1. A universal method for million bit integer decomposition based on quantum annealing algorithm is characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,

continuously updating and column-dividing the integer binary multiplication table based on the information limit of the integer binary multiplication table;

constructing a target function of the integer binary multiplication table after column division, and simplifying the target function of each column through square item attributes;

introducing an auxiliary variable according to a dimension reduction formula to perform dimension reduction operation on the polynomial of the objective function which is more than 2-time term;

performing variable replacement on the target function of each column respectively, and transforming a value range from {0,1} to { -1,1 };

inputting the final local field coefficient matrix h and the coupling term coefficient matrix J of the target function into a quantum computing qbsolv software environment to execute a quantum annealing process;

and finally outputting the minimum value of energy, wherein the minimum value corresponds to a solution of successful integer decomposition.

2. The general method of qubit integer decomposition based on a quantum annealing algorithm according to claim 1, characterized in that: the information includes structure information, carry information, and target value information.

3. The general method of million bit integer decomposition based on quantum annealing algorithm according to claim 1 or 2, characterized by: the square term attribute includes the number of square terms,

4. the general method of qubit integer decomposition based on a quantum annealing algorithm according to claim 3, characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,

performing variable replacement (1-s) on the target function of each column respectively_i)/2,s_i∈{-1,1},i＝1,2,3,L；

And extracting the single term coefficient and the quadratic term coefficient of each column of objective function as a local field coefficient matrix h and a coupling term coefficient matrix J, so that the integer decomposition problem is converted into an Ising model which can be processed by a qbsolv software environment.

5. The general method of qubit integer decomposition based on a quantum annealing algorithm according to claim 4, characterized in that: the generalized target value limiting conditions include,

x_i+x_j+x_k＝1→x_ix_j＝x_jx_k＝x_ix_k＝0

1+c_z＝0→c_z＝1

wherein p is_i，q_i，x_i，x_j，x_kRepresenting bits of a multiplier, c_zRepresenting carry, all variables p_i，q_i，x_i，x_j，x_k，c_zAre all binary and take values of {0,1 }.

6. The general method of qubit integer decomposition based on a quantum annealing algorithm according to claim 5, characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,

decomposition integers N ═ p × q (p ═ 10bit, q ═ 10bit)

And p and q are two prime factors of the integer N to be decomposed, and the integer multiplication table is continuously updated and classified through the limitation of the structure information, the carry information and the target value information of the integer binary multiplication table.

7. The general method of qubit integer decomposition based on a quantum annealing algorithm according to claim 6, characterized in that: the method comprises the steps of carrying out preprocessing optimization on a high-order column and a low-order column of an integer binary multiplication table, and carrying out multi-module distributed independent processing.

8. The general method of qubit integer decomposition based on a quantum annealing algorithm according to claim 7, characterized in that: introducing an auxiliary variable according to a dimension reduction formula to perform dimension reduction operation on a polynomial of a target function which is more than 2-degree terms, including,

Background

Quantum computing integer decomposition techniques currently include two types: 1. a Shor algorithm based on a quantum circuit; 2. quantum Adiabatic (Quantum Adiabatic); the development of quantum computing provides a serious challenge for the existing public key cryptography, and public key cryptography RSA can be attacked by using the Shor algorithm.

As is well known, the security of the RSA cryptosystem lies in the difficulty of the integer decomposition problem, which relies on the number theory problem that cannot be solved in an efficient polynomial time. The core problem of RSA is the integer decomposition problem.

Currently, there are two main research directions for implementing integer decomposition through quantum computation: one is the circuit model algorithm of the Shor algorithm. The Shor algorithm works by reducing the factorization problem to an order-solving problem. There have been many attempts to implement the Shor algorithm on quantum computing hardware to date. The general quantum device is still in the primary stage, and the Shor algorithm decoding public key cryptography based on the general quantum circuit still stays in the theoretical stage, so that the decomposable integer scale is limited, and the size of the decomposed large number of the general quantum Shor algorithm which can be physically realized at present does not exceed the integer 100.

Another Quantum Adiabatic Computation (QAC), also known as quantum annealing, can solve the integer decomposition problem. The D-Wave system realizes quantum annealing by using quantum tunneling effect, is expected to solve the NP problem solved by the combination optimization problem in polynomial time, and is beneficial to solving the search problem of exponential solution space. On the premise that a general quantum computer is slow in development and cannot be put into practical use in a short period, further exploration and optimization of a large number decomposition scheme based on D-Wave quantum annealing are urgently needed. The current D-Wave quantum computer is developed rapidly, and the large-scale decomposition of more than several orders of magnitude than that of a general quantum computer is achieved by sacrificing part of physical quantum bit resources, so that the D-Wave quantum computer has great exploration value.

