CN103138917A - Application method of Hamming distance model on SM4 cryptographic algorithm lateral information channel energy analysis and based on S box input - Google Patents

Abstract

The invention discloses an application method of a Hamming distance model on SM4 cryptographic algorithm lateral information channel energy analysis and based on S box input. The application method is characterized in that the Hamming distance model is established by selecting an S box or a round function as an attacking point in the process that the SM4 cryptographic algorithm lateral information channel energy analysis is carried out, the input of the S box is used as an initial state v1 of the Hamming distance model, the output of the S box is used as subsequent state v2 of the Hamming distance (HD (v1, v2)) model when the S box is attacked, and the output / input of the round function is used as the subsequent state v2 of the Hamming distance (HD (v1, v2)) model when the round function is attacked. The method can be applied to CPA / DPA lateral information channel energy analysis of the SM4 cryptographic algorithm. Correlation between a correct guess secret key and energy information is improved, and validity and success rate of the analysis are enhanced.

Description

Be input as the Hamming distance model on basis with the S box in the application of SM4 cryptographic algorithm side channel energy analysis

Technical field

The invention belongs to the cryptographic algorithm technical field of analysis and detection; relate to specifically in cryptographic algorithms' implementation, the analysis of side channel energy, crypto module testing process; carry out the analysis of side channel energy for the crypto module of realizing the SM4 cryptographic algorithm; obtain the Energy Analysis for High of shielded key information; that is, be input as the Hamming distance model on basis in the application of SM4 cryptographic algorithm side channel energy analysis with the S box.

Background technology

Along with the development of information technology, various cryptographic algorithms just are being widely used in the important departments such as economy, military affairs, administration, the fail safe of protection information.In view of the importance of cryptographic algorithm, the cryptographic algorithm software and hardware realizes that the analysis and research of (crypto module) have great importance safely to protection information.In recent years, multiple attack to crypto module is widely known by the people, and the purpose of all these attacks is all in order to obtain the key in crypto module.Common attack pattern can be divided into the intrusive mood attack, half intrusive mood is attacked and non-intrusion type is attacked.In recent years, be widely used because the side Multiple Channel Analysis in the non-intrusion type attack is implemented conveniently, relative cost is cheap.The side Multiple Channel Analysis can be subdivided into chronometric analysis, energy spectrometer and emi analysis.Side channel energy analysis wherein is one of method the most frequently used in numerous analysis means, and it has broken through the analytical model of conventional cipher algorithm, and ability is powerful, implements relatively easy.Side channel energy analysis and utilization the consumption of crypto module energy and data operation and carry out between correlation, set up energy model based on the energy leakage function of cryptographic algorithms' implementation, use statistical method, the protected key of conjecture and the use of authentication password module.Side channel energy analytical method generally comprises, simple energy analysis (SPA), differential power analysis (DPA), correlation energy analysis (CPA) and higher difference energy spectrometer (HODPA).

Wherein, the DPA principle is: for the enciphering/deciphering computing of N group plain/cipher text data, obtain N bar energy mark, the energy mark here refers to the energy consumption measurement vector that collects in Password Operations process; To each conjecture key K, produce corresponding median (object of attack), determine choice function according to median; By choice function, energy mark collection is divided into two subsets; Corresponding energy consumption is averaged to two subsets respectively, and two average energy consumption values are asked poor, and this equal value difference is that median corresponding to choice function is to the impact effect of energy mark.According to statistical theory, if the K conjecture is incorrect, when the number N of energy mark convergence is infinitely great, the equal value difference of two subsets will level off to zero; When if K conjecture is correct, the maximum sharpness (absolute value maximum) of an equal value difference will appear in certain sampling point in the energy mark, can determine correct key by maximum sharpness.

The CPA principle is: for the enciphering/deciphering computing of N group plain/cipher text data, obtain N bar energy mark; To each conjecture key K, produce corresponding median (object of attack); Set up energy model according to median; By energy model, median is mapped as the consumption of emulation energy; Linearly dependent coefficient between the consumption of Calculation Simulation energy and energy mark, scope is between [1,1]; Choosing the maximum of absolute value in coefficient correlation, is 1 in theory, but owing to unavoidably having noise jamming in collecting energy mark process, maximum is less than 1, and conjecture key corresponding to this coefficient correlation maximum is correct key.

The SM4 cryptographic algorithm is first commercial cipher grouping algorithm that China publishes, and the packet of SM4 cryptographic algorithm and key length are 128 bits, and the cryptographic algorithm of SM4 cryptographic algorithm and key schedule all adopt 32 to take turns the nonlinear iteration structure.

The structure of SM4 cryptographic algorithm is as follows:

If

Be encrypting plaintext,

Be the algorithm input of i wheel,

Be the round key of i wheel, round function F is:

$F(X_i,X_{i+1},X_{i+2},X_{i+3},{\mathrm{rk}}_i)=X_i\⊕T(X_{i+1}\⊕X_{i+2}\⊕X_{i+3}\⊕{\mathrm{rk}}_i)---\left(1\right)$

Wherein, T:

Be an inverible transform, be composited by nonlinear transformation τ and linear transformation L, be i.e. T (.)=L (τ (.)).

