CN106301755B - A kind of noise-reduction method and system of the energy leakage signal based on wavelet analysis - Google Patents
A kind of noise-reduction method and system of the energy leakage signal based on wavelet analysis Download PDFInfo
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Abstract
The present invention provides the noise-reduction method and system of a kind of energy leakage signal based on wavelet analysis, and method is by obtaining energy leakage signal；Multiscale Wavelet Decomposition is carried out to energy leakage signal, obtains the low frequency coefficient of energy leakage signal；Decompose the Hankel matrix for the low frequency coefficient that building obtains, the sparse matrix after obtaining noise reduction；Low frequency coefficient after noise reduction is calculated；Inverse wavelet transform is carried out to the low frequency coefficient after noise reduction, the energy leakage signal after obtaining noise reduction.System is equipped with energy leakage signal acquisition module, noise reduction parameters choose module, observing matrix constructs, separation module and low frequency coefficient rebuild module and energy leakage signal reconstruction module.The present invention can accurately and comprehensively remove the noise of energy leakage signal, it can be realized the accurate noise reduction to single or a small amount of energy leakage signal simultaneously, the attack performance of correlation energy attack is improved, coherent detection mechanism provides analysis foundation accurately and securely with certification to effective assessment of crypto chip.
Description
Technical field
The present invention relates to side channelization codes analytical technologies, and in particular to a kind of energy leakage signal based on wavelet analysis
Noise-reduction method and system.
Background technique
Encryption device can unconsciously generate the sides such as sound, electromagnetism, energy channel information, side letter when running cryptographic algorithm
Road cryptanalysis can successfully extract the secret information inside encryption device using these side channel informations.Side channelization codes leakage letter
Number processing be directly related to subsequent side channelization codes analyse whether can with biggish probability success, be related to coherent detection machine
Effective assessment and certification of the structure to crypto chip.
Traditional side channelization codes energy leakage signal processing method, is the superposed average by a large amount of energy leakage signals
Achieve the purpose that noise reduction；And it is limited in fact, it is possible to be used for the energy leakage signal that side channelization codes are analyzed, while noise
Form is varied, and therefore, useful leakage signal frequency range can not be determined accurately, causes noise reduction effect limited；In addition, using at present
In the methods of the wavelet transformation of the noise reduction of energy leakage signal, empirical mode decomposition and optimization based on signal-to-noise ratio (SNR) Criterion there is also
Side channelization codes energy leakage signal Incomplete matching and the problems such as single or a small amount of energy leakage signal can not be analyzed.
Summary of the invention
For the defects in the prior art, the present invention provides a kind of noise reduction side of energy leakage signal based on wavelet analysis
Method, which comprises
In the side channel information that step 1. generates in encryption or decryption process, the energy leakage signal is obtained；
Step 2. carries out Multiscale Wavelet Decomposition to the energy leakage signal according to selected morther wavelet and Decomposition order,
Obtain the low frequency coefficient of the energy leakage signal；
Step 3. decomposes the Hankel matrix for the low frequency coefficient that building obtains, the sparse matrix after obtaining noise reduction；
Low frequency coefficient of the step 4. according to the sparse matrix after noise reduction, after noise reduction is calculated；
Step 5. carries out inverse wavelet transform to the low frequency coefficient after the noise reduction, the energy leakage letter after obtaining noise reduction
Number.
Further, the step 1, comprising:
It is carried out in the side channel information generated in encryption or decryption process in encryption device, with probe in operation aes algorithm
FPGA on acquire the energy leakage signal, include encrypted message, ambient noise, noise of equipment in the energy leakage signal
And sampling noise.
Further, the step 2, comprising:
2-1. determines the Decomposition order according to the time frequency distribution map of the energy leakage signal, and small in Daubechies
Morther wavelet is chosen in wave system；
2-2. according to the Decomposition order and selected morther wavelet, using Mallat algorithm to the energy leakage signal into
Row Multiscale Wavelet Decomposition obtains the low frequency coefficient of the energy leakage signal:
In formula (1), j is a certain layer in decomposition layer, ajFor the low frequency coefficient of jth layer, a when j=0jFor primary energy leakage
The value of signal, h0For morther wavelet generate decomposition low-frequency filter coefficient,For the conjugate of low-frequency filter coefficient, n is to obtain
The a certain moment of corresponding coefficient value, l are count value.