Therefore, the invention proposes a general model of large number decomposition based on D-Wave quantum annealing (N ═ p × q, p ═ 10bit, q ═ 10bit, where p and q are two prime factors of an integer N to be decomposed), and breaks through the structural limitation of topological connection of D-Wave quantum computer hardware.

Disclosure of Invention

This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.

The present invention has been made in view of the above-mentioned conventional problems.

Therefore, the technical problem solved by the invention is as follows: the method solves the challenges brought by hardware connection and quantum bit resource limitation of the D-Wave quantum computer.

In order to solve the technical problems, the invention provides the following technical scheme: continuously updating and column-dividing an integer binary multiplication table based on information limitation of the integer binary multiplication table; constructing a target function of the integer binary multiplication table after column division, and simplifying the target function of each column through square item attributes; introducing an auxiliary variable according to a dimension reduction formula to perform dimension reduction operation on the polynomial of the objective function which is more than 2-time term; performing variable replacement on the target function of each column respectively, and transforming a value range from {0,1} to { -1,1 }; inputting the final local field coefficient matrix h and the coupling term coefficient matrix J of the target function into a quantum computing qbsolv software environment to execute a quantum annealing process; and finally outputting the minimum value of energy, wherein the minimum value corresponds to a solution of successful integer decomposition.

As a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: the information includes structure information, carry information, and target value information.

As a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: the square term attribute includes the number of square terms,

as a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: comprising performing variable replacement (1-s) on the target function of each column respectively_i)/2,s_iE { -1,1}, i { -1, 2,3, L; and extracting the single term coefficient and the quadratic term coefficient of each column of objective function as a local field coefficient matrix h and a coupling term coefficient matrix J, so that the integer decomposition problem is converted into an Ising model which can be processed by a qbsolv software environment.

As a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: the generalized target value limiting conditions include,

x_i+x_j+x_k＝1→x_ix_j＝x_jx_k＝x_ix_k＝0

1+c_z＝0→c_z＝1

wherein p is_i，q_i，x_i，x_j，x_kRepresenting bits of a multiplier, c_zRepresenting carry, all variables p_i，q_i，x_i，x_j，x_k，c_zAre all binary and take values of {0,1 }.

As a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: including, the decomposition integers N ═ p × q (p ═ 10bit, q ═ 10bit)

And p and q are two prime factors of the integer N to be decomposed, and the integer multiplication table is continuously updated and classified through the limitation of the structure information, the carry information and the target value information of the integer binary multiplication table.

As a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: the method comprises the steps of carrying out preprocessing optimization on a high-order column and a low-order column of an integer binary multiplication table, and carrying out multi-module distributed independent processing.

As a preferred scheme of the universal method for the million bit integer decomposition based on the quantum annealing algorithm, the method comprises the following steps: introducing an auxiliary variable according to a dimension reduction formula to perform dimension reduction operation on a polynomial of a target function which is more than 2-degree terms, including,

the invention has the beneficial effects that: on one hand, the D-Wave quantum annealing deciphering RSA needs to be considered to convert an integer decomposition problem into an exponential decomposition space search problem, a global optimal solution is obtained by means of quantum tunneling effect, and the key point is to convert the limiting condition of an actual problem into the weight and the coupling strength of a quantum bit, so that once the target function obtains the minimum value, and under the condition of meeting the limiting condition, the minimum value of the target function corresponds to the solution of the actual problem; on the other hand, the final model of target value limitation is not considered in the conventional integer decomposition algorithm based on quantum annealing, so that too many carry variables are introduced into the model, and the scale of the decomposed integer is limited.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:

FIG. 1 is a flow chart of a general method for million bit integer decomposition based on quantum annealing algorithm according to an embodiment of the present invention;

FIG. 2 is a block diagram of a generalized model framework of a large number decomposition based on D-Wave quantum annealing attack RSA of the generalized method of million-bit integer decomposition based on quantum annealing algorithm according to an embodiment of the present invention;

fig. 3 is a comparison diagram of performance tests of a general method of million-bit integer decomposition based on a quantum annealing algorithm according to an embodiment of the present invention.

Detailed Description

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.

Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.

The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.

Meanwhile, in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation and operate, and thus, cannot be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.

Example 1

Referring to fig. 1 and 2, for a first embodiment of the present invention, there is provided a general method of million bit integer decomposition based on a quantum annealing algorithm, comprising:

s1: the integer binary multiplication table is continuously updated and columnar based on the information limitations of the integer binary multiplication table.

