CN109657478B - Isomerization quantification method and system - Google Patents
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- 238000004364 calculation method Methods 0.000 claims description 6
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- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/50—Monitoring users, programs or devices to maintain the integrity of platforms, e.g. of processors, firmware or operating systems
- G06F21/57—Certifying or maintaining trusted computer platforms, e.g. secure boots or power-downs, version controls, system software checks, secure updates or assessing vulnerabilities
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- G06F2221/00—Indexing scheme relating to security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F2221/03—Indexing scheme relating to G06F21/50, monitoring users, programs or devices to maintain the integrity of platforms
- G06F2221/034—Test or assess a computer or a system
Abstract
The application discloses a method and a system for quantifying isomerism, wherein the method comprises the following steps: determining complexity C of an executive component set K Determining differences FD of an executive component set Qk Based on the formulaThe heterogeneity of the executable set is calculated. The method can quantify isomerism through complexity and diversity, has certain universality, and can be applied to not only isomerism redundant systems, but also safety systems similar to isomerism redundant architectures.
Description
Technical Field
The application relates to the technical field of network security, in particular to a method and a system for quantifying isomerism.
Background
The network space is widely provided with loopholes and backdoors, and security events are continuously generated due to the unification of software and hardware of the network space. In order to solve the problem, a plurality of novel defense technologies based on software and hardware diversity are continuously presented, but the specific implementation means of the diversity are different from the target. The heterogeneous redundancy technology is based on diversified technologies, adopts the framework of a heterogeneous redundancy system, and uses the characteristics of isomerism, redundancy and the like to enable the system to have a better safety mechanism so as to improve the safety of the system. While heterogeneous redundancy technology has proven its effectiveness in engineering practice, it is controversial in terms of how much security gain it can bring, because it is difficult to quantitatively evaluate.
The existing quantitative isomerism method is mainly realized by methods of similarity and complexity quantification. Different distance functions are generally selected according to different application fields so as to achieve better description effect. However, these distance functions are often used in the situation of low dimension, and if they are simply used in high-dimensional data, the conclusion is often meaningless, and the attribute dimension of the execution body of the heterogeneous redundant system is high, which is obviously not suitable for the method. The existing method for quantifying the abnormal shape has certain defects: calculating the similarity between features by a method of maximum information compression index, which requires defining the relationship between attribute values, which definition may lead to inaccurate quantization; the method for determining the approximate entropy has the advantages that the complexity of the system is determined, the problem of lower relative consistency is not well solved, and the inter-execution body difference of the heterogeneous redundant system cannot be quantified; the fuzzy probability model formally describes assumptions and problems, and draws validity conclusion of diversity through reasoning, and although the conclusion proves that the heterogeneous redundancy technology can ensure to improve the reliability of the system under a certain mode, a specific quantitative evaluation method is not provided. The clustering algorithm is only applicable to the case of large-scale data, and cannot be used to quantify the heterogeneity of heterogeneous redundant systems containing a small number of executives.
Therefore, how to effectively quantify isomerism is a problem to be solved.
Disclosure of Invention
In view of this, the present application provides a method for quantifying isomerism, which can quantify isomerism through complexity and diversity, and has a certain versatility, and can be applied not only to isomerism redundancy systems, but also to security systems similar to isomerism redundancy architecture.
The application provides a method for quantifying isomerism, which comprises the following steps:
determining complexity C of an executive component set K ；
Determining differences FD of an executive component set Qk ；
Based on the formulaThe heterogeneity of the executable set is calculated.
Preferably, the determining the complexity C of the executable build set K Comprising the following steps:
based on the formulaDetermining complexity C of an executive component set K Wherein S represents the number of component types contained in the actuator component set, and p ki Representing the proportion of software or hardware i in the set of executable components.
Preferably, the determining performs the differences FD of the body member set Qk Comprising the following steps:
based on formula FDDetermining differences FD of an executive component set Qk Wherein d kij Is a key parameter for differential quantization, representing the difference between two software or hardware in the set of executive components i, j.