Further, the step 3, comprising:
3-1. chooses the long L of window:
In formula (2), N is the length of low frequency coefficient；
3-2. constructs the Hankel matrix X of the low frequency coefficient according to the long L of the windowL×K；
In formula (3), siFor i-th of low frequency coefficient value, K=N-L+1；
3-3. to the Hankel matrix XL×KCarry out the principal component decomposition of robustness:
In formula (4), M is the low-rank matrix in the principal component decomposition of robustness, and Y is dilute in the principal component decomposition of robustness
Matrix is dredged, | | M | |*For the nuclear norm of low-rank matrix, | | Y | |0For zero norm of sparse matrix, λ is two objective functions of balance
Parameter, F are the Nice Fu Luobin norm, and ε indicates the parameter of unknown disturbances part；
3-4. uses ADM algorithm, the isolated sparse matrix Y in formula (4).
Further, the step 4, comprising:
Diagonally opposing corner average operation is carried out to the sparse matrix after noise reduction, the low frequency coefficient after noise reduction is calculated
In formula (5), x*It is the element in sparse coefficient matrix Y, L*It is expressed as L*=min { L, K }, K*It is expressed as K*=max
{L,K}；N is the length of low frequency coefficient；N is to obtain a certain moment of corresponding coefficient value, and L is that window is long, K=N-L+1.
Further, the step 5, comprising:
Inverse wavelet transform is carried out to the low frequency coefficient after the noise reduction, the energy leakage signal y after obtaining noise reduction
(n):
In formula (6),Low frequency coefficient when for a certain counting,For the low frequency coefficient after noise reduction, g0It is by female small
The reconstruction low-frequency filter coefficient that wave generates,For the conjugate for rebuilding low frequency filtering coefficient, n is to obtain certain of corresponding coefficient value
One moment, l are count value.
On the other hand, the noise reduction system of the present invention also provides a kind of energy leakage signal based on wavelet analysis, it is described
System includes:
Energy leakage signal acquisition module in the side channel information for generating in encryption or decryption process, obtains institute
State energy leakage signal；
Noise reduction parameters choose module, for being carried out according to selected morther wavelet and Decomposition order to the energy leakage signal
Multiscale Wavelet Decomposition obtains the low frequency coefficient of the energy leakage signal；
Observing matrix building and separation module are obtained for decomposing the Hankel matrix for the low frequency coefficient that building obtains
Sparse matrix after to noise reduction；
Low frequency coefficient rebuilds module, for the low frequency system according to the sparse matrix after noise reduction, after noise reduction is calculated
Number；
Energy leakage signal reconstruction module is dropped for carrying out inverse wavelet transform to the low frequency coefficient after the noise reduction
The energy leakage signal after making an uproar.
Further, the energy leakage signal acquisition module includes:
Side channel information acquisition unit carries out the side channel generated in encryption or decryption process letter for obtaining encryption device
Breath；
Energy leakage signal acquiring unit is used in the side channel information, with probe in the FPGA for running aes algorithm
It is upper to acquire the energy leakage signal, it include encrypted message, ambient noise, noise of equipment and sampling in the energy leakage signal
Noise.
Further, the noise reduction parameters selection module includes:
Decomposition order selection unit, for determining the decomposition layer according to the time frequency distribution map of the energy leakage signal
Number；
Morther wavelet selection unit, for choosing morther wavelet in the small wave system of Daubechies；
Low frequency coefficient acquiring unit, for according to the Decomposition order and selected morther wavelet, using Mallat algorithm pair
The energy leakage signal carries out Multiscale Wavelet Decomposition, obtains the low frequency coefficient of the energy leakage signal.
Further, the observing matrix building and separation module, comprising:
The long selection unit of window is long for choosing window；
Hankel matrix construction unit, for according to the window it is long, construct the Hankel matrix of the low frequency coefficient；
Hankel matrix decomposition unit, for carrying out the principal component decomposition of robustness to the Hankel matrix；
Sparse matrix acquiring unit, for using ADM algorithm, the isolated sparse matrix.