S2: and constructing an objective function for the integer binary multiplication table after column division, and simplifying the objective function of each column through square item attributes.

S3: and introducing an auxiliary variable according to a dimension reduction formula to perform dimension reduction operation on the polynomial of the objective function which is more than 2-degree term.

S4: and performing variable replacement on the target function of each column respectively to transform the value range from {0,1} to { -1,1 }.

S5: and inputting the final local field coefficient matrix h and the coupling term coefficient matrix J of the objective function into a quantum computing qbsolv software environment to execute a quantum annealing process.

S6: and finally outputting the minimum value of energy, wherein the minimum value corresponds to a solution of successful integer decomposition.

Specifically, the information includes:

structure information, carry information, and target value information;

the square term attribute includes the number of square terms,

respectively carrying out variable replacement (1-s) on the target function of each column_i)/2,s_i∈{-1,1},i＝1,2,3,L；

And extracting the single term coefficient and the quadratic term coefficient of each column of objective function as a local field coefficient matrix h and a coupling term coefficient matrix J, so that the integer decomposition problem is converted into an Ising model which can be processed by a qbsolv software environment.

Further, the generalized target value limiting conditions include:

x_i+x_j+x_k＝1→x_ix_j＝x_jx_k＝x_ix_k＝0

1+c_z＝0→c_z＝1

wherein p is_i，q_i，x_i，x_j，x_kRepresenting bits of a multiplier, c_zRepresenting carry, all variables p_i，q_i，x_i，x_j，x_k，c_zThe values are all binary and are {0,1 };

decomposition integers N ═ p × q (p ═ 10bit, q ═ 10bit)

Wherein, p and q are two prime factors of the integer N to be decomposed, and the integer multiplication table is continuously updated and classified through the limitation of the structure information, the carry information and the target value information of the integer binary multiplication table;

and preprocessing and optimizing the high-order column and the low-order column of the integer binary multiplication table, and performing multi-module distributed independent processing.

Preferably, the introducing of the auxiliary variable according to the dimension reduction formula performs dimension reduction operation on the polynomial of the objective function which is greater than the 2-degree term, and the method comprises the following steps:

the target function of each column can obtain a solution set, the solution sets of each column are combined through classical calculation, common solutions are taken out, solutions which are successful in integer decomposition always exist in the common solution sets, and finally, which solutions in the common solutions enable the integer decomposition to be successful are verified.

Example 2

Referring to fig. 3, a second embodiment of the present invention, which is different from the first embodiment, provides an experimental comparison of a general method for million bit integer decomposition based on quantum annealing algorithm, specifically including:

in order to better verify and explain the technical effects adopted in the method of the invention, the embodiment selects the traditional Shor algorithm and the method of the invention to carry out comparison test, and compares the test results by means of scientific demonstration to verify the real effect of the method of the invention.

The traditional Shor algorithm works by reducing the factorization problem to an order-solving problem. There have been many attempts to implement the Shor algorithm on quantum computing hardware so far, the general quantum device is still in the primary stage, and the Shor algorithm based on the general quantum circuit breaks the public key cryptography and still stays in the theoretical stage, resulting in the limitation of the decomposable integer scale.

In order to verify that the method of the invention can better reduce the number of quantum bits required by integer decomposition compared with the traditional Shor algorithm under the condition of meeting the limiting condition, thereby reducing the requirement of quantum hardware and decomposing larger-scale integers, the traditional Shor algorithm and the method of the invention are adopted in the embodiment to respectively carry out real-time measurement and comparison on the test sample of the simulation platform.

And (3) testing environment: the running program packages of the two methods are led into a simulation platform for simulation running, an RSA password system is used as a test sample, decomposition test is carried out by respectively utilizing a Shor algorithm of a traditional method, test result data are obtained, by adopting the method, automatic test equipment is started, MATLB is used for realizing simulation test of the method, simulation data are obtained according to the experiment results, 1000 groups of data are tested by each method, the time for obtaining each group of data is calculated, and comparison error calculation is carried out on the time and the actual predicted value input by simulation.

Referring to fig. 3, a solid line is a curve output by the method of the present invention, a dotted line is a curve output by a conventional method, and it can be seen intuitively from the schematic diagram of fig. 3 that the solid line and the dotted line show different trends along with the increase of simulation time, the solid line shows a stable rising trend in the former period compared with the dotted line, although the solid line slides down in the latter period, the fluctuation is not large and is always above the dotted line and keeps a certain distance, and the dotted line shows a large fluctuation trend and is unstable, so that the resolving power of the solid line is always greater than that of the dotted line, i.e. the true effect of the method of the present invention is verified.

It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.