阅读说明：本技术 一种侧信道曲线特征提取方法及装置 (Side channel curve feature extraction method and device ) 是由 陈佳哲 魏伟 石竑松 王永涛 成林 刘宏伟 于 2021-08-16 设计创作，主要内容包括：本发明公开了一种侧信道曲线特征提取方法及装置,包括：对原始侧信道曲线中的各个点进行预处理,获得目标侧信道曲线；在所述目标侧信道曲线中确定参照特征,并基于所述参照特征和所述目标侧信道曲线进行分析,获得相关性曲线。确定预设参数,并对所述预设参数进行参数调整,得到目标参数；基于所述目标参数和所述相关性曲线,在原始侧信道曲线中进行特征提取,获得特征信息。本发明利用信号处理后的曲线计算相关性,提高了特征提取的准确性,并且可以在特征提取之前对预设参数进行调整,避免固定参数提取的不准确的问题。(The invention discloses a side channel curve characteristic extraction method and a side channel curve characteristic extraction device, wherein the side channel curve characteristic extraction method comprises the following steps: preprocessing each point in the original side channel curve to obtain a target side channel curve; and determining a reference characteristic in the target side channel curve, and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve. Determining preset parameters, and performing parameter adjustment on the preset parameters to obtain target parameters; and extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information. The invention utilizes the curve after signal processing to calculate the correlation, improves the accuracy of feature extraction, can adjust the preset parameters before feature extraction, and avoids the problem of inaccurate fixed parameter extraction.)

1. A side channel curve feature extraction method is characterized by comprising the following steps:

preprocessing each point in the original side channel curve to obtain a target side channel curve;

determining a reference characteristic in the target side channel curve, and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve;

determining preset parameters, and performing parameter adjustment on the preset parameters to obtain target parameters;

and extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information.

2. The method of claim 1, wherein the preprocessing each point in the original side-channel curve to obtain the target side-channel curve comprises:

acquiring an original side channel curve;

carrying out numerical value processing and filtering processing on each point of the original side channel curve to obtain each processed point;

and determining a target side channel curve based on the processed points.

3. The method of claim 1, wherein the analyzing based on the reference feature and the target-side channel profile to obtain a correlation profile comprises:

calculating a correlation coefficient of the reference characteristic and the target side channel curve;

based on the correlation coefficient, a correlation curve is determined.

4. The method of claim 1, wherein the preset parameters comprise:

the starting point of the curve for starting to extract the feature, the interval between two features, the length of the feature to be extracted and the position of the feature for starting to extract.

5. The method according to claim 4, wherein the adjusting the preset parameter to obtain the target parameter comprises:

carrying out curve extraction on the correlation curves to obtain a plurality of curves;

obtaining the distance between the point corresponding to the maximum value in the adjacent interval based on the point corresponding to the maximum value in each curve;

removing abnormal distances based on the distances, and calculating the removed distances to obtain a target spacing distance between the two features;

and adjusting the interval between the two features based on the target interval distance to obtain a target parameter.

6. The method of claim 1, wherein the feature information comprises:

the correlation value comprises a target feature, a target curve corresponding to the target feature in the original side channel curve, position information of the target feature in the target curve and a correlation value corresponding to the target feature.

7. A side channel curve feature extraction device, comprising:

the preprocessing unit is used for preprocessing each point in the original side channel curve to obtain a target side channel curve;

the analysis unit is used for determining a reference characteristic in the target side channel curve and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve;

the adjusting unit is used for determining preset parameters and adjusting the preset parameters to obtain target parameters;

and the extraction unit is used for extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information.

8. The apparatus of claim 7, wherein the pre-processing unit comprises:

the acquisition subunit is used for acquiring an original side channel curve;

the processing subunit is used for carrying out numerical processing and filtering processing on each point of the original side channel curve to obtain each processed point;

and the first determining subunit is used for determining the target side channel curve based on the processed points.

9. The apparatus of claim 7, wherein the analysis unit comprises:

a second determining subunit, configured to determine a reference feature in the target-side channel curve;

the calculating subunit is used for calculating a correlation coefficient between the reference characteristic and the target side channel curve;

a third determining subunit, configured to determine a correlation curve based on the correlation coefficient.

10. The apparatus of claim 7, wherein the preset parameters comprise: starting points of features to be extracted, interval intervals between two features, feature lengths to be extracted and feature positions to be extracted are arranged in the curve;

wherein the adjusting unit is specifically configured to:

determining preset parameters;

carrying out curve extraction on the correlation curves to obtain a plurality of curves;

obtaining the distance between the point corresponding to the maximum value in the adjacent interval based on the point corresponding to the maximum value in each curve;

removing abnormal distances based on the distances, and calculating the removed distances to obtain a target spacing distance between the two features;

and adjusting the interval between the two features based on the target interval distance to obtain a target parameter.