As shown from the above technical solution, the noise reduction side of a kind of energy leakage signal based on wavelet analysis provided by the invention
Method and system can accurately and comprehensively remove the noise of energy leakage signal, while can be realized to single or a small amount of energy
The accurate noise reduction of leakage signal, improves the attack performance of correlation energy attack, and coherent detection mechanism is effectively commented crypto chip
Estimate and authenticates the analysis foundation provided accurately and securely.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to make one simply to introduce, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without creative efforts, can be with root
Other attached drawings are obtained according to these attached drawings.
Fig. 1 is a kind of flow diagram of the noise-reduction method of energy leakage signal based on wavelet analysis of the invention；
Fig. 2 is the flow diagram of step 101 in method of the invention；
Fig. 3 is the flow diagram of step 102 in method of the invention；
Fig. 4 is a kind of noise reduction system schematic diagram of energy leakage signal based on wavelet analysis of the invention；
Fig. 5 is the schematic diagram of energy leakage signal acquisition module 10 in system of the invention；
Fig. 6 is the schematic diagram that noise reduction parameters choose module 11 in system of the invention；
Fig. 7 is the schematic diagram of observing matrix building and separation module 12 in system of the invention；
Fig. 8 is the flow diagram of noise-reduction method in concrete application example of the invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
As shown in Figure 1, a kind of noise-reduction method of the energy leakage signal based on wavelet analysis of the present invention, detailed process is such as
Under:
100. in the side channel information generated in encryption or decryption process, obtaining energy leakage signal；
Encryption device can unconsciously generate the sides such as sound, electromagnetism, energy channel information when running cryptographic algorithm, in order to
The secret information inside encryption device is successfully extracted using these side channel informations；In the encryption or decryption process of encryption device
In the side channel information of generation, the energy leakage signal generated in encryption process is obtained, energy leakage signal is to pass through spy
The signal that head acquires on the FPGA of operation aes algorithm；The energy leakage signal that such mode acquires accurately and securely, while energy
The noise with sampling in leakage signal is measured, so that subsequent more accurate and glitch-free noise reduction, ensure that the effect of noise reduction.
101. carrying out Multiscale Wavelet Decomposition to energy leakage signal according to selected morther wavelet and Decomposition order, energy is obtained
Measure the low frequency coefficient of leakage signal；
According to the time frequency distribution map for the energy leakage signal drawn in advance, the layer decomposed to energy leakage signal is determined
Number, and morther wavelet is chosen in the western small echo of more shellfishes (Daubechies small echo) race；Wherein, small echo (Wavelet) transformation is the time
The localization of (space) frequency is analyzed, it gradually carries out multi-scale refinement to signal (function) by flexible shift operations, finally
Reach high frequency treatment time subdivision, frequency is segmented at low frequency, can adapt to the requirement of time frequency signal analysis, automatically so as to focus on letter
Number any details, solve Fourier transformation difficult problem, become after Fourier transformation since in scientific method
Important breakthrough；Using the mode of wavelet analysis, so that the noise reduction process of this method is accurately and securely.
102. decomposing the Hankel matrix for the low frequency coefficient that building obtains, the sparse matrix after obtaining noise reduction；
Wherein, Hankel matrix (Hankel Matrix) refers to all equal square matrix of the element on each counter-diagonal；
The number of nonzero element is far smaller than the sum of matrix element in matrix, and the distribution of nonzero element is usually recognized without rule
When being less than or equal to 0.05 than the value of upper matrix all elements sum for the sum of nonzero element in matrix, then the matrix is referred to as sparse
Matrix (sparse matrix).
103. the low frequency coefficient according to the sparse matrix after noise reduction, after noise reduction is calculated；
104. the low frequency coefficient after pair noise reduction carries out inverse wavelet transform, the energy leakage signal after obtaining noise reduction；
Inverse wavelet transform is carried out according to the low frequency coefficient after noise reduction and by the reconstruction low-frequency filter coefficient that morther wavelet generates,
Energy leakage signal after the noise reduction rebuild completes noise reduction, and then accurately and comprehensively removes making an uproar for energy leakage signal
Sound, while can be realized the accurate noise reduction to single or a small amount of energy leakage signal.
Wherein, step 100, specific as follows:
It is carried out in the side channel information generated in encryption or decryption process in encryption device, with probe in operation aes algorithm
FPGA on collecting energy leakage signal, include that encrypted message, ambient noise, noise of equipment and sampling are made an uproar in energy leakage signal
Sound.