A system for quantifying isomerism, comprising:
a first determination module for determining the complexity C of the execution body member set K ；
A second determination module for determining the differences FD of the execution body member sets Qk ；
A calculation module for based on formulaThe heterogeneity of the executable set is calculated.
Preferably, the first determining module is specifically configured to:
based on the formulaDetermining complexity C of an executive component set K Wherein S represents the number of component types contained in the actuator component set, and p ki Representing the proportion of software or hardware i in the set of executable components.
Preferably, the second determining module is specifically configured to:
based on the formulaDetermining differences FD of an executive component set Qk Wherein d kij Is a key parameter for differential quantization, representing the difference between two software or hardware in the set of executive components i, j.
In summary, the present application discloses a method for quantifying isomerism, when isomerism is required to be quantified, firstly determining the complexity C of an execution body component set K And determining differences FD of the set of effector members Qk Then based on the formulaThe heterogeneity of the executable set is calculated. The method quantifies isomerism through complexity and diversity, has certain universality, and can be applied to isomerism redundant systems, and can also be applied to the method for detecting isomerismCan be applied to a security system similar to a heterogeneous redundancy architecture.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an embodiment 1 of a method for quantifying isomerism disclosed herein;
FIG. 2 is a flow chart of embodiment 2 of a method for quantifying isomerism disclosed herein;
FIG. 3 is a schematic diagram of an embodiment 1 of a heterogeneous quantization system disclosed in the present application;
fig. 4 is a schematic structural diagram of an embodiment 2 of a heterogeneous quantization system disclosed in the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
Aiming at the limitations of the existing isomerism quantification method, the purpose of the application is to provide a quantification method suitable for quantifying isomerism, the complexity degree of the types of executives cannot show the degree of the existence of the same loopholes among the executives, so the degree of the existence of the same loopholes among the executives is more needed to be shown when the isomerism of an isomerism redundancy system is defined, and the degree of the existence of the same loopholes among all the executives is defined as the degree of the difference among the executives because the known loopholes and the unknown loopholes in all the executives are difficult to mine, so the fact proves that the possibility of existence of symbiotic loopholes is lower if two software are different.
As shown in fig. 1, which is a flowchart of an embodiment 1 of a method for quantifying isomerism disclosed in the present application, the method may include the following steps:
s101, determining the complexity C of the executive component set K ；
When the isomerism needs to be quantified, the complexity of the set of executive components is first determined.
S102, determining the difference FD of the executive component set Qk ；
At the same time, the differences in the set of executive body components are determined.
S103, based on formulaThe heterogeneity of the executable set is calculated.
And finally, calculating the isomerism of the execution body set according to the determined complexity and the determined difference. It should be noted that, the greater the inter-executable isomerism in the system executable set, the lower the existence probability of symbiotic vulnerabilities, the lower the probability of causing a system consistent attack effect, and the higher the system security. Therefore, when evaluating the safety of the heterogeneous redundant system, the isomerism of the execution set in the system can be used as one of the indexes for evaluating the safety. In the engineering practice of the heterogeneous redundancy system, the execution body set is not selected to be composed of the identical execution bodies, so when the isomerism of the execution body set is discussed in the application, the situation that the execution body set contains the identical execution bodies is not included.
In summary, in the above embodiment, when the isomerism needs to be quantified, the complexity C of the execution volume component set is first determined K And determining differences FD of the set of effector members Qk Then based on the formulaThe heterogeneity of the executable set is calculated. The method quantifies isomerism through complexity and diversity, has certain universality, and can be applied to isomerism redundant systemsBut also to security systems like heterogeneous redundancy architecture.