Technical Field

The invention relates to the technical field of information processing, in particular to a side channel curve feature extraction method and device.

Background

During the operation of the cryptographic algorithm in the chip, some leaked physical information may be generated, for example, the leaked physical information may include power consumption, electromagnetic signals, and the like, and the information is often related to the intermediate operation process of the cryptographic algorithm, and even a secret key. The side channel analysis uses equipment such as an oscilloscope and the like to record the physical information to form a side channel curve, and the cryptographic algorithm running in the chip is analyzed through the physical information.

In the side channel analysis of the public key cryptographic algorithm, it is often necessary to extract a part of features in the side channel curve for further analysis. The existing side channel curve feature extraction method is that cross correlation calculation is carried out on a reference feature and a target side channel curve, a minimum correlation parameter is set, if the calculated correlation is larger than the minimum correlation, the feature is extracted, the extracted feature is extracted from a plurality of points before the current point for calculating the correlation, and the extraction is finished after a plurality of points of the extraction length are referred. Some information may be recorded in the extracted curve, including the position of the extracted curve in the original curve, the position of the extracted curve in the curve, and the like.

However, in the feature extraction method, correlation calculation and feature extraction are completed together, and a curve cannot be preprocessed, so that the accuracy of extracted features is reduced, and all the extraction processes determine the minimum correlation parameter, so that the extracted features include certain non-attention features, and therefore the extracted features are not accurate enough and may not meet actual requirements.

Disclosure of Invention

In view of the above problems, the present invention provides a method and an apparatus for extracting side channel curve features, so as to improve the accuracy of the extracted side channel curve features.

In order to achieve the purpose, the invention provides the following technical scheme:

a side channel curve feature extraction method comprises the following steps:

preprocessing each point in the original side channel curve to obtain a target side channel curve;

determining a reference characteristic in the target side channel curve, and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve;

determining preset parameters, and performing parameter adjustment on the preset parameters to obtain target parameters;

and extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information.

Optionally, the preprocessing each point in the original side channel curve to obtain a target side channel curve includes:

acquiring an original side channel curve;

carrying out numerical value processing and filtering processing on each point of the original side channel curve to obtain each processed point;

and determining a target side channel curve based on the processed points.

Optionally, the analyzing based on the reference feature and the target side channel curve to obtain a correlation curve includes:

calculating a correlation coefficient of the reference characteristic and the target side channel curve;

based on the correlation coefficient, a correlation curve is determined.

Optionally, the preset parameters include:

the starting point of the curve for starting to extract the feature, the interval between two features, the length of the feature to be extracted and the position of the feature for starting to extract.

Optionally, the performing parameter adjustment on the preset parameter to obtain a target parameter includes:

carrying out curve extraction on the correlation curves to obtain a plurality of curves;

obtaining the distance between the point corresponding to the maximum value in the adjacent interval based on the point corresponding to the maximum value in each curve;

removing abnormal distances based on the distances, and calculating the removed distances to obtain a target spacing distance between the two features;

and adjusting the interval between the two features based on the target interval distance to obtain a target parameter.

Optionally, the feature information includes:

the correlation value comprises a target feature, a target curve corresponding to the target feature in the original side channel curve, position information of the target feature in the target curve and a correlation value corresponding to the target feature.

A side-channel curve feature extraction apparatus comprising:

the preprocessing unit is used for preprocessing each point in the original side channel curve to obtain a target side channel curve;

and the analysis unit is used for determining a reference characteristic in the target side channel curve and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve.

The adjusting unit is used for determining preset parameters and adjusting the preset parameters to obtain target parameters;

and the extraction unit is used for extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information.

Optionally, the pre-processing unit comprises:

the acquisition subunit is used for acquiring an original side channel curve;

the processing subunit is used for carrying out numerical processing and filtering processing on each point of the original side channel curve to obtain each processed point;

and the first determining subunit is used for determining the target side channel curve based on the processed points.

Optionally, the analysis unit comprises:

a second determining subunit, configured to determine a reference feature in the target-side channel curve;

the calculating subunit is used for calculating a correlation coefficient between the reference characteristic and the target side channel curve;

a third determining subunit, configured to determine a correlation curve based on the correlation coefficient.