As shown in Fig. 2, step 101, specific as follows:
200. determine Decomposition order according to the time frequency distribution map of energy leakage signal, and select in the small wave system of Daubechies
Take morther wavelet；
201. according to Decomposition order and selected morther wavelet, more to energy leakage signal progress small echo using Mallat algorithm
Scale Decomposition obtains the low frequency coefficient of energy leakage signal:
In formula (1), j is a certain layer in decomposition layer, ajFor the low frequency coefficient of jth layer, a when j=0jFor primary energy leakage
The value of signal, h0For morther wavelet generate decomposition low-frequency filter coefficient,
A when=0jFor the value of primary energy leakage signal, h0For morther wavelet generate decomposition low-frequency filter coefficient,For
The conjugate of low-frequency filter coefficient, n are to obtain a certain moment of corresponding coefficient value, and l is count value.As shown in figure 3, step
102, specific as follows:
300. choose the long L of window:
In formula (2), N is the length of low frequency coefficient；
301., according to the long L of window, construct the Hankel matrix X of low frequency coefficientL×K；
In formula (3), siFor i-th of low frequency coefficient value, K=N-L+1；
302. couples of Hankel matrix XL×KCarry out the principal component decomposition of robustness:
In formula (4), M is the low-rank matrix in the principal component decomposition of robustness, and Y is dilute in the principal component decomposition of robustness
Matrix is dredged, | | M | |*For the nuclear norm of low-rank matrix, | | Y | |0For zero norm of sparse matrix, λ is two objective functions of balance
Parameter, F are the Nice Fu Luobin norm, and ε indicates the parameter of unknown disturbances part；
303. use ADM algorithm, the isolated sparse matrix Y in formula (4).
Wherein, step 103, comprising:
Diagonally opposing corner average operation is carried out to the sparse matrix after noise reduction, the low frequency coefficient after noise reduction is calculated
In formula (5), x*It is the element in sparse coefficient matrix Y, L*It is expressed as L*=min { L, K }, K*It is expressed as K*=max
{L,K}；N is the length of low frequency coefficient；N is to obtain a certain moment of corresponding coefficient value, L is that window is long, K=N-L+1.
Wherein, step 104, comprising:
Inverse wavelet transform is carried out to the low frequency coefficient after noise reduction, the energy leakage signal y (n) after obtaining noise reduction:
In formula (6),Low frequency coefficient when for a certain counting,For the low frequency coefficient after noise reduction, g0It is by female small
The reconstruction low-frequency filter coefficient that wave generates,For the conjugate for rebuilding low frequency filtering coefficient, n is to obtain certain of corresponding coefficient value
One moment, l are count value.As shown in figure 4, the noise reduction of the present invention also provides a kind of energy leakage signal based on wavelet analysis
System is specifically equipped in system:
Energy leakage signal acquisition module 10 in the side channel information for generating in encryption or decryption process, obtains
Energy leakage signal；
Technical solution in the corresponding above method of energy leakage signal acquisition module 10 in step 100, encryption device are being transported
The sides such as sound, electromagnetism, energy channel information can be unconsciously generated when row cryptographic algorithm, in order to using these side channel informations at
Function extracts the secret information inside encryption device；In the side channel information generated in the encryption or decryption process of encryption device,
The energy leakage signal generated in encryption process is obtained, energy leakage signal is by probe in operation aes algorithm
The signal acquired on FPGA；The energy leakage signal that such mode acquires accurately and securely, while having in energy leakage signal
The noise of sampling, so that subsequent more accurate and glitch-free noise reduction, ensure that the effect of noise reduction.
Noise reduction parameters choose module 11, small for being carried out according to selected morther wavelet and Decomposition order to energy leakage signal
Wave multi-resolution decomposition obtains the low frequency coefficient of energy leakage signal；
Noise reduction parameters choose step 101 in the corresponding above method of module 11, according to selected morther wavelet and Decomposition order pair
Energy leakage signal in energy leakage signal acquisition module 10 carries out Multiscale Wavelet Decomposition, obtains the low of energy leakage signal
Frequency coefficient decomposes energy leakage signal according to the time frequency distribution map for the energy leakage signal drawn in advance, determination
The number of plies, and morther wavelet is chosen in the western small echo of more shellfishes (Daubechies small echo) race.