As shown in fig. 2, which is a flowchart of embodiment 2 of a method for quantifying isomerism disclosed in the present application, the method may include the following steps:
s201, based on formulaDetermining complexity C of an executive component set K ；
When the isomerism needs to be quantified, some basic definitions are given in advance:
(1) System component set: a set of components of some kind of functionally equivalent software or hardware of all executives (including both online and offline executives) of a pseudo-structured web server, denoted as E k ＝{E kj |E kj Is one kind of software or hardware of the system and satisfies any two kinds of software and hardware E kp And E is connected with kq Where p+.q, j=1, 2, … …, m }, if operating system is taken as a class of functionally equivalent software, the set of operating systems is { centros 6.5,Debian 7.0,Ubuntu 14.10,Ubuntu 16.10,Windows Server 2008,Windows Server 2012}.
(2) Feature matrix of the execution volume set: the feature matrix of the executable set A of the mimicry-structured web server may be formally described as:
wherein each column represents an execution body, each row represents a type of functionally equivalent software and hardware, and n is the number of execution bodies in the execution body set. Each eigenvalue of the eigenvalue matrix C represents a software and hardware number, not a mathematically operable number.
(3) Component set of execution volume set: the k-th class of functionally equivalent software or hardware of the execution volume set A is recorded as EC k ＝{EC kj |EC kj Is a software or hardware of the execution body set A and satisfies anyTwo kinds of software and hardware EC kp And EC (EC) kq Where p noteq, j = 1,2, … …, m }.
Wherein, attention is paid to E k And EC (EC) k Is different from E k The execution bodies in the execution body set A comprise an execution body with an upper line and an execution body with a lower line, and EC k The component set of (2) is only for the on-line execution body, so:
in the case of quantitative isomerization, C k Representing the complexity of the execution volume set, complexity C in the formula k Quantization can be performed by using a method for quantizing biological diversity, and the shannon diversity index is used for estimating the complexity of an executive body set. Component set E of execution volume set k The complexity calculation formula of (2) is as follows:
for heterogeneous redundant systems, S represents the set of executive components EC k The number of the contained component types, software or hardware i in the component set EC k The proportion of (2) is denoted as p ki . When executing the body component set EC k When only one software or hardware exists, the shannon index reaches a minimum value of 0; when executing the body component set EC k Where there are more than two types of software or hardware, and there is only one member for each component, the shannon index reaches a maximum lnS.
Wherein p is ki Relative abundance eigenvector: component set EC of actuator A k The vector of each component in the abundance of the total number of such total components is denoted pk= (pk 1, pk2,.. kS ) T ，p ki C is ki And the richness of the same components, and
s202, based on formulaDetermining differences FD of an executive component set Qk ；
Then determining the differences FD of the executive component sets Qk ，FD Qk To perform the differential quantification of the volumes, this value is measured using the method of quadratic entropy, which can calculate the squared distance between any two randomly selected population members, rao proposes a method of differential quadratic entropy between fusion species as a measure of biodiversity. Many researchers have proposed research methods to quantify the relative abundance of species and the relative variability between species based on the second entropy of Rao, performing a set of body building blocks EC k The difference of (2) is calculated as follows:
wherein d kij Is a key parameter for the differential quantization of the executive body of the heterogeneous redundant system and represents a component set EC k Differences between the two software or hardware of i, j (d kij ＝d kji ，d kii ＝0)。d kij The values may be arbitrarily defined as long as d is satisfied kij ＝d kji And d kii The limitation of =0 is sufficient. The application determines d by calculating the probability that two components contain different vulnerabilities kij . If for all d kij =1, i+.j, and satisfy again the set of executable components EC k Where there are more than two types of software or hardware, and there is only one member for each component, then the second entropy becomes the Simpson index, FD Qk Has a maximum value (1-1/S). If the body component set EC is executed k When only one software or hardware exists, then for all d kij =0, i+.j, and FD Qk There is a minimum value of 0. D when the ratio of the i and j software or hardware is fixed kij The larger the execution volume difference is, the larger d kij The values of (2) are as follows:
wherein v is ki And v kj Respectively means the component c ki And c kj Number of loopholes contained, v kij Representing component c ki And c kj Contains the same number of loopholes and 0.ltoreq.d kij ≤1。
S203, based on formulaThe heterogeneity of the executable set is calculated.
