to be verified, hash the data block M to get an integer n, n = H (M), set the expected value g, g is a positive integer less than n, set the smoothing parameters B1, B2 and B3; Optional curve E (A, B): By 2 =x 3 +Ax 2 +x(mod n) and a point P0(x0,z0) on it; define a quantum register, and introduce the quantized integer decomposition method based on the defined quantum register to find a solution that satisfies g=x Q mod n point Q, generate zero-knowledge proof π = {B1, B2, B3, E(A, B), P0(x0, z0), x Q}, x Q represents the horizontal coordinate of point Q;

[0018] Verifier: The verifier receives the zero-knowledge proof π and recomputes the path to verify whether it can find a solution that satisfies g = x. Q If the point Q of modn passes the verification, it proves that the data M is complete, otherwise it returns verification failure.

[0019] In this embodiment, the calculation path is repeated to verify whether a path satisfying g = x can be found. Q mod n, that is, the point Q obtained by the zero-knowledge proof π={B1,B2,B3,E(A,B),P0(x0,z0),x Q}, the verifier executes the same algorithm as the prover, defines quantum registers, and introduces the quantized integer decomposition method based on the defined quantum registers to find a solution that satisfies g = x Q mod n point Q, if the horizontal coordinate of the point Q found by the verifier is the same as the coordinate x recorded in the zero-knowledge proof π Q If they are the same, the verification is successful, proving that the data M is complete; otherwise, it proves that the data has been tampered with.

[0020] Preferably, the setting of smoothing parameters B1, B2 and B3 comprises:

[0021] Select a positive integer B1 and set it to n of the integer n to be decomposed 1 / 4 ;

[0022] Choose a positive integer B2, set to 2×B1 or n 1 / 3 ;

[0023] Select a positive integer B3, set B3 = 3 × B2 or B3 = n 1 / 2 .

[0024] Preferably, the quantum register includes: |x> for recording the x coordinate of the current accumulation point; |z> for recording the z coordinate of the current accumulation point; |x0> and |z0> for recording the x coordinate and z coordinate of the initial point; |b> for storing each bit b of the binary accumulated prime number i ;|ω>Auxiliary registers are used to store intermediate calculation results.

[0025] Preferably, the quantized integer decomposition method comprises:

[0026] S11: constructing a point addition circuit and a point doubling circuit, wherein the point addition circuit is used to calculate the sum of two input points, and the point doubling circuit is used to calculate the multiple of the input point;

[0027] S12: Based on the defined quantum register, point addition circuit and point doubling circuit, we use integer decomposition method to find the solution satisfying g = x in three stages. Q mod n point Q; where, in the first stage, search from 0 to B1 to satisfy g = x Q If the point Q mod n is found to satisfy g = x Q The point Q mod n outputs the zero-knowledge proof π and terminates. Otherwise, the second stage is executed. In the second stage, search from B1 to B2 to satisfy g = x Q If the point Q mod n is found to satisfy g = x Q If the point Q mod n is equal to zero knowledge proof π, the system will terminate. Otherwise, the system will execute the third stage, searching for a point between B1 and B3 that satisfies g = x. Q Point Q mod n.

[0028] Preferably, in the first stage, searching between 0 and B1 satisfies g=x Q The points Q mod n include:

[0029] S111: Encode P0(x0,z0) as quantum states and store them in quantum registers |x0>, |z0>, |x> and |z>;

[0030] S112: For prime number p i ≤B1, record r1 represents the number of prime numbers less than B1, and each bit of the binary digit of k1 is stored in register |b>;

[0031] S113: Use the initial point P0 as the two input points of the point addition circuit to add the two points to obtain point P 01 , point P 01 Store it in register |x>, traverse each bit stored in register |b>, if the current bit of register |b> is 1, then point P 01The input point doubling circuit doubles the point to obtain point Q; wherein the doubling of the point ends at the highest bit of register b;

[0032] S114: Set the horizontal coordinate x of point Q Q Store to register |x>, get the state of register |x>;

[0033]

[0034] Among them, M1 represents the number of points Q, and i represents the i-th point Q;

[0035] S115: Apply Grover's algorithm to register |x> to obtain the horizontal coordinate x of the target point Q Q ;

[0036] S116: Verify x Q Whether mod n is equal to the target value g;

[0037] S117: If g = x Q mod n, output point Q.

[0038] Preferably, the step S115 includes:

[0039] S1151: Initialize auxiliary register |ω>=|0>, then the system status Defined as:

[0040]

[0041] S1152: Define Oracle function:

[0042]

[0043] if Then the horizontal axis is The phase of the target point is flipped;

[0044] S1153: Apply the diffusion operator μ to convert the horizontal coordinate of the target point The amplitude of the expansion:

[0045]

[0046] S1154: Measure the register |x> to obtain the horizontal coordinate x of the target point Q .