Observing matrix building and separation module 12 are obtained for decomposing the Hankel matrix for the low frequency coefficient that building obtains
Sparse matrix after noise reduction；
The low frequency system that decomposition building in observing matrix building and the corresponding above method of separation module 12 in step 102 obtains
Several Hankel matrixs, the technology contents of the sparse matrix after obtaining noise reduction, observing matrix building and separation module 12 decompose structure
Build the Hankel matrix for the low frequency coefficient that noise reduction parameters are chosen in module 11, the sparse matrix after obtaining noise reduction.
Low frequency coefficient rebuilds module 13, for the low frequency coefficient according to the sparse matrix after noise reduction, after noise reduction is calculated；
Low frequency coefficient rebuilds step 103 in the corresponding above method of module 13.
Energy leakage signal reconstruction module 14 obtains noise reduction for carrying out inverse wavelet transform to the low frequency coefficient after noise reduction
Energy leakage signal afterwards；Technology contents in the corresponding above method in step 104, are detailed in the technology contents of the above method, this
Place repeats no more.
Inverse wavelet transform is carried out according to the low frequency coefficient after noise reduction and by the reconstruction low-frequency filter coefficient that morther wavelet generates,
Energy leakage signal after the noise reduction rebuild completes noise reduction, and then accurately and comprehensively removes making an uproar for energy leakage signal
Sound, while can be realized the accurate noise reduction to single or a small amount of energy leakage signal.
As shown in figure 5, energy leakage signal acquisition module 10 includes:
Side channel information acquisition unit 20 carries out the side channel generated in encryption or decryption process for obtaining encryption device
Information；
Energy leakage signal acquiring unit 21 is used in the channel information of side, with probe on the FPGA of operation aes algorithm
Collecting energy leakage signal includes encrypted message, ambient noise, noise of equipment and sampling noise, energy in energy leakage signal
Energy leakage signal is sent to noise reduction parameters and chooses module 11 by leakage signal acquiring unit 21.
As shown in fig. 6, noise reduction parameters selection module 11 includes:
Decomposition order selection unit 30 receives the energy leakage signal that energy leakage signal acquiring unit 21 issues, and root
Decomposition order is determined according to the time frequency distribution map of energy leakage signal；
Morther wavelet selection unit 31, for choosing morther wavelet in the small wave system of Daubechies；
Low frequency coefficient acquiring unit 32, for according to Decomposition order and selected morther wavelet, using Mallat algorithm to energy
It measures leakage signal and carries out Multiscale Wavelet Decomposition, obtain the low frequency coefficient of energy leakage signal, and low frequency coefficient is sent to sight
Survey matrix building and separation module 12.
As shown in fig. 7, observing matrix building and separation module 12, comprising:
The long selection unit 40 of window is long for choosing window；
Hankel matrix construction unit 41, the low frequency coefficient for being sent according to window length and low frequency coefficient acquiring unit 32,
Construct the Hankel matrix of low frequency coefficient；
Hankel matrix decomposition unit 42, for carrying out the principal component decomposition of robustness to Hankel matrix；
Sparse matrix acquiring unit 43 for using ADM algorithm, isolated sparse matrix, and sparse matrix is sent
Tremendously low frequency coefficient reconstruction module 13.
As shown in figure 8, the present invention provides a kind of specifically answering for the noise-reduction method of energy leakage signal based on wavelet analysis
Use-case, as follows:
S01. the energy leakage signal s (t) that aes algorithm generates in encryption process is obtained, s (t) is existed by probe
The energy leakage signal acquired on the FPGA of aes algorithm is run, the signal of acquisition had both included the useful letter closely related with key
It ceases, also all noises including environment, equipment and sampling；
The energy leakage signal s (t) that aes algorithm generates in encryption process is obtained, s (t) is being run by probe
The energy leakage signal acquired on the FPGA of aes algorithm；
Cryptographic algorithm can leak energy information relevant to password internal arithmetic when running on encryption device, generally for
This symmetrical cryptographic algorithm of AES, the point of attack are often selected as nonlinear S box part；
The energy leakage signal acquired from the channel FPGA evaluation board of side, each sampled point contain multiple kinds of energy information
It is as follows:
Ptotal=Pexp+Pnoise+Pconst (1-1)
Wherein, PtotalFor the gross energy of each sampled point, PexpFor available leakage signal related to key information, Pnoise
For the noise generated in collection process, PconstFor the static energy loss for acquiring equipment.