And finally, calculating the isomerism of the execution body set according to the determined complexity and the determined difference. According to the isomerism quantization formula, the isomerism of the executable set has the following properties:
property 1, if the executor of the executor set A satisfies A 1 ＝A 2 ＝……＝A n The isomerism of the execution volume set reaches a minimum value H min ＝0；
Property 2, if the executor of the executable set A satisfies A 1 ≠A 2 ≠……≠A n And any two members in the same type of member set of any executing body set satisfy c ki ≠c kj I+.j, the heterogeneity of the execution volume set reaches a maximum, the formula is as follows:
property 3 reducibility: if the executing body set A has x-type component sets, any two components in each type component set satisfy c ki ＝c kj I.noteq.j, H A ＝H A' Wherein A' is the execution body set after A reduces the x-type component set.
From property 2, it can be derived that the isomerism H of an execution set is related to the differences of its component set class M, the component class S contained in each class of component set, and the components in the same component set. In the case where there is a difference in the members within the execution volume set, the isomerism of the execution volume set may be different even if S and M are the same; similarly, even if the executing set has the same isomerism, S and M may be different, so when selecting a member, a member composition set having a large difference is selected, and the isomerism of the member set is increased.
In summary, the present application is mainly characterized by having a certain versatility, and can be applied to not only heterogeneous redundancy systems, but also security systems similar to heterogeneous redundancy architecture.
As shown in fig. 3, a schematic structural diagram of an embodiment 1 of a heterogeneous quantization system disclosed in the present application, where the system may include:
a first determining module 301 for determining a complexity C of the set of executable components K ；
When the isomerism needs to be quantified, the complexity of the set of executive components is first determined.
A second determination module 302 for determining a differential FD of the set of executive body members Qk ；
At the same time, the differences in the set of executive body components are determined.
A calculation module 303 for formula-basedThe heterogeneity of the executable set is calculated.
And finally, calculating the isomerism of the execution body set according to the determined complexity and the determined difference. It should be noted that, the greater the inter-executable isomerism in the system executable set, the lower the existence probability of symbiotic vulnerabilities, the lower the probability of causing a system consistent attack effect, and the higher the system security. Therefore, when evaluating the safety of the heterogeneous redundant system, the isomerism of the execution set in the system can be used as one of the indexes for evaluating the safety. In the engineering practice of the heterogeneous redundancy system, the execution body set is not selected to be composed of the identical execution bodies, so when the isomerism of the execution body set is discussed in the application, the situation that the execution body set contains the identical execution bodies is not included.
In summary, in the above embodiment, when the isomerism needs to be quantified, the execution volume component set is first determinedComplexity C K And determining differences FD of the set of effector members Qk Then based on the formulaThe heterogeneity of the executable set is calculated. The method is characterized in that the isomerism is quantified through complexity and diversity, and the method has certain universality, and can be applied to not only isomerism redundant systems, but also safety systems similar to isomerism redundant architectures.
As shown in fig. 4, a schematic structural diagram of an embodiment 2 of a heterogeneous quantization system disclosed in the present application, where the system may include:
a first determining module 401 for formula-basedDetermining complexity C of an executive component set K ；
When the isomerism needs to be quantified, some basic definitions are given in advance:
(1) System component set: a set of components of some kind of functionally equivalent software or hardware of all executives (including both online and offline executives) of a pseudo-structured web server, denoted as E k ＝{E kj |E kj Is one kind of software or hardware of the system and satisfies any two kinds of software and hardware E kp And E is connected with kq Where p+.q, j=1, 2, … …, m }, if operating system is taken as a class of functionally equivalent software, the set of operating systems is { centros 6.5,Debian 7.0,Ubuntu 14.10,Ubuntu 16.10,Windows Server 2008,Windows Server 2012}.