Optionally, the preset parameters include: starting points of features to be extracted, interval intervals between two features, feature lengths to be extracted and feature positions to be extracted are arranged in the curve;

wherein the adjusting unit is specifically configured to:

determining preset parameters;

carrying out curve extraction on the correlation curves to obtain a plurality of curves;

obtaining the distance between the point corresponding to the maximum value in the adjacent interval based on the point corresponding to the maximum value in each curve;

removing abnormal distances based on the distances, and calculating the removed distances to obtain a target spacing distance between the two features;

and adjusting the interval between the two features based on the target interval distance to obtain a target parameter.

Optionally, the feature information includes:

the correlation value comprises a target feature, a target curve corresponding to the target feature in the original side channel curve, position information of the target feature in the target curve and a correlation value corresponding to the target feature.

Compared with the prior art, the invention provides a side channel curve feature extraction method and a side channel curve feature extraction device, and the method comprises the following steps: preprocessing each point in the original side channel curve to obtain a target side channel curve; and determining a reference characteristic in the target side channel curve, and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve. Determining preset parameters, and performing parameter adjustment on the preset parameters to obtain target parameters; and extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information. The invention utilizes the curve after signal processing to calculate the correlation, improves the accuracy of feature extraction, can adjust the preset parameters before feature extraction, and avoids the problem of inaccurate fixed parameter extraction.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.

Fig. 1 is a schematic flow chart of a side channel curve feature extraction method according to an embodiment of the present invention;

fig. 2 is a schematic diagram of a side channel curve of a public key cryptographic algorithm according to an embodiment of the present invention;

fig. 3 is a schematic diagram of a curve characteristic of a side channel curve after partial amplification according to an embodiment of the present invention;

fig. 4 is a schematic flow chart of another side channel curve feature extraction method according to an embodiment of the present invention;

fig. 5 is a schematic structural diagram of a side channel curve extraction apparatus according to an embodiment of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The terms "first" and "second," and the like in the description and claims of the present invention and the above-described drawings are used for distinguishing between different objects and not for describing a particular order. Furthermore, the terms "comprising" and "having," as well as any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not set forth for a listed step or element but may include steps or elements not listed.

In the embodiment of the present invention, a side channel curve feature extraction method is provided, and referring to fig. 1, the method may include the following steps:

s101, preprocessing each point in the original side channel curve to obtain a target side channel curve.

Referring to fig. 2, a schematic diagram of a side channel curve of a public key cryptographic algorithm is shown, that is, an original side channel curve in the embodiment of the present invention is an unprocessed side channel curve directly obtained from the cryptographic algorithm. After the curve features of the block portion in fig. 2 are enlarged, the enlarged curve features shown in fig. 3 are obtained, which include some periodic features, and the extraction of these features can be used for subsequent statistical analysis, machine learning analysis, and the like.

In order to extract features more accurately in the embodiment of the present invention, each point in the original side channel curve needs to be preprocessed, wherein a signal processing method for making the features more obvious is mainly adopted. For example, in one possible implementation, the preprocessing each point in the original side channel curve to obtain the target side channel curve includes: acquiring an original side channel curve; carrying out numerical value processing and filtering processing on each point of the original side channel curve to obtain each processed point; and determining a target side channel curve based on the processed points.

In this embodiment, the numerical processing mainly includes a processing mode of taking an absolute value, and the filtering processing mainly includes a processing mode of low-pass filtering and median filtering derivation, and the like. It should be noted that, in the embodiment of the present invention, the signal processing method is not limited as long as the characteristic in the side channel curve can be made more obvious.

S102, determining a reference characteristic in the target side channel curve, and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve.

The reference feature is a relatively important feature determined by an analyst, such as a curve corresponding to a modulo multiplication and a modulo square of an SA algorithm in an encryption algorithm, a dot addition and a doubling dot of an ECC algorithm in the encryption algorithm, and the like.

And after the reference characteristic is obtained, performing cross correlation analysis by using the reference characteristic and the curve after signal processing to obtain a correlation curve.

S103, determining preset parameters, and adjusting the preset parameters to obtain target parameters.

The preset parameters can be understood as preliminarily determined parameters, and the parameters do not need to be particularly accurate, because the invention also comprises a parameter self-adaptive adjusting process, namely, the preset parameters are adjusted to obtain the target parameters. The aim of reducing the error rate by automatically adjusting the parameters according to the correlation curve by using a statistical method is fulfilled. The preset parameters include, but are not limited to: the starting point of starting to extract the feature in the curve, the interval between two features, the length of the feature to be extracted, the position of starting to extract the feature and the like, wherein the position of starting to extract the feature mainly refers to how many points ahead of time to start to extract the feature. The main purpose of automatically adjusting the parameters is to adjust the canon region between two features to overcome the problem that all features extracted in the prior art with correlation greater than the minimum correlation result in extraction of non-interesting features.