[0047] Preferably, in the second stage, searching between B1 and B2 satisfies g=x Q The points Q mod n include:

[0048] S121: Order Will Encoded as quantum states and stored in quantum registers |x0>, |z0>, |x> and |z>;

[0049] S122: For prime numbers p, B1≤p i ≤B2, record r2 represents the number of prime numbers greater than B1 and less than B2. Each bit of the binary digit of k2 is stored in the control register |b>;

[0050] S123: Use the initial point Q1 as the two input points of the point addition circuit to add the two points to obtain point P 01 , point P 01 Store it in register |x>, traverse each bit stored in control register |b>, if the current bit of control register |b> is 1, then point P 01 The input point doubling circuit doubles the point to obtain point Q; wherein the doubling of the point ends at the highest bit of register b;

[0051] S124: Set the horizontal coordinate x of point Q Q Store to register |x>, get the state of register |x>;

[0052]

[0053] Among them, M2 represents the number of points Q, i represents the i-th point Q;

[0054] S125: Apply Grover's algorithm to register |x> to obtain the horizontal coordinate x of the target point Q Q ;

[0055] S126: Verify x Q Whether mod n is equal to the target value g;

[0056] S127: If g = x Q mod n, output point Q.

[0057] Preferably, the step S125 includes:

[0058] S1251: Initialize auxiliary register |ω>=|0>, then the system status Defined as:

[0059]

[0060] S1252: Define Oracle function:

[0061]

[0062] if Then the horizontal axis is The phase of the target point is flipped;

[0063] S1253: Amplify the amplitude of the abscissa of the target point by applying the diffusion operator μ :

[0064]

[0065] S1254: Measure the register |x> to obtain the abscissa x of the target point Q .

[0066] Preferably, the step of searching for the point Q that satisfies g = x Q mod n between B1 and B3 in the third stage includes:

[0067] S131: For each prime number B1 < p ≤ B3, denote

[0068] S132: Calculate (x Q , z Q ) = p · Q2;

[0069] S133: If g = x Q mod n, output the point Q, otherwise output FAIL.

[0070] In summary, 1. Improve verification efficiency: Through the quantum-optimized integer factorization algorithm, the present invention introduces the elliptic curve point addition and point doubling rules, and combines the Grover algorithm to efficiently search for candidate points, significantly improving the verification efficiency. Compared with the traditional zero-knowledge proof scheme, the present invention has significant computational performance advantages in large-data scenarios and complex verification conditions.

[0071] 2. Enhance data security: The present invention constructs the verification path by utilizing the mathematical complexity of the integer factorization problem, and dynamically adjusts the smooth parameter and the verification range, ensuring the irreversibility and anti-tampering of the verification process. This scheme provides strong security guarantees for the mathematical derivation of the verification results and can effectively resist malicious attacks.

[0072] 3. Protect data privacy: The zero-knowledge proof scheme of the present invention allows the verifier to verify the authenticity and integrity of the data without contacting or understanding the content of the original data. By optimizing the verification conditions (such as performing modulo operations on the abscissa of the candidate points), the risk of exposing the original data is further reduced, thus maximizing the protection of data privacy.

[0073] 4. Adapt to multi-scenario applications: The present invention has good flexibility and adaptability, and can be widely applied to fields such as blockchain transaction verification, digital signature enhancement, and data integrity verification, while meeting the requirements of distributed systems, privacy protection, and real-time verification. This scheme supports the dynamic generation of verification conditions and can cope with complex actual application scenarios.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm, characterized in that: include: Prover: Receive the data block M to be verified, hash the data block M to get an integer n, n = H (M), set the expected value g, g is a positive integer less than n, set the smoothing parameters B1, B2 and B3; Optional curve E (A, B): By 2 =x 3 +Ax 2 +x(mod n) and a point P0(x0,z0) on it; define a quantum register, and introduce the quantized integer decomposition method based on the defined quantum register to find a solution that satisfies g=x Q mod n point Q, generate zero-knowledge proof π = {B1, B2, B3, E(A, B), P0(x0, z0), x Q }, x Q represents the horizontal coordinate of point Q; Verifier: The verifier receives the zero-knowledge proof π and recomputes the path to verify whether it can find a solution that satisfies g = x. Q If the point Q mod n passes the verification, it proves that the data M is complete, otherwise it returns verification failure.

2. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 1, characterized in that: The setting of smoothing parameters B1, B2 and B3 comprises: Select a positive integer B1 and set it to n of the integer n to be decomposed 1 / 4 ; Choose a positive integer B2, set to 2×B1 or n 1 / 3 ; Select a positive integer B3, set B3 = 3 × B2 or B3 = n 1 / 2 .

3. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 1, characterized in that: The quantum register includes: |x> for recording the x coordinate of the current accumulation point; |z> for recording the z coordinate of the current accumulation point; |x0> and |z0> for recording the x coordinate and z coordinate of the initial point; |b> for storing each bit b of the binary of the prime number accumulation i ;|ω>Auxiliary registers are used to store intermediate calculation results.

4. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 3, characterized in that: The quantized integer decomposition method comprises: S11: constructing a point addition circuit and a point doubling circuit, wherein the point addition circuit is used to calculate the sum of two input points, and the point doubling circuit is used to calculate the multiple of the input point; S12: Based on the defined quantum register, point addition circuit and point doubling circuit, we use integer decomposition method to find the solution satisfying g = x in three stages. Q mod n point Q; where, in the first stage, search from 0 to B1 to satisfy g = x Q If the point Q mod n is found to satisfy g = x Q The point Q mod n outputs the zero-knowledge proof π and terminates. Otherwise, the second stage is executed. In the second stage, search from B1 to B2 to satisfy g = x Q If the point Q mod n is found to satisfy g = x Q If the point Q mod n is equal to zero knowledge proof π, the system will terminate. Otherwise, the system will execute the third stage, searching for a point between B1 and B3 that satisfies g = x. Q Point Q mod n.

5. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 4, characterized in that: In the first stage, the search between 0 and B1 satisfies g=x Q The points Q mod n include: S111: Encode P0(x0,z0) as quantum states and store them in quantum registers |x0>, |z0>, |x> and |z>; S112: For prime number p i ≤B1, record r1 represents the number of prime numbers less than B1, and each bit of the binary digit of k1 is stored in register |b>; S113: Use the initial point P0 as the two input points of the point addition circuit to add the two points to obtain point P 01 , point P 01 Store it in register |x>, traverse each bit stored in register |b>, if the current bit of register |b> is 1, then point P 01 The input point doubling circuit doubles the point to obtain point Q; wherein the doubling of the point ends at the highest bit of register b; S114: Set the horizontal coordinate x of point Q Q Store to register |x>, get the state of register |x>; Among them, M1 represents the number of points Q, and i represents the i-th point Q; S115: Apply Grover's algorithm to register |x> to obtain the horizontal coordinate x of the target point Q Q ; S116: Verify x Q Whether mod n is equal to the target value g; S117: If g = x Q mod n, output point Q.

6. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 5, characterized in that: The step S115 comprises: S1151: Initialize auxiliary register |ω>=|0>, then the system status Defined as: S1152: Define Oracle function: if Then the horizontal axis is The phase of the target point is flipped; S1153: Apply the diffusion operator μ to convert the horizontal coordinate of the target point The amplitude of the expansion: S1154: Measure the register |x〉 to obtain the horizontal coordinate x of the target point Q .

7. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 5, characterized in that: In the second stage, the search between B1 and B2 satisfies g=x Q The points Q mod n include: S121: Order Will Encoded as quantum states and stored in quantum registers |x0>, |z0>, |x> and |z>; S122: For prime numbers p, B1≤p i ≤B2, record r2 represents the number of prime numbers greater than B1 and less than B2. Each bit of the binary value of k2 is stored in the control register |b>; S123: Use the initial point Q1 as the two input points of the point addition circuit to add the two points to obtain point P 01 , point P 01 Store it in register |x>, and traverse each bit stored in control register |b>. If the current bit of control register |b> is 1, point P 01 The input point doubling circuit doubles the point to obtain point Q; wherein the doubling of the point ends at the highest bit of register b; S124: Set the horizontal coordinate x of point Q Q Store to register |x>, get the state of register |x>; Among them, M2 represents the number of points Q, i represents the i-th point Q; S125: Apply Grover's algorithm to register |x> to obtain the horizontal coordinate x of the target point Q Q ; S126: Verify x Q Whether mod n is equal to the target value g; S127: If g = x Q mod n, output point Q.

8. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 7, characterized in that: The step S125 comprises: S1251: Initialize auxiliary register |ω>=|0>, then the system status Defined as: S1252: Define Oracle function: if Then the horizontal axis is The phase of the target point is flipped; S1253: Apply the diffusion operator μ to convert the horizontal coordinate of the target point The amplitude of the expansion: S1254: Measure the register |x> to obtain the horizontal coordinate x of the target point Q .

9. A zero-knowledge proof method based on a quantum optimized integer factorization algorithm according to claim 7, characterized in that: In the third stage, the search between B1 and B3 satisfies g=x. Q The points Q mod n include: S131: For each prime number B1 < p ≤ B3, denote S132: Calculate (x Q ,z Q ) = p·Q2; S133: If g = x Q mod n, output point Q, otherwise output FAIL.

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