τ is made of 4 parallel S boxes, as shown in Figure 2, establishes and is input as Be output as $B=({\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">b</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">b</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">b</figure-callout>}}_2,b_3)\&Element;{\left(Z_2^8\right)}^4,$ :

(b ₀，b ₁，b ₂，b ₃)＝τ(A)＝(Sbox(a ₀)，Sbox(a ₁)，Sbox(a ₂)，Sbox(a ₃)) (2)

The output of nonlinear transformation τ is the input of linear transformation L.If be input as

Be output as $C\&Element;{\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">Z</figure-callout>}}_2^{32},$ :

$C=L\left(B\right)=B\&CirclePlus;(B<<<2)\&CirclePlus;(B<<<10)\&CirclePlus;(B<<<18)\&CirclePlus;(B<<<24)---\left(3\right)$

Suppose A _iBe the input of i wheel S box, B _iBe the output of i wheel S box, the input of L displacement, C _iBe the output of i wheel L displacement.Satisfy as follows according to algorithm:

$A_i=(X_{i+1}\&CirclePlus;X_{i+2}\&CirclePlus;X_{i+3}\&CirclePlus;{\mathrm{rk}}_i)---\left(4\right)$

B _i＝τ(A _i) (5)

C _i＝L(B _i) (6)

$X_{i+4}=X_i\&CirclePlus;C_i---\left(7\right)$

According to following formula (4), (5), (6), (7), can get the wheel input (X of i+1 wheel _i+1, X _I+2,X _i+3, X _I+4), computing 32 is taken turns successively, namely can obtain exporting ciphertext $Y=({\mathrm{<figure-callout\; id="0"\; label="Y"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">Y</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="Y"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">Y</figure-callout>}}_2,Y_3)=({\mathrm{<figure-callout\; id="35"\; label="X"\; filenames="HSA00000846957900051.png,HSA00000846957900072.png"\; state="\{\{state\}\}">X</figure-callout>}}_{35},X_{34},X_{33},X_{32})\&Element;{\left(Z_2^{32}\right)}^4,$ The cryptographic structure flow process of above-mentioned SM4 cryptographic algorithm as shown in Figure 1.

The key schedule of SM4 cryptographic algorithm and cryptographic algorithm structure are similar, and as Fig. 2, only linear transformation L shift function is inconsistent.Make that the initial encryption key is (MK ₀, MK ₁, MK ₂, MK ₃).

$({\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">K</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">K</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">K</figure-callout>}}_2,K_3)=({\mathrm{MK}}_0\&CirclePlus;{\mathrm{FK}}_0,{\mathrm{MK}}_1\&CirclePlus;{\mathrm{FK}}_1,{\mathrm{MK}}_2\&CirclePlus;{\mathrm{FK}}_2,{\mathrm{MK}}_3\&CirclePlus;{\mathrm{FK}}_3)---\left(8\right)$

Wherein, (FK ₀, FK ₁, FK ₂, FK ₃) be known constant.

${\mathrm{rk}}_i=K_{i+4}=K_i\&CirclePlus;T^{\&prime;}(K_{i+1}\&CirclePlus;K_{i+2}\&CirclePlus;K_{i+3}\&CirclePlus;{\mathrm{CK}}_i)=K_i\&CirclePlus;L^{\&prime;}\left(\mathrm{\&tau;}(K_{i+1}\&CirclePlus;K_{i+2}\&CirclePlus;K_{i+3}\&CirclePlus;{\mathrm{CK}}_i)\right)---\left(9\right)$

Wherein, τ function is consistent with the τ function in above-mentioned SM4 cryptographic algorithm cryptographic structure, rk _iBe the encryption key of i wheel, i=0,1 ..., 31, CK _iBe known constant.

Linear transformation L ' is:

$L^{\&prime;}\left(x\right)=x\&CirclePlus;(x<<<13)\&CirclePlus;(x<<<23)---\left(10\right)$

According to formula (9), can obtain respectively 32 and take turns round key (rk ₀, rk ₁..., rk ₃₁), length is 32 bits.

The algorithm structure of data deciphering and data encryption is identical, is the use reversed in order of round key, and the decryption round key is the backward of encryption round key.During deciphering, use round key order (rk ₃₁, rk ₃₀..., rk ₀).

The Energy Analysis for High of SM4 cryptographic algorithm is chosen usually the output of output, L displacement of S box as object of attack, used Hamming weight, single-bit model, utilize DPA and CPA method to analyze.These methods have only been utilized typical analysis site, can not effectively implement to analyze to the SM4 cryptographic algorithm comprehensively.In addition, seldom the time, will affect the success rate that the SM4 cryptographic algorithm is analyzed when the available energy leakage information of above-mentioned analysis site.Therefore, need to propose more effective side channel energy analytical method.

Summary of the invention

In the SM4 cryptographic algorithm is analyzed, whether side channel energy analytical method is effective, its key is that the object of attack in cryptographic algorithm chooses the selection with corresponding energy model, chooses appropriate object of attack and can improve the signal to noise ratio of sampled energy information and the success rate of analysis.

