A zero-knowledge proof method based on quantum optimization integer factorization algorithm

Abstract

The application discloses a zero-knowledge proof method based on a quantum optimization integer factorization algorithm, which is based on quantum computing, realizes efficient calculation of a candidate verification point by combining elliptic curve point addition and point doubling rules, adopts Grover algorithm to optimize candidate point search, thereby improving verification efficiency, takes a three-stage process as the core, gradually narrows down the verification range, and dynamically generates or verifies a target value, thereby ensuring the accuracy and security of the verification process, and constructs zero-knowledge proof based on the complexity of integer factorization, provides smooth parameters, a calculation path and a verification point abscissa, and the verifier reproduces the calculation path of the prover to verify whether the candidate point meets the expected mathematical characteristics without contacting the original data, so that the method is widely applicable to blockchain transaction verification, digital signature enhancement and data integrity protection, and has the characteristics of high efficiency, zero-knowledge and strong adaptability.

Description

Technical Field

[0001] This invention belongs to the field of cryptography and quantum computing technology, and in particular relates to a zero-knowledge proof method based on a quantum-optimized integer factorization algorithm. Background Technology

[0002] Zero-knowledge proofs, an important branch of modern cryptography, allow the prover to demonstrate the truth of a statement to the verifier without revealing any actual information. This technology is widely used in blockchain transaction verification, privacy protection, and identity authentication, offering high security and practicality. Integer factorization is an important mathematical problem widely used in modern cryptography; for example, the security of the RSA encryption algorithm is based on the difficulty of factoring large integers.

[0003] Existing research indicates that the combination of quantum computing and zero-knowledge proofs holds broad application prospects, but numerous challenges remain in practical implementation. These include how to leverage quantum computing to improve verification efficiency while maintaining the zero-knowledge property, and how to ensure the security and adaptability of the solution. Therefore, combining quantum computing with zero-knowledge proofs offers a novel approach to data integrity verification and privacy protection. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention provides a zero-knowledge proof method based on a quantum-optimized integer factorization algorithm, aiming to solve the problems of low verification efficiency, poor quantum computing compatibility, and insufficient privacy protection in existing zero-knowledge proof technologies.

[0005] To achieve the above-mentioned technical objectives, the present invention provides the following technical solution:

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

[0007] Proof: Receive the data block M to be verified, hash the data block M to obtain an integer n, n = H(M), set the expected value g, g is a positive integer less than n, and set smoothing parameters B1, B2, and B3; arbitrarily select 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 based on the defined quantum register, introduce a quantized integer factorization method to find the expression g = x Q For a point Q mod n, generate a zero-knowledge proof π = {B1, B2, B3, E(A, B), P0(x0, z0), x Q}, x Q Represents the x-coordinate of point Q;

[0008] Verifier: The verifier receives the zero-knowledge proof π and reproduces the calculation path to verify whether a solution satisfying g = x can be found. Q If the point Q mod n passes the verification, it proves that the data M is complete; otherwise, it returns a verification failure.

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

[0010] 1. Improved Verification Efficiency: This invention significantly improves verification efficiency by incorporating a quantum-optimized integer factorization algorithm, introducing elliptic curve point addition and doubling rules, and combining this with Grover's algorithm for efficient candidate point search. Compared to traditional zero-knowledge proof schemes, this invention exhibits significant computational performance advantages in big data scenarios and complex verification conditions.

[0011] 2. Enhanced Data Security: This invention utilizes the mathematical complexity of integer factorization to construct the verification path, while dynamically adjusting smoothing parameters and verification range to ensure the irreversibility and tamper resistance of the verification process. This scheme provides strong security for the mathematical derivation of verification results and can effectively resist malicious attacks.

[0012] 3. Protecting Data Privacy: The zero-knowledge proof scheme of this invention allows the verifier to verify the authenticity and integrity of data without accessing or understanding the original data content. By optimizing the verification conditions (such as performing modulo operations on the x-coordinates of candidate points), the risk of potentially exposing the original data is further reduced, thereby maximizing the protection of data privacy.

[0013] 4. Adaptable to Multiple Application Scenarios: This invention boasts excellent flexibility and adaptability, making it widely applicable in areas such as blockchain transaction verification, digital signature enhancement, and data integrity verification. It also meets the needs of distributed systems, privacy protection, and real-time verification. The solution supports dynamically generated verification conditions, enabling it to handle complex real-world application scenarios. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0015] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed 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 are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0016] Please see Figure 1 This invention provides a zero-knowledge proof method based on a quantum-optimized integer factorization algorithm, comprising:

[0017] Proof: Receive the data block M to be verified, hash the data block M to obtain an integer n, n = H(M), set the expected value g, g is a positive integer less than n, and set smoothing parameters B1, B2, and B3; arbitrarily select 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 based on the defined quantum register, introduce a quantized integer factorization method to find the expression g = x Q For a point Q mod n, generate a zero-knowledge proof π = {B1, B2, B3, E(A, B), P0(x0, z0), x Q}, x Q Represents the x-coordinate of point Q;

[0018] Verifier: The verifier receives the zero-knowledge proof π and reproduces the calculation path to verify whether a solution satisfying g = x can be found. Q If the point Q mod n passes the verification, it proves that the data M is complete; otherwise, it returns a verification failure.

[0019] In this embodiment, the computation path is reproduced to verify whether a value satisfying g = x can be found. Q The point Q mod n, i.e., proving π = {B1,B2,B3,E(A,B),P0(x0,z0),x} through acquired zero-knowledge. Q The verifier executes the same algorithm as the prover, defines a quantum register, and introduces a quantized integer factorization method based on the defined quantum register to find the expression g = x. Q If the x-coordinate of point Q mod n is found by the verification method and its coordinate x is the same as the coordinate recorded in the zero-knowledge proof of π, then... Q If they are the same, the verification passes, proving that data M is complete; otherwise, it proves that the data has been tampered with.

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

[0021] Choose a positive integer B1 and set it as the n of the integer to be factored. 1 / 4 ;

[0022] Choose a positive integer B2 and set it as 2 × B1 or n. 1 / 3 ;

[0023] Choose a positive integer B3, and 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; and |b> for storing each bit b of the binary representation of the prime number accumulation. i The auxiliary register is used to store intermediate calculation results.

[0025] Preferably, the quantized integer factorization method includes:

[0026] S11: Construct a point addition circuit and a point doubling circuit. 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 points.

[0027] S12: Based on the defined quantum register, point addition circuit, and point doubling circuit, the integer factorization method is used to find the solution g = x in three stages. Q Point Q mod n; where, in the first stage, a search is conducted between 0 and B1 to find the point Q that satisfies g = x. Q If a point Q mod n is found that satisfies g = x, then... Q If the value Q is modulo n, then the zero-knowledge proof of π is output and the process terminates; otherwise, the second phase is executed, in which a search is performed between B1 and B2 to find the value of g = x. Q If a point Q mod n is found that satisfies g = x, then... Q If the value Q is modulo n, then the zero-knowledge proof of π is output and the process terminates; otherwise, the third stage is executed, in which a search is performed between B1 and B3 to find the value of g = x. Q The point Q is modulo n.

[0028] Preferably, in the first stage, the search for g = x between 0 and B1 is performed. Q Points Q modulo n include:

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

[0030] S112: For prime number p i ≤B1, denote r1 represents the number of prime numbers less than B1. Store each bit of the binary representation of k1 into register |b>.

[0031] S113: Add the initial point P0 as the two input points of the point addition circuit to obtain point P. 01 Point P 01 Store the data in register |x>, iterate through each bit in register |b>, and if the current bit in register |b> is 1, then set point P. 01The input point doubling circuit doubles the input point to obtain point Q; where the doubling occurs at the highest bit of register b.

[0032] S114: Change the x-coordinate of point Q. Q Store the data in register |x> to obtain the state of register |x>;

[0033]

[0034] Where 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 x-coordinate of the target point Q. Q ;

[0036] S116: Verify x Q Does mod n equal the target value g?

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

[0038] Preferably, step S115 includes:

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

[0040]

[0041] S1152: Define Oracle functions:

[0042]

[0043] if Then the x-coordinate is Phase flip of the target point;

[0044] S1153: Apply the diffusion operator μ to the x-coordinate of the target point Amplitude expansion:

[0045]

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

[0047] Preferably, the second stage involves searching between B1 and B2 for a value satisfying g = x. Q Points Q modulo n include:

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

[0049] S122: For prime numbers p, B1 ≤ p i ≤B2, denoted r2 represents the number of prime numbers greater than B1 and less than B2. Store each bit of the binary representation of k2 into the control register |b>.

[0050] S123: Add the initial point Q1 as the two input points of the point addition circuit to obtain point P. 01 Point P 01 Store the data in register |x>, iterate through each bit in control register |b>, and if the current bit in control register |b> is 1, then set point P. 01 The input point doubling circuit doubles the input point to obtain point Q; where the doubling occurs at the highest bit of register b.

[0051] S124: Change the x-coordinate of point Q. Q Store the data in register |x> to obtain the state of register |x>;

[0052]

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

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

[0055] S126: Verify x Q Does mod n equal the target value g?

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

[0057] Preferably, step S125 includes:

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

[0059]

[0060] S1252: Define Oracle functions:

[0061]

[0062] if Then the x-coordinate is Phase flip of the target point;

[0063] S1253: Apply the diffusion operator μ to expand the amplitude of the abscissa of the target point :

[0064]

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

[0066] Preferably, the searching for a 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.[[ID=XXX]] [[ID=XXX]]

[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 traditional zero-knowledge proof schemes, 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 a verification path by utilizing the mathematical complexity of the integer factorization problem, and dynamically adjusts the smooth parameter and verification range, ensuring the irreversibility and anti-tampering of the verification process. This scheme provides strong security guarantees for the mathematical derivation of 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 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 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 dynamic generation of verification conditions and can handle complex actual application scenarios.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within 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: Proof side: Receive the data block M to be verified, hash the data block M to obtain an integer n, Set the expected value g, where g is a positive integer less than n, and set the smoothing parameter. , and ; Optional curve : and a point above it Define a quantum register, and based on the defined quantum register, introduce a quantized integer factorization method to find the satisfying... point Generate zero-knowledge proofs , Point The x-coordinate; The quantum register includes: Used to record the x-coordinate of the current accumulation point; Used to record the z-coordinate of the current accumulation point; and Used to record the x and z coordinates of the initial point; Each bit of the binary representation used to store the accumulation of prime numbers. ; Auxiliary registers are used to store intermediate calculation results; The quantized integer factorization method includes: S11: Construct a point addition circuit and a point doubling circuit. 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 points. S12: Based on the defined quantum register, point addition circuit, and point doubling circuit, the integer factorization method is used to find the satisfying condition in three stages. point In the first phase, from 0~ Search between satisfying point If the search finds a match point Then output the zero-knowledge proof. And terminate; otherwise, execute the second phase, starting from the second phase. ~ Search between satisfying point If the search finds a match point Then output the zero-knowledge proof. And terminate; otherwise, execute the third phase, from the third phase... ~ Search between satisfying point ; Verifier: The verifier accepts zero-knowledge proofs. Reproduce the computation path to verify whether a satisfactory result can be found. point If the verification passes, it proves that the data M is complete; otherwise, it returns a verification failure.

2. The zero-knowledge proof method based on quantum-optimized integer factorization algorithm according to claim 1, characterized in that, The setting of smoothness parameters , and include: Choose a positive integer Set as the integer n to be factored ; Choose a positive integer Set as or ; Choose a positive integer ,set up or .

3. The zero-knowledge proof method based on quantum-optimized integer factorization algorithm according to claim 1, characterized in that, In the first stage from 0~ Search between satisfying point include: S111: Will Encode as a quantum state and store in a quantum register , , and ; S112: For prime numbers ,remember , Indicates less than The number of prime numbers, Each bit of the binary number is stored in the register. ; S113: Set the initial point The two input points of the point addition circuit are added together to obtain the point. , will point Store in register traverse registers Each bit stored in the register, if If the current bit is 1, then the point will be... The input point doubling circuit doubles the input point to obtain point Q; where the doubling occurs at the highest bit of register b. S114: Set the x-coordinate of point Q. Stored in register , obtain register The state; in, This represents the number of points Q, where i represents the i-th point Q; S115: Register The x-coordinate of the target point Q is obtained by applying Grover's algorithm. ; S116: Verification Is it equal to the target value g? S117: If Output point Q.

4. The zero-knowledge proof method based on quantum-optimized integer factorization algorithm according to claim 3, characterized in that, Step S115 includes: S1151: Initialize auxiliary registers Then the system state Defined as: S1152: Define Oracle functions: if Then the x-coordinate is Phase flip of the target point; S1153: Applying the diffusion operator x-coordinate of the target point Amplitude expansion: S1154: Register Measurements were performed to obtain the x-coordinate of the target point. .

5. The zero-knowledge proof method based on quantum-optimized integer factorization algorithm according to claim 3, characterized in that, In the second phase from ~ Search between satisfying point include: S121: Order ,Will Encode as a quantum state and store in a quantum register , , and ; S122: For prime numbers p, the following conditions are satisfied ,remember , Indicates greater than Less than The number of prime numbers, Each bit of the binary number is stored in the control register. ; S123: Set the initial point The two input points of the point addition circuit are added together to obtain the point. , will point Store in register Traverse the control registers Each bit stored in the control register If the current bit is 1, then the point will be... The input point doubling circuit doubles the input point to obtain point Q; where the doubling occurs at the highest bit of register b. S124: Set the x-coordinate of point Q. Stored in register , obtain register The state; Among them, among them, This represents the number of points Q, where i represents the i-th point Q; S125: Register The x-coordinate of the target point Q is obtained by applying Grover's algorithm. ; S126: Verification Is it equal to the target value g? S127: If Output point Q.

6. The zero-knowledge proof method based on quantum-optimized integer factorization algorithm according to claim 5, characterized in that, Step S125 includes: S1251: Initialize auxiliary registers Then the system state Defined as: S1252: Define Oracle functions: if Then the x-coordinate is Phase flip of the target point; S1253: Applying the diffusion operator x-coordinate of the target point Amplitude expansion: S1254: Register Measurements were performed to obtain the x-coordinate of the target point. .

7. A zero-knowledge proof method based on a quantum-optimized integer factorization algorithm according to claim 5, characterized in that, The third stage from ~ Search between satisfying point include: S131: For each prime number ,remember ; S132: Calculation ; S133: If Output point Q if the condition is met, otherwise output FAIL.

Images