(2) Feature matrix of the execution volume set: the feature matrix of the executable set A of the mimicry-structured web server may be formally described as:
wherein each column represents an execution body, each row represents a type of functionally equivalent software and hardware, and n is the number of execution bodies in the execution body set. Each eigenvalue of the eigenvalue matrix C represents a software and hardware number, not a mathematically operable number.
(3) Component set of execution volume set: the k-th class of functionally equivalent software or hardware of the execution volume set A is recorded as EC k ＝{EC kj |EC kj Is one software or hardware of the execution body set A and meets any two kinds of software and hardware EC kp And EC (EC) kq Where p noteq, j = 1,2, … …, m }.
Wherein, attention is paid to E k And EC (EC) k Is different from E k The execution bodies in the execution body set A comprise an execution body with an upper line and an execution body with a lower line, and EC k The component set of (2) is only for the on-line execution body, so:
in the case of quantitative isomerization, C k Representing the complexity of the execution volume set, complexity C in the formula k Quantization can be performed by using a method for quantizing biological diversity, and the shannon diversity index is used for estimating the complexity of an executive body set. Component set E of execution volume set k The complexity calculation formula of (2) is as follows:
for heterogeneous redundant systems, S represents the set of executive components EC k The number of the contained component types, software or hardware i in the component set EC k The proportion of (2) is denoted as p ki . When executing the body component set EC k When only one software or hardware exists, the shannon index reaches a minimum value of 0; when executing the body component set EC k Where there are more than two types of software or hardware, and there is only one member for each component, the shannon index reaches a maximum lnS.
Wherein p is ki Relative abundance eigenvector: component set of actuator AEC k The vector of each component in the abundance of the total number of such total components is denoted pk= (pk 1, pk2,.. kS ) T ，p ki C is ki And the richness of the same components, and
a second determination module 402 for formula-basedDetermining differences FD of an executive component set Qk ；
Then determining the differences FD of the executive component sets Qk ，FD Qk To perform the differential quantification of the volumes, this value is measured using the method of quadratic entropy, which can calculate the squared distance between any two randomly selected population members, rao proposes a method of differential quadratic entropy between fusion species as a measure of biodiversity. Many researchers have proposed research methods to quantify the relative abundance of species and the relative variability between species based on the second entropy of Rao, performing a set of body building blocks EC k The difference of (2) is calculated as follows:
wherein d kij Is a key parameter for the differential quantization of the executive body of the heterogeneous redundant system and represents a component set EC k Differences between the two software or hardware of i, j (d kij ＝d kji ，d kii ＝0)。d kij The values may be arbitrarily defined as long as d is satisfied kij ＝d kji And d kii The limitation of =0 is sufficient. The application determines d by calculating the probability that two components contain different vulnerabilities kij . If for all d kij =1, i+.j, and satisfy again the set of executable components EC k When two or more kinds of software or hardware exist and each member has only one member, the second entropy becomes the simpson index,FD Qk has a maximum value (1-1/S). If the body component set EC is executed k When only one software or hardware exists, then for all d kij =0, i+.j, and FD Qk There is a minimum value of 0. D when the ratio of the i and j software or hardware is fixed kij The larger the execution volume difference is, the larger d kij The values of (2) are as follows:
wherein v is ki And v kj Respectively means the component c ki And c kj Number of loopholes contained, v kij Representing component c ki And c kj Contains the same number of loopholes and 0.ltoreq.d kij ≤1。
A calculation module 403 for formula-basedThe heterogeneity of the executable set is calculated.
And finally, calculating the isomerism of the execution body set according to the determined complexity and the determined difference. According to the isomerism quantization formula, the isomerism of the executable set has the following properties:
property 1, if the executor of the executor set A satisfies A 1 ＝A 2 ＝……＝A n The isomerism of the execution volume set reaches a minimum value H min ＝0；
Property 2, if the executor of the executable set A satisfies A 1 ≠A 2 ≠……≠A n And any two members in the same type of member set of any executing body set satisfy c ki ≠c kj I+.j, the heterogeneity of the execution volume set reaches a maximum, the formula is as follows:
property 3 reducibility: if the executing body set A has x-type component sets, any two components in each type component setPart satisfies c ki ＝c kj I.noteq.j, H A ＝H A' Wherein A' is the execution body set after A reduces the x-type component set.