The process of noise reduction is elimination noise P as far as possiblenoise。
S02. wavelet and Decomposition order are chosen and calculates the height for carrying out Multiscale Wavelet Decomposition to energy leakage signal
Frequency coefficient and low frequency coefficient；
Morther wavelet is selected from the small wave system of Daubechies, uses db5 in the application example, the number of plies of multi-scale wavelet decomposition according to
The time-frequency distributions of sampled signal determine that leakage signal concentrates on low frequency part, therefore 4 layers of wavelet decomposition are used in the application example.
High frequency coefficient and low frequency coefficient are calculated according to selected morther wavelet and Decomposition order.Decompose low-frequency filter coefficient h0
With decomposition high frequency filter coefficient h1It can directly be read from coefficient figure.The low frequency coefficient of jth layer can be calculate by the following formula:
Wherein, ajFor the low frequency coefficient of jth layer, a when initial j=0jFor the value of primary energy leakage signal.
The high frequency coefficient of jth layer can be calculate by the following formula:
Wherein, djFor the high frequency coefficient of jth layer, a when initial j=0jFor the value of primary energy leakage signal.
S03. selection window is long constructs the track a Hankel matrix to low frequency coefficient；
Window length is selected as the following formula:
C=2 is selected in this example, and the track Hankel matrix is constructed to low frequency coefficient, is originally shown
The 4th layer of low frequency coefficient is constructed as follows in example:
Wherein, the length of N low frequency coefficient, L are that selected window is long, K=N-L+1, siFor i-th of low frequency coefficient value.
S04. the principal component decomposition of robustness, the sparse coefficient after being denoised are done to the track the Hankel matrix after building
Matrix；
The principal component decomposition that robustness is done to the track the Hankel matrix after building, that is, solve following optimization problem:
Wherein M is the low-rank matrix in the principal component decomposition of robustness, and Y is the sparse square in the principal component decomposition of robustness
Battle array, | | | |*The nuclear norm of matrix is represented, | | | |0Zero norm of matrix is represented, parameter lambda is used to balance two objective functions,
Parameter ε is for indicating unknown disturbances part.
The principal component decomposition for solving robustness can be acquired by algorithm of changing direction (ADM), and wherein lambda parameter is 2e-2, parameter ε
For 5e-3× | | X | |, separate sparse coefficient matrix Y.
It is average that diagonally opposing corner is done as the following formula to sparse coefficient matrix Y:
Wherein x*It is the element in sparse coefficient matrix Y, hnIt is the low frequency coefficient rebuild, L*And K*It is expressed as L*=
Min { L, K }, K*=max { L, K }.
S05. the low frequency coefficient after diagonally opposing corner averagely obtains noise reduction is done to the sparse coefficient matrix after denoising.
S06. the energy leakage signal after inverse wavelet transform is denoised is done to the low frequency coefficient after noise reduction；
The corresponding reconstruction low-frequency filter coefficient of morther wavelet db5 is read, is rebuild as the following formula:
WhereinIt is the low frequency coefficient after denoising, g0It is the reconstruction low-frequency filter coefficient generated by morther wavelet, y (n) is
Energy leakage signal after the denoising of reconstruction.
Time domain energy leakage signal after the calculating of (1-7) formula, after noise reduction can be obtained.
System provided by the present invention can be realized by MATLAB.
In addition to digital filter, the methods of wavelet transformation, empirical mode decomposition are also applied to the drop of energy leakage signal
It makes an uproar.On the one hand, the wavelet transformation based on threshold value and empirical mode decomposition method are calculated according to theoretical noise model,
Can not effectively it match with side channelization codes energy leakage signal；On the other hand, empirical mode decomposition method, which exists, lacks
Complete mathematical theory, to the problems such as sampling and noise-sensitive cause in practical applications noise reduction effect it is limited；In addition, based on warp
It is also more sensitive to many kinds of parameters setting to test the noise-reduction method of mode decomposition its effect, is not fully suitable for side channelization codes energy
Measure the noise reduction of leakage signal.The current performance to improve the analysis of side channelization codes, some optimization methods based on signal-to-noise ratio (SNR) Criterion
It is suggested, but this mode not can avoid the use of a large amount of energy leakage signals.Especially when only single energy mark is used for password
When analysis, these noise-reduction methods will be unable to play its effect；And the present invention is by wavelet analysis technology, it can accurately and comprehensively
The noise of energy leakage signal is removed, while can be realized the accurate noise reduction to single or a small amount of energy leakage signal, improves phase
The attack performance of Attacks is closed, coherent detection mechanism provides accurately and securely effective assessment of crypto chip with certification
Analysis foundation.
In specification of the invention, numerous specific details are set forth.Although it is understood that the embodiment of the present invention can
To practice without these specific details.In some instances, well known method, structure and skill is not been shown in detail
Art, so as not to obscure the understanding of this specification.Similarly, it should be understood that disclose in order to simplify the present invention and helps to understand respectively
One or more of a inventive aspect, in the above description of the exemplary embodiment of the present invention, each spy of the invention
Sign is grouped together into a single embodiment, figure, or description thereof sometimes.However, should not be by the method solution of the disclosure
Release is in reflect an intention that i.e. the claimed invention requires more than feature expressly recited in each claim
More features.More precisely, as the following claims reflect, inventive aspect is less than single reality disclosed above
Apply all features of example.Therefore, it then follows thus claims of specific embodiment are expressly incorporated in the specific embodiment,
It is wherein each that the claims themselves are regarded as separate embodiments of the invention.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme should all cover within the scope of the claims and the description of the invention.
Claims (5)
1. a kind of noise-reduction method of the energy leakage signal based on wavelet analysis, which is characterized in that the described method includes:
In the side channel information that step 1. generates in encryption or decryption process, the energy leakage signal is obtained；
Step 2. carries out Multiscale Wavelet Decomposition to the energy leakage signal according to selected morther wavelet and Decomposition order, obtains
The low frequency coefficient of the energy leakage signal；
Step 3. decomposes the Hankel matrix for the low frequency coefficient that building obtains, the sparse matrix after obtaining noise reduction；
Low frequency coefficient of the step 4. according to the sparse matrix after noise reduction, after noise reduction is calculated；
Step 5. carries out inverse wavelet transform to the low frequency coefficient after the noise reduction, the energy leakage signal after obtaining noise reduction；
Wherein, step 2 include: the Decomposition order is determined according to the time frequency distribution map of the energy leakage signal, and
Morther wavelet is chosen in the small wave system of Daubechies；According to the Decomposition order and selected morther wavelet, using Mallat algorithm pair
The energy leakage signal carries out Multiscale Wavelet Decomposition, obtains the low frequency coefficient of the energy leakage signal:
In formula (1), j is a certain layer in decomposition layer, ajFor the low frequency coefficient of jth layer, a when j=0jFor primary energy leakage signal
Value, h0For morther wavelet generate decomposition low-frequency filter coefficient,For the conjugate of low-frequency filter coefficient, n is to obtain phase
The a certain moment of coefficient value is answered, l is count value；
The step 3 includes:
3-1. chooses the long L of window:
In formula (2), N is the length of low frequency coefficient；
3-2. constructs the Hankel matrix X of the low frequency coefficient according to the long L of the windowL×K；
In formula (3), siFor i-th of low frequency coefficient value, K=N-L+1；
3-3. is to the Hankel matrix XL×KCarry out the principal component decomposition of robustness:
In formula (4), M is the low-rank matrix in the principal component decomposition of robustness, and Y is the sparse square in the principal component decomposition of robustness
Battle array, | | M | |*For the nuclear norm of low-rank matrix, | | Y | |0For zero norm of sparse matrix, λ is the ginseng for balancing two objective functions
Number, F are the Nice Fu Luobin norm, and ε indicates the parameter of unknown disturbances part；
3-4. uses ADM algorithm, the isolated sparse matrix Y in formula (4)；
The step 4 includes:
Diagonally opposing corner average operation is carried out to the sparse matrix after noise reduction, the low frequency coefficient after noise reduction is calculated
In formula (5), x*It is the element in sparse coefficient matrix Y, L*It is expressed as L*=min { L, K }, K*It is expressed as K*=max L,
K}；N is the length of low frequency coefficient；N is to obtain a certain moment of corresponding coefficient value, and L is that window is long, K=N-L+1, k indicate it is cumulative and
Value range in variable.
2. the method according to claim 1, wherein the step 1, comprising:
It is carried out in the side channel information generated in encryption or decryption process in encryption device, with probe in operation aes algorithm
Acquire the energy leakage signal on FPGA, include in the energy leakage signal encrypted message, ambient noise, noise of equipment and
Sample noise.
3. the method according to claim 1, wherein the step 5, comprising:
Inverse wavelet transform is carried out to the low frequency coefficient after the noise reduction, the energy leakage signal y (n) after obtaining noise reduction:
In formula (6),Low frequency coefficient when for a certain counting,For the low frequency coefficient after noise reduction, g0It is to be given birth to by morther wavelet
At reconstruction low-frequency filter coefficient,For the conjugate for rebuilding low frequency filtering coefficient, n is to obtain certain a period of time of corresponding coefficient value
It carves, l is count value.
4. a kind of noise reduction system of the energy leakage signal based on wavelet analysis, which is characterized in that the system comprises:
Energy leakage signal acquisition module in the side channel information for generating in encryption or decryption process, obtains the energy
Measure leakage signal；
Noise reduction parameters choose module, for carrying out small echo to the energy leakage signal according to selected morther wavelet and Decomposition order
Multi-resolution decomposition obtains the low frequency coefficient of the energy leakage signal；
Observing matrix building and separation module are dropped for decomposing the Hankel matrix for the low frequency coefficient that building obtains
Sparse matrix after making an uproar；
Low frequency coefficient rebuilds module, for the low frequency coefficient according to the sparse matrix after noise reduction, after noise reduction is calculated；
Energy leakage signal reconstruction module, for carrying out inverse wavelet transform to the low frequency coefficient after the noise reduction, after obtaining noise reduction
The energy leakage signal；
Wherein, noise reduction parameters selection module includes:
Decomposition order selection unit, for determining the Decomposition order according to the time frequency distribution map of the energy leakage signal；
Morther wavelet selection unit, for choosing morther wavelet in the small wave system of Daubechies；
Low frequency coefficient acquiring unit, for according to the Decomposition order and selected morther wavelet, using Mallat algorithm to described
Energy leakage signal carries out Multiscale Wavelet Decomposition, obtains the low frequency coefficient of the energy leakage signal:
In formula (1), j is a certain layer in decomposition layer, ajFor the low frequency coefficient of jth layer, a when j=0jFor primary energy leakage signal
Value, h0For morther wavelet generate decomposition low-frequency filter coefficient,For the conjugate of low-frequency filter coefficient, n is to obtain phase
The a certain moment of coefficient value is answered, l is count value；
Observing matrix building and separation module, comprising:
The long selection unit of window is long for choosing window；
In formula (2), N is the length of low frequency coefficient；
Hankel matrix construction unit, for according to the window it is long, construct the Hankel matrix of the low frequency coefficient；,
In formula (3), siFor i-th of low frequency coefficient value, K=N-L+1；
Hankel matrix decomposition unit, for carrying out the principal component decomposition of robustness to the Hankel matrix；
In formula (4), M is the low-rank matrix in the principal component decomposition of robustness, and Y is the sparse square in the principal component decomposition of robustness
Battle array, | | M | |*For the nuclear norm of low-rank matrix, | | Y | |0For zero norm of sparse matrix, λ is the ginseng for balancing two objective functions
Number, F are the Nice Fu Luobin norm, and ε indicates the parameter of unknown disturbances part；
Sparse matrix acquiring unit, for using ADM algorithm, the isolated sparse matrix；
The low frequency coefficient is rebuild module and is specifically used for:
Diagonally opposing corner average operation is carried out to the sparse matrix after noise reduction, the low frequency coefficient after noise reduction is calculated
In formula (5), x*It is the element in sparse coefficient matrix Y, L*It is expressed as L*=min { L, K }, K*It is expressed as K*=max L,
K}；N is the length of low frequency coefficient；N is to obtain a certain moment of corresponding coefficient value, and L is that window is long, K=N-L+1.
5. system according to claim 4, which is characterized in that the energy leakage signal acquisition module includes:
Side channel information acquisition unit carries out the side channel information generated in encryption or decryption process for obtaining encryption device；
Energy leakage signal acquiring unit, for being adopted on the FPGA of operation aes algorithm with probe in the side channel information
Collect the energy leakage signal, includes that encrypted message, ambient noise, noise of equipment and sampling are made an uproar in the energy leakage signal
Sound.
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