And S104, extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information.

In the characteristic extraction process, by using the target parameters obtained after the adjustment is completed, at intervals of every characteristic interval, according to the maximum value of the correlation curve in the interval, the characteristic corresponding to the required length of the original curve near the maximum value is provided, the number of the characteristic in the original curve and the position of the characteristic in the curve are recorded, and the value of the correlation corresponding to the characteristic is recorded. Therefore, in the embodiment of the present invention, the feature information extracted in the original side channel curve includes, but is not limited to: the correlation value comprises a target feature, a target curve corresponding to the target feature in the original side channel curve, position information of the target feature in the target curve and a correlation value corresponding to the target feature. The final extracted characteristic information can be determined according to the analysis requirement of the actual side channel curve.

The embodiment of the invention provides a side channel curve feature extraction method, which comprises the following steps: preprocessing each point in the original side channel curve to obtain a target side channel curve; and determining a reference characteristic in the target side channel curve, and analyzing based on the reference characteristic and the target side channel curve to obtain a correlation curve. Determining preset parameters, and performing parameter adjustment on the preset parameters to obtain target parameters; and extracting features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information. The invention utilizes the curve after signal processing to calculate the correlation, improves the accuracy of feature extraction, can adjust the preset parameters before feature extraction, and avoids the problem of inaccurate fixed parameter extraction.

In an implementation manner of the embodiment of the present invention, the analyzing based on the reference feature and the target side channel curve to obtain a correlation curve includes: calculating a correlation coefficient of the reference characteristic and the target side channel curve; based on the correlation coefficient, a correlation curve is determined.

I.e. in this embodiment the correlation curve is determined by calculating a correlation coefficient, which is a measure of the degree of linear correlation between the variables, the correlation coefficient being defined on the basis of the subject. In the embodiment of the present invention, the correlation coefficient refers to a parameter of a degree of correlation between the reference feature and the target side channel curve obtained after the preprocessing. Correspondingly, cross correlation analysis can also be performed by using the reference feature and the target side channel curve after signal processing to obtain a correlation curve, wherein cross correlation can also be understood as convolution performed by using the reference feature and the target side channel curve.

In the embodiment of the present invention, the process of adjusting the preset parameter to obtain the target parameter includes:

carrying out curve extraction on the correlation curves to obtain a plurality of curves;

obtaining the distance between the point corresponding to the maximum value in the adjacent interval based on the point corresponding to the maximum value in each curve;

removing abnormal distances based on the distances, and calculating the removed distances to obtain a target spacing distance between the two features;

and adjusting the interval between the two features based on the target interval distance to obtain a target parameter.

Firstly, a plurality of curves are taken out from the correlation curve, then maximum points are searched for each curve, the obtained points are used as base points, the points with the maximum values are searched for in the characteristic interval from the points to the left and the right, the distance between the maximum points of the adjacent intervals is recorded, the distance distribution is estimated, abnormal values are removed, and the maximum, the minimum and the average values of the rest values are calculated. And calculating a new interval between the two characteristics according to the calculated maximum, minimum and average values, and adjusting the interval between the two characteristics by using the interval.

Referring to fig. 4, a schematic flow chart of another side channel curve feature extraction method provided in the embodiment of the present invention is shown. The method comprises the following steps:

(1) the original curve is subjected to signal preprocessing, and can be processed by using a signal processing mode which can make the characteristics more obvious, such as taking an absolute value, low-pass filtering, median filtering derivation and the like, so that the curve after signal processing is obtained.

(2) Selecting a reference feature, and calculating a correlation curve, wherein the method for calculating the correlation curve comprises the following steps: and selecting a reference characteristic from the curve after the signal processing, and performing cross correlation analysis by using the reference characteristic and the curve after the signal processing to obtain a correlation curve.

(3) Setting preset parameters, wherein the preset parameters may not need to be very accurate, because there is also an adaptive parameter adjusting process in the present invention. The preset parameters include: the starting point of the curve for starting to extract the feature, the interval between two features, the length of the feature to be extracted, the position for starting to extract the feature and the like.

(4) And automatically adjusting parameters, wherein the main purpose of automatically adjusting the parameters is to adjust the interval between each characteristic of the chain so as to remove the non-concerned characteristics in the final result.

(5) And extracting features from the original curve by using the adjusted parameters and the correlation curve. In the process of extracting the characteristics, the adjusted parameters are utilized, the characteristics corresponding to the required length of the original curve near the maximum value are provided at intervals of every other characteristic interval according to the maximum value of the correlation curve in the interval. And the number of features in the raw curve and their positions in the bar are recorded and the value of the correlation corresponding to the feature is recorded.

Wherein the process of determining the interval between two features comprises: firstly, a plurality of curves are taken out from the correlation curve, then maximum points are searched for each curve, the obtained points are used as base points, the points with the maximum values are searched for in the characteristic interval from the points to the left and the right, the distance between the maximum points of the adjacent intervals is recorded, the distance distribution is estimated, abnormal values are removed, and the maximum, the minimum and the average values of the rest values are calculated. And calculating a new interval between the two characteristics according to the calculated maximum, minimum and average values, and adjusting the interval between the two characteristics by using the interval.

In the embodiment of the invention, the curve after signal processing is used for calculating the correlation so as to improve the accuracy. In the process of extracting the features, the next feature is extracted after a certain interval, so that the extraction of the unnecessary features is avoided. And the interval is automatically adjusted according to the correlation curve by using a statistical method, so that the error rate is reduced.

Based on the foregoing embodiment, referring to fig. 5, an embodiment of the present invention further provides a side channel curve feature extraction apparatus, including:

the preprocessing unit 10 is configured to preprocess each point in the original side channel curve to obtain a target side channel curve;

and the analysis unit 20 is configured to determine a reference feature in the target side channel curve, and perform analysis based on the reference feature and the target side channel curve to obtain a correlation curve.

The adjusting unit 30 is configured to determine a preset parameter, and perform parameter adjustment on the preset parameter to obtain a target parameter;

and the extracting unit 40 is configured to perform feature extraction in the original side channel curve based on the target parameter and the correlation curve to obtain feature information.

Optionally, the pre-processing unit comprises:

the acquisition subunit is used for acquiring an original side channel curve;

the processing subunit is used for carrying out numerical processing and filtering processing on each point of the original side channel curve to obtain each processed point;

and the first determining subunit is used for determining the target side channel curve based on the processed points.

Optionally, the analysis unit comprises:

a second determining subunit, configured to determine a reference feature in the target-side channel curve;

the calculating subunit is used for calculating a correlation coefficient between the reference characteristic and the target side channel curve;

a third determining subunit, configured to determine a correlation curve based on the correlation coefficient.

Optionally, the preset parameters include: starting points of features to be extracted, interval intervals between two features, feature lengths to be extracted and feature positions to be extracted are arranged in the curve;

wherein the adjusting unit is specifically configured to:

determining preset parameters;

carrying out curve extraction on the correlation curves to obtain a plurality of curves;

obtaining the distance between the point corresponding to the maximum value in the adjacent interval based on the point corresponding to the maximum value in each curve;

removing abnormal distances based on the distances, and calculating the removed distances to obtain a target spacing distance between the two features;

and adjusting the interval between the two features based on the target interval distance to obtain a target parameter.

Optionally, the feature information includes:

the correlation value comprises a target feature, a target curve corresponding to the target feature in the original side channel curve, position information of the target feature in the target curve and a correlation value corresponding to the target feature.

The embodiment of the invention provides a side channel curve characteristic extraction device, which comprises: the preprocessing unit preprocesses each point in the original side channel curve to obtain a target side channel curve; the analysis unit determines a reference characteristic in the target side channel curve, and performs analysis based on the reference characteristic and the target side channel curve to obtain a correlation curve. The method comprises the steps that an adjusting unit determines preset parameters and adjusts the preset parameters to obtain target parameters; the extraction unit extracts features in the original side channel curve based on the target parameters and the correlation curve to obtain feature information. The invention utilizes the curve after signal processing to calculate the correlation, improves the accuracy of feature extraction, can adjust the preset parameters before feature extraction, and avoids the problem of inaccurate fixed parameter extraction.

Based on the foregoing embodiments, embodiments of the present invention provide a computer-readable storage medium storing one or more programs, which are executable by one or more processors to implement the steps of the side-channel curve feature extraction method as any one of the above.

The embodiment of the invention also provides electronic equipment which comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor executes the steps of the side channel curve feature extraction method realized when the processor executes the program.

The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.

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 components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether these functions are performed in hardware or software depends on the particular application of the solution and the constraints involved. 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. A software module may reside 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 invention. 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 invention. Thus, the present invention 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.