From property 2, it can be derived that the isomerism H of an execution set is related to the differences of its component set class M, the component class S contained in each class of component set, and the components in the same component set. In the case where there is a difference in the members within the execution volume set, the isomerism of the execution volume set may be different even if S and M are the same; similarly, even if the executing set has the same isomerism, S and M may be different, so when selecting a member, a member composition set having a large difference is selected, and the isomerism of the member set is increased.
In summary, the present application is mainly characterized by having a certain versatility, and can be applied to not only heterogeneous redundancy systems, but also security systems similar to heterogeneous redundancy architecture.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative elements and steps are described above generally in terms of functionality in order to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software modules may be disposed in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (2)
1. A method for quantifying isomerism, comprising:
determining complexity C of an executive component set K ；
Determining differences FD of an executive component set Qk ；
Based on the formulaCalculating the isomerism of the execution body set;
the execution bodies in the execution body set are different;
complexity C of the determining execution volume build set K Comprising the following steps:
based on the formulaDetermining complexity C of an executive component set K Wherein S represents the number of component types contained in the actuator component set, and p ki Representing the proportion of software or hardware i in the set of executable components;
the formula is based onCalculating the heterogeneity of the executable set, comprising:
if the executor of the executor set A meets A 1 ＝A 2 ＝……＝A n The isomerism of the executing body set A reaches a minimum value H min ＝0；
If the executor of the executor set A meets A 1 ≠A 2 ≠……≠A n And any two members in the same type of member set of any executing body set satisfy c ki ≠c kj I+.j, the heterogeneity of the execution volume set reaches a maximum, the formula is as follows:
if the executing body set A has x-type component sets, any two components in each type component set satisfy c ki ＝c kj I.noteq.j, H A ＝H A' Wherein A' is an execution body set after A reduces the x-type component set;
the differences FD of the set of determined executive components Qk Comprising the following steps:
based on the formulaDetermining differences FD of an executive component set Qk Wherein d kij Is a key parameter for differential quantization, representing the difference between two software or hardware in the set of executive components i, j.
2. A system for quantifying isomerism, comprising:
a first determination module for determining the complexity C of the execution body member set K ；
A second determination module for determining the differences FD of the execution body member sets Qk ；
A calculation module for based on formulaCalculating the isomerism of the execution body set;
the execution bodies in the execution body set are different;
the first determining module is specifically configured to:
based on the formulaDetermining complexity C of an executive component set K Wherein S represents the number of component types contained in the actuator component set, and p ki Representing the proportion of software or hardware i in the set of executable components;
the computing module is specifically configured to:
if the executor of the executor set A meets A 1 ＝A 2 ＝……＝A n The isomerism of the executing body set A reaches a minimum value H min ＝0；
If the executor of the executor set A meets A 1 ≠A 2 ≠……≠A n And any two members in the same type of member set of any executing body set satisfy c ki ≠c kj I+.j, the heterogeneity of the execution volume set reaches a maximum, the formula is as follows:
if the executing body set A has x-type component sets, any two components in each type component set satisfy c ki ＝c kj I.noteq.j, H A ＝H A' Wherein A' is an execution body set after A reduces the x-type component set;
the second determining module is specifically configured to:
based on the formulaDetermining differences FD of an executive component set Qk Wherein d kij Is a key parameter for differential quantizationRepresenting the difference between the two software or hardware in the set of executive components i, j.
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| CN112035838B (en) * | 2020-07-30 | 2022-11-18 | 中国人民解放军战略支援部队信息工程大学 | Conditional probability voting method and device based on execution body isomerism |
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