The realization character that the object of the invention is to network analysis SM4 cryptographic algorithm, creatively select respectively the S box output, round function (follow-up state) of SM4 cryptographic algorithm as the point of attack, proposed to innovation with the Hamming distance model of S box input as Hamming distance reference state (front and continued state), different energy leakage information during to the computing of SM4 cryptographic algorithm, this model has improved correct conjecture key and the correlation between energy information, has strengthened validity and the success rate analyzed.

Realize that above-mentioned purpose technical scheme of the present invention is, be input as the Hamming distance model on basis with the S box in the application of SM4 cryptographic algorithm side channel energy analysis, carry out in SM4 cryptographic algorithm side channel energy analytic process, select S box or round function to set up the Hamming distance model as the point of attack, with the input of the S box front and continued state v as the Hamming distance model ₁

When the S box is attacked, Hamming distance (HD (v ₁, v ₂)) the follow-up state v of model ₂The output of S box; When round function is attacked, Hamming distance (HD (v ₁, v ₂)) the follow-up state v of model ₂It is the round function input/output.Above-mentioned to before S box output/Hamming distance (HD (v that attacks employing is taken turns at end 4 ₁, v ₂)) model is equivalent to S box input and the attack of output XOR value as Hamming weight (HW) model of the point of attack; To before round function/Hamming distance (HD (v that attacks employing 4 is taken turns in the end ₁, v ₂)) model is equivalent to the attack as Hamming weight (HW) model of the point of attack of the XOR value of S box input and round function input/output.

The above-mentioned Hamming distance model on basis that is input as with the S box is for the CPA/DPA side channel energy analysis to the SM4 cryptographic algorithm.

Basic Hamming distance model is as follows to the CPA side channel energy analytical procedure of SM4 cryptographic algorithm when being input as with the S box:

(1) collecting energy mark specifically carries out every group of plain/cipher text and is encrypted/decrypt operation, gathers energy expenditure information corresponding to Measuring Time point, is the energy mark, sets up the sampled energy absorption matrix; (2) choosing object of attack is S box or round function, determines Hamming distance algorithm attack model; (3) determine object of attack and model after, the conjecture round key calculates the median of wheel computing and determines the median matrix; (4) in utilization, median and the median matrix in step are mapped as emulation energy consumption values and emulation energy absorption matrix; (5) linearly dependent coefficient of Calculation Simulation energy absorption matrix and sampled energy absorption matrix obtains correct conjecture key.

The concrete grammar that utilizes CPA to carry out above-mentioned steps (3) is: known k (k ∈ 0 ..., N-1}) group plain/cipher text input $X^k=(X_0^k,X_1^k,X_2^k,X_3^k)$ Or ciphertext/plaintext output $X^k=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k)$ The time, conjecture i wheel round key

In byte

rk _{I, j}The conjecture value be respectively rk _{I, j, s}=s, s ∈ 0 ..., 255}, before selecting the output of S box/when end 4 is taken turns and is attacked, conjecture round key byte rk _{I, j, s}Corresponding median is, $v_{i,j,s}^k=\mathrm{\&tau;}((X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}$ Wherein,

For carrying out the computing of k group plain/cipher text i wheel encrypt/decrypt, guess j key byte corresponding median when being s,

Difference X _{I+1, j}, X _{I+2, j}, X _{I+3, j}Be the intermediate operations value

J byte; Select round function output front 4 to take turns when taking turns with end 4 attack of carrying out, conjecture round key byte rk _{I, j, s}Corresponding median is respectively $v_{i,j,s}^k={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}$ With $={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}((X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}$ $v_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s}),$ Wherein, $={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})$ L ^-1(x) j is

Carry out L ^-1J byte after displacement, $\begin{array}{c}{L}^{-1}\left(x\right)=x\&CirclePlus;(x<<<2)\&CirclePlus;(x<<<4)\&CirclePlus;(x<<<8)\&CirclePlus;(x<<<12)\&CirclePlus;(x<<<14)\&CirclePlus;(x<<<16)\&CirclePlus;\\ (x<<<18)\&CirclePlus;(x<<<22)\&CirclePlus;(x<<<24)\&CirclePlus;(x<<<30)\end{array},;$ When bright/the ciphertext of N group is carried out the enciphering/deciphering operation, calculate successively 256 conjecture round key byte rk _{I, j, s}Corresponding median is determined the median matrix $V(N\&times;256)=\left(\begin{array}{ccc}{v}_{i,j,0}^0& ...& v_{i,j,255}^0\\ .& & .\\ .& v_{i,j,s}^k& .\\ .& & .\\ v_{i,j,0}^{N-1}& ...& v_{i,j,255}^{N-1}\end{array}\right);$ The concrete grammar that utilizes CPA to carry out step (4) is: the emulation energy consumption of median mapping of (3) step is:

I.e. expressly emulation energy consumption corresponding to s conjecture key byte of j byte of i wheel of k group, HW (x) is 1 number for bit place value in x, and N group plain/cipher text is encrypted/decryption oprerations, determines round key byte rk _{I, j, s}Corresponding emulation energy absorption matrix is:

The concrete grammar that utilizes CPA to carry out above-mentioned steps (5) is: to the sampled energy absorption matrix of step (1) $W(N\&times;T)=\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">s</figure-callout>}}_0^0& ...& s_{T-1}^0\\ .& & .\\ .& s_t^k& .\\ .& & .\\ s_0^{N-1}& ...& s_{T-1}^{N-1}\end{array}\right)$ And the emulation energy absorption matrix H of step (4) calculates respectively the correlation coefficient ρ of both s row and t row _{S, t}:

${\mathrm{\&rho;}}_{s,t}\&ap;r_{s,t}=\frac{\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}][s_t^k-\stackrel{\&OverBar;}{s_t^k}]}{\sqrt{\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}}{[h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}]}^2\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{[s_t^k-\stackrel{\&OverBar;}{s_t^k}]}^2}$ Wherein,

Be expressed as k plain/cipher text, sampled energy consumption figures that a t time point is corresponding, T is the time point number in the energy mark, Be the mean value of matrix H s row,

Be the mean value of matrix W t row, ρ _{S, t}Represent s emulation energy corresponding to conjecture key consume with t time point sampled energy consumption between linearly dependent coefficient, r _{S, t}Be the approximate calculation value of this coefficient correlation, calculate the coefficient correlation between all row row, the correlation matrix that obtains the consumption of emulation energy and sampled energy consumption is $R(256\&times;T)=\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">r</figure-callout>\; </figure-callout>}}_{\mathrm{0,0}}& <figure-callout\; id="0"\; label="...\; r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">.</figure-callout>..& r_{}{}_{0,T-1}\\ .& & .\\ .& r_{s,\mathrm{<figure-callout\; id="0"\; label="t\; ...\; r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">t</figure-callout>}}& .\\ .& & .\\ r_{}{}_{\mathrm{255,0}}& ...& r_{255,T-1}\end{array}\right),$ Choose the maximum r in R _{M, n}=max (r _{S, t}), r _{M, n}Corresponding conjecture key rk _{I, j, m}Be correct conjecture round key byte, namely obtain correct j byte rk of i wheel round key _{I, j}Repeat (1)-(5) step, can obtain respectively other 3 key bytes of round key, thereby obtain the correct round key rk of i wheel _i, take turns for front 4, use round key rk _iCarry out i wheel crypto-operation, obtain the N group wheel output of i wheel, i.e. the wheel input of i+1 wheel

Obtain successively the front 4 encryption round key (rk that take turns ₀, rk ₁, rk ₂, rk ₃)=(K ₄, K ₅, K ₆, K ₇) or decryption round key (rk ₀, rk ₁, rk ₂, rk ₃)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂); Take turns for rear 4, use round key rk _iCarry out i wheel crypto-operation, obtain the wheel output of i-1 wheel

4 encryption round key (the rk that take turns after obtaining successively ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂) or decryption round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₄, K ₅, K ₆, K ₇); Inverse operation obtains the enciphering/deciphering key according to key schedule.

The Hamming distance model that is input as the basis with the S box is as follows to the DPA side channel energy analytical procedure of SM4 cryptographic algorithm:

(a) collecting energy mark specifically carries out every group of plain/cipher text and is encrypted/decrypt operation, gathers energy expenditure information corresponding to Measuring Time point, is the energy mark, sets up the sampled energy absorption matrix; (b) choosing object of attack is S box or round function, determines the DPA choice function; Known i wheel round key j (j ∈ 0,1,2,3}) individual byte rk _{I, j}Corresponding object of attack

With plain/cipher text and conjecture key byte rk _{I, j}As parameter, and desired value

Here the choice function of definition is $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& \mathrm{HW}\left(v_{i,j}^k\right)<4\\ 0& \mathrm{HW}\left(v_{i,j}^k\right)>4\end{array};\right.$ (c) conjecture round key is divided into two average energy mouse collection matrixes with average energy consumption; (d) two average energy mouse collection that obtain according to (c) step ask poor, determine correct conjecture key.

The concrete grammar that utilizes DPA to carry out step (c) is: the input of known k group plain/cipher text $X^k=(X_0^k,X_1^k,X_2^k,X_3^k)$ Or ciphertext/plaintext output $X^k=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k)$ The time, conjecture i wheel round key rk _iIn byte rk _{I, j}, rk _{I, j}The conjecture value be respectively rk _{I, j, s}=s, s ∈ 0 ..., 255}, conjecture round key byte rk _{I, j, s}Corresponding choice function D (X ^k, j, rk _{I, j, s})=1 o'clock, total number

rk _{I, j, s}Corresponding choice function D (X ^k, j, rk _{I, j, s})=0 o'clock, total number

For time point t in the energy mark, obtain the total power consumption average of two of this points: ${d0}_{i,j,s}^t=\frac{\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}(1-D(X^k,j,{\mathrm{rk}}_{i,j,s}))s_{\mathrm{<figure-callout\; id="0"\; label="t\; k\; n"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">t</figure-callout>}}^k}{n_{}}$ With ${d0}_{i,j,s}^t=\frac{\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}D(X^k,j,{\mathrm{rk}}_{i,j,s})s_{\mathrm{<figure-callout\; id="1"\; label="t\; k\; n"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">t</figure-callout>}}^k}{n_{}},$ Wherein,

For using conjecture round key byte rk _{I, j, s}When carrying out N group encryption/decryption oprerations, choice function equals the n of 0 corresponding time point t ₀The group energy consumes mean value;

Equal the n of 1 corresponding time point t by choice function ₁The group energy consumes mean value, n ₀+ n ₁=N asks the energy consumption average by following formula to all time points, obtains two energy consumption matrix D ₀(256 * T) and D ₁(256 * T), be respectively:

$D_0(256\&times;T)=\left(\begin{array}{ccc}{d0}_{i,j,0}^0& ...& {d0}_{i,j,0}^{T-1}\\ .& & .\\ .& {d0}_{i,j,s}^t& .\\ .& & .\\ {d0}_{i,j,255}^0& ...& {d0}_{i,j,255}^{T-1}\end{array}\right)$ With $D_1(256\&times;T)=\left(\begin{array}{ccc}{d1}_{i,j,0}^0& ...& {d1}_{i,j,0}^{T-1}\\ .& & .\\ .& {d1}_{i,j,s}^t& .\\ .& & .\\ {d1}_{i,j,255}^0& ...& {d1}_{i,j,255}^{T-1}\end{array}\right);$ The concrete grammar that utilizes DPA to carry out step (d) is: the average energy consumption matrix D that calculation procedure (c) obtains ₀(256 * T) and D ₁(256 * T) poor matrix Δ D=D ₁-D ₀, select the maximum equal value difference of energy consumption

Corresponding conjecture round key byte rk _{I, j, m}Be correct key byte, namely obtain j byte of correct i wheel round key, repeat (a)-(d) step, can obtain respectively other 3 key bytes of round key, thereby obtain the correct round key rk of i wheel _i, take turns for front 4, use round key rk _iCarry out i wheel crypto-operation, obtain the N group wheel output of i wheel, i.e. the wheel input of i+1 wheel

Obtain successively the front 4 encryption round key (rk that take turns ₀, rk ₁, rk ₂, rk ₃)=(K ₄, K ₅, K ₆, K ₇) or decryption round key (rk ₀, rk ₁, rk ₂, rk ₃)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂); Take turns for rear 4, use round key rk _iCarry out i wheel crypto-operation, obtain the wheel output of i-1 wheel

4 encryption round key (the rk that take turns after obtaining successively ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂) or decryption round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₄, K ₅, K ₆, K ₇); Inverse operation obtains the enciphering/deciphering key according to key schedule.

Above-mentioned when choosing object of attack, before selecting the output of S box/last 4 take turns the Hamming distance (HD (v that attacks employing ₁, v ₂)) the front and continued state v of model ₁The input of S box, follow-up state v ₂Be S box output, it is equivalent to the XOR value exported with the input of S box and S box as the attack of Hamming weight (HW) model of object of attack, namely $v_{i,j}^k={(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k)}_j\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;\mathrm{\&tau;}({(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k)}_j\&CirclePlus;{\mathrm{rk}}_{i,j});$ Before selecting round function/Hamming distance (HD (v of the attack employing of carrying out is taken turns at end 4 ₁, v ₂)) the front and continued state v of model ₁The input of S box, follow-up state v ₂Be the round function input/output, it is equivalent to the input of S box and adopts the attack of Hamming weight (HW) model as object of attack with the XOR value of taking turns input/output, namely $v_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;{\left(L^{-1}{X}_{i+4}^k\right)}_j$ $=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j})$ Or $v_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;{\left(L^{-1}{X}_i^k\right)}_j$ $=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}),,$ Here

The wheel input of i wheel, Be the wheel output of i wheel, i is followed successively by 0,1, and 2,3 or 31,30,29,28.。

Technical scheme of the present invention has the following advantages, and (1) is existing single to the energy leakage analysis site of SM4 cryptographic algorithm, can not adapt to well the realization of various types of SM4 cryptographic algorithms.The present invention is directed to the specific implementation of SM4 cryptographic algorithm, innovation ground has proposed two kinds of novel Hamming distance models, uses the new method of the present invention's proposition can be more effective, all sidedly the SM4 cryptographic algorithms' implementation is carried out the analysis of side channel energy; (2) energy consumption mainly comprises the dynamic power consumption of front and continued and 0 → 1,1 → 0 conversion of follow-up two status bits, and the power consumption values of these two kinds of conversions of HD model hypothesis equates, thereby sets up a proportional relation of changing between quantity and energy consumption.And HW model essence is a special case of HD model, and its all bit of hypothesis front and continued output state is all 0, and energy consumption is only relevant to succeeding state numerical value, and is simpler than HD model, so the accuracy that the HD model is portrayed the emulation energy consumption is far longer than the HW model.Hardware for the SM4 cryptographic algorithm is realized, register is triggered by clock signal, therefore in each clock cycle, previous and the current state of register is only changed once, carry out the analysis of side channel energy by the Hamming distance that adopts continuous clock register-stored numerical value in the cycle, can strengthen analyzing the validity of hard-wired crypto module.The present invention can analyze the SM4 cryptographic algorithm effectively, obtains key information, has expanded the side channel energy analytical method to the SM4 cryptographic algorithm.

Description of drawings

Fig. 1 is the cryptographic structure flow chart of SM4 cryptographic algorithm;

Fig. 2 is the key schedule flow chart of SM4 cryptographic algorithm;

Fig. 3 is the HD model object of attack of S box output;

Fig. 4 is that the HD model front 4 of round function output is taken turns object of attack;

Fig. 5 is that object of attack is taken turns at the HD model end 4 of round function output;

Fig. 6 is CPA analysis process figure;

Fig. 7 is DPA analysis process figure;

Fig. 8 is the sample waveform of 1000 group encryption computings;

Fig. 9 takes turns S box output HD model analysis, correct coefficient correlation waveform corresponding to round key, respectively corresponding 4 S boxes to the 1st;

Figure 10 takes turns S box output HW model analysis, correct coefficient correlation waveform corresponding to round key, respectively corresponding 4 S boxes to the 1st;

Figure 11 is the sample waveform of 1000 group encryption computings in the second embodiment;

Figure 12 is that the second embodiment takes turns S box output HD model analysis, correct coefficient correlation waveform corresponding to round key, respectively corresponding 4 S boxes to the 1st;

Figure 13 is that the second embodiment takes turns S box output HW model analysis, correct coefficient correlation waveform corresponding to round key, respectively corresponding 4 S boxes to the 1st

Embodiment

The below specifically describes technical scheme of the present invention, and at first the round function take the SM4 cryptographic algorithm carries out the CPA analysis as example, and technical scheme of the present invention is described.Fig. 6 is CPA analysis process figure.For the cryptographic calculation of SM4 cryptographic algorithm, if expressly, analyzing front 4 of cryptographic algorithm, known encryption takes turns.Suppose to carry out N group cryptographic calculation expressly, make k that group expressly is input as

K ∈ 0 ..., and N-1}, the wheel of i wheel is input as

I is followed successively by 0,1,2,3, and its step is as follows: (1) collecting energy mark, expressly be encrypted computing to every group, gather the energy expenditure information of Measuring Time point correspondence, be the energy mark, set up sampled energy absorption matrix W (N * T):

$W(N\&times;T)=\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">s</figure-callout>}}_0^0& ...& s_{T-1}^0\\ .& & .\\ .& s_t^k& .\\ .& & .\\ s_0^{N-1}& ...& s_{T-1}^{N-1}\end{array}\right)$

Wherein,

Be expressed as k expressly, sampled energy consumption figures that a t time point is corresponding, T is the time point number in the energy mark;

(2) choose object of attack, determine the algorithm attack model; With the input of the S box front and continued state v as Hamming distance ₁, chosen respectively the output of the output of two point of attack S boxes and round function as follow-up state v ₂, set up two Hamming distances (HD) model.HD (v ₁, v ₂) be v ₁And v ₂Hamming distance, the number that namely in two states, bit 0 → 1,1 → 0 changes, HW (v) is 1 number for bit in v:

Be front and continued state v ₁With follow-up state v ₂Hamming distance HD (v ₁, v ₂) be equivalent to the Hamming weight after both XORs

Therefore the HD model is actual is with Hamming weight (HW) model of the data after front and continued state and follow-up state XOR as the point of attack.Therefore, as the front and continued state, the output of S box is actual as the HD model of succeeding state is with the input of S box and the HW model of output XOR value as the point of attack with the input of S box; As the front and continued state, round function output is actual as the HD model of succeeding state be that the XOR value exported with the input of S box and round function is as the HW model of the point of attack with S box input.

To the HD model of S box output based on hypothesis: the S box input value v that supposes to collect the SM4 crypto module ₁With S box output valve v ₂, the energy leakage point is two state v ₁, v ₂Bit reversal.According to the cryptographic structure of SM4 cryptographic algorithm as can be known, 4 S boxes are separate, and the L shift operation is reversible, are also independently to the wheel computing of 4 bytes of round key, therefore, can select respectively the object of attack corresponding to each key byte of round key.Be the HW model with the HD model conversation, i takes turns round key rk _iByte rk _{I, j}Corresponding object of attack is: $v_{i,j,}^k=\mathrm{\&tau;}((X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,},$ As shown in Figure 3.

To the HD model of round function output based on hypothesis: suppose S box input value v ₁With round function output valve v ₂Be stored in same register, the energy leakage point is two state v ₁, v ₂Bit reversal, can adopt the HD model of same register output state flip.After being the Hamming weight model according to the Hamming distance model conversation, i wheel round key rk _iByte rk _{I, j}Corresponding object of attack is:

$\begin{array}{c}{v}_{i,j}^k={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j}\\ ={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}((X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j}\end{array},$ Concrete object of attack as shown in Figure 4.

(3) the conjecture round key, calculate the median of wheel computing.After determining object of attack and model, conjecture i wheel round key rk _iJ (j ∈ 0,1,2,3}) individual byte rk _{I, j}, j is followed successively by 0,1, and 2,3.rk _{I, j}The conjecture value be respectively rk _{I, j, s}=s, s ∈ 0 ..., 255}.。

For 256 conjecture key byte rk _{I, j, s}, carry out respectively the encryption round computing of i wheel.

To the HD model of S box output, conjecture round key byte rk _{I, j, s}Corresponding median is:

$v_{i,j,s}^k=\mathrm{\&tau;}((X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}.$

To the HD model of round function output, conjecture round key byte rk _{I, j, s}Corresponding median is

$v_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}((X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}.$

According to the median of front formula, when the N group expressly is encrypted operation, calculate successively 256 conjecture round key byte rk _{I, j, s}Corresponding median obtains respectively median matrix V (N * 256):

$V(N\&times;256)=\left(\begin{array}{ccc}{v}_{i,j,0}^0& ...& v_{i,j,256}^0\\ .& & .\\ .& v_{i,j,s}^k& .\\ .& & .\\ v_{i,j,0}^{N-1}& ...& v_{i,j,256}^{N-1}\end{array}\right).$

(4) median is mapped as emulation energy absorption matrix.Go on foot determined energy model according to (3), the emulation energy consumption of median mapping is

For

For carrying out expressly i wheel cryptographic calculation of k group, guess the corresponding emulation energy consumption when being s of j key byte.The N group expressly is encrypted operation, 256 conjecture round key byte rk _{I, j, s}Corresponding emulation energy absorption matrix is:

(5) linearly dependent coefficient of the consumption of Calculation Simulation energy and energy mark, obtain correct conjecture key byte.

To sampled energy absorption matrix W and emulation energy absorption matrix H, calculate respectively the correlation coefficient ρ of both s row and t row _{S, t}: ${\mathrm{\&rho;}}_{s,t}\&ap;r_{s,t}=\frac{\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}][s_t^k-\stackrel{\&OverBar;}{s_t^k}]}{\sqrt{\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}}{[h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}]}^2\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{[s_t^k-\stackrel{\&OverBar;}{s_t^k}]}^2},$ Wherein,

Be the mean value of matrix H s row,

Mean value for matrix W t row.ρ _{S, t}Represent s emulation energy corresponding to conjecture key consume with t time point sampled energy consumption between linearly dependent coefficient, r _{S, t}Approximate calculation value for this coefficient correlation.Calculate the coefficient correlation between all row row, the correlation matrix that obtains the consumption of emulation energy and sampled energy consumption is:

$R(256\&times;T)=\left(\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">r</figure-callout>\; </figure-callout>}}_{\mathrm{0,0}}& ...& {\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">r</figure-callout>}}_{0,T-1}\\ .& & .\\ .& r_{s,t}& .\\ .& & .\\ {\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{255,0}}& ...& r_{255,T-1}\end{array}\right),$ r _{S, t}Larger, be listed as the s conjecture key rk larger, corresponding with the matching degree of row t _{I, j, s}Stronger with the correlation of sampled energy information.Choose the maximum r in R _{M, n}=max (r _{S, t}), r _{M, n}Corresponding conjecture key rk _{I, j, m}Be correct conjecture round key byte, namely obtain correct j byte of i wheel round key.In like manner, according to above-mentioned (1)-(5) step, obtain respectively other 3 key bytes of round key, thereby obtain the correct round key rk of i wheel _i

After i wheel crypto-operation is carried out CPA analysis end, obtain correct round key rk _i, use round key rk _iCarry out i wheel cryptographic calculation, obtain the N group wheel output of i wheel, i.e. the wheel input of i+1 wheel

K ∈ 0,1 ..., N-1}.According to above-mentioned (1)-(5) step analytical method, the round key of four-wheel before obtaining successively: (rk ₀, rk ₁, rk ₂, rk ₃)=(K ₄, K ₅, K ₆, K ₇).

According to the key schedule inverse operation of SM4 cryptographic algorithm,

$K_i=L^{\&prime;}\left(\mathrm{\&tau;}(K_{i+1}\&CirclePlus;K_{i+2}\&CirclePlus;K_{i+3}\&CirclePlus;{\mathrm{CK}}_i)\right)\&CirclePlus;K_{i+4},$ $({\mathrm{<figure-callout\; id="0"\; label="MK"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">MK</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="MK"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">MK</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="MK"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">MK</figure-callout>}}_2,{\mathrm{MK}}_3)=({\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">K</figure-callout>}}_0\&CirclePlus;{\mathrm{<figure-callout\; id="0"\; label="FK"\; filenames="HSA00000846957900042.png"\; state="\{\{state\}\}">FK</figure-callout>}}_0,{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="FK"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">FK</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CirclePlus;{\mathrm{<figure-callout\; id="2"\; label="FK"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">FK</figure-callout>}}_2,{\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="HSA00000846957900011.png,HSA00000846957900012.png"\; state="\{\{state\}\}">F</figure-callout>}}_3\&CirclePlus;{\mathrm{FK}}_3),$ Determine the key (MK of SM4 cryptographic algorithm cryptographic calculation ₀, MK ₁, MK ₂, MK ₃).

If the known encryption ciphertext is analyzed end 4 and taken turns cryptographic operation, analytical method and front 4 is taken turns roughly the same, is only selecting object of attack slightly different.

When supposing to carry out the computing of N group encryption, the ciphertext of k group is output as

Order

Be the wheel output of the SM4 cryptographic algorithm of i wheel, i is followed successively by 31,30, and 29,28.Analytical method to two kinds of Hamming distance models is: analytical method is taken turns at the HD model end 4 to S box output, and its analytical method and front 4 is taken turns identical.After the HD model conversation was the HW model, object of attack was the input and output XOR value of this S box of taking turns, as shown in Figure 3.Conjecture round key byte rk _{I, j, s}Corresponding attack median and front 4 is taken turns in full accord.Obtain successively end 4 and take turns correct round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂), by the key of key schedule inverse operation successful analysis acquisition SM4 cryptographic algorithm cryptographic calculation.

The last four-wheel analytical method of the HD model of round function input, its analytical method and front 4 is taken turns identical, and is only slightly different to attacking object choice.After the HD model conversation was the HW model, end 4 objects of attack of taking turns as shown in Figure 5.Conjecture round key byte rk _{I, j, s}Corresponding attack median is:

$v_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})$

$={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s}),$

According to above-mentioned (1)-(5) step, obtain successively end 4 and take turns correct round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂), according to the key of key schedule inverse operation successful analysis acquisition SM4 cryptographic algorithm cryptographic calculation.

For the decrypt operation of SM4 cryptographic algorithm, can use equally above-mentioned CPA analytical method to obtain decruption key.If known ciphertext is analyzed front 4 of SM4 cryptographic algorithm decrypt operation and taken turns, it is identical that analytical method and front 4 of analysis SM4 cryptographic algorithm cryptographic calculation are taken turns, and obtains successively round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈), inverse operation obtains decruption key according to key schedule; If known-plaintext is analyzed the end 4 of SM4 cryptographic algorithm decrypt operation and taken turns, it is identical that take turns at attack method and the end 4 of analysis SM4 cryptographic algorithm cryptographic calculation, obtains successively round key (rk ₀, rk ₁, rk ₂, rk ₃), inverse operation obtains decruption key according to key schedule.

According to above-mentioned CPA analytical method, adopt respectively the HW model (being the HD model of S box) take S box input and output XOR value as object of attack and be output as the HW model of object of attack with the S box, the 1st of cryptographic calculation is taken turns analyze, known this wheel round key is 0x 85 23 5C E2.

Gather 1000 groups to the waveform of plain text encryption computing, it is the energy mark, as shown in Figure 8, totally 5000 time points, wherein, the sampled energy consumption relevant to the SM4 cryptographic calculation between 43 μ s-50 μ s, totally 408 of the time points corresponding with crypto-operation, sampled energy absorption matrix W (1000 * 408); Select the 1st XOR value of input and output of taking turns the S box as object of attack, set up the HW model; The 1st byte of conjecture round key obtains emulation energy absorption matrix H (1000 * 256); The coefficient correlation of Calculation Simulation energy consumption matrix H and sampling energy consumption matrix W obtains correlation matrix R, selects conjecture key byte corresponding to maximum in R as the 1st byte of round key; Analyze successively other 3 bytes of round key, obtain the 1st and take turns round key rk ₁

Analysis result is as shown in table 1, when having listed respectively 4 round key bytes of conjecture, and the coefficient correlation of front 10 maximums and corresponding conjecture key byte thereof.Take turns for the 1st, correct coefficient correlation corresponding to conjecture key byte is far longer than the coefficient correlation corresponding to conjecture key byte of other 9 mistakes.

Table 1: the S box output HD model that cryptographic calculation the 1st is taken turns carries out the CPA analysis result

Equally, to the energy mark of Fig. 8, select the output of S box as object of attack, set up the HW model, take turns round key 0x 85 23 5C E2 according to above-mentioned steps analysis the 1st, analysis result sees Table 2.As known from Table 2, the coefficient correlation value difference of front 10 maximums is not small, adjacent both all less than 0.02, can't judicious round key, analyze and obtain wrong round key 0x 83 0,A50 82; And the coefficient correlation that in table 1, correct key is corresponding guesses that than other maximum correlation coefficient corresponding to keys is large at least 0.45, thereby is easy to distinguish correct round key.

Table 2: the S box output HW model that cryptographic calculation the 1st is taken turns carries out the CPA analysis result

In addition, Fig. 9, Figure 10 are respectively the coefficient correlation figure of corresponding all time points of correct round key byte when selecting two kinds of objects of attack to analyze.As shown in Figure 9, an obvious spike appears in coefficient correlation corresponding to sampled point, and this spike shows: when the round key conjecture is correct, with the correlation of the sampling energy consumption leak point time point much larger than other; And Figure 10 is without obvious spike, when the round key conjecture is correct, can't distinguish real energy consumption leak point, and coefficient correlation corresponding to all time points is much smaller than the kurtosis of Fig. 9.Therefore, be the input of S box and the conversion of output state when the energy of SM4 cryptographic algorithm computing consumes the leak point, adopt the side channel energy analytical method of the HD model of S box to be better than the side channel energy analytical method of the HW model of employing S box.

According to above-mentioned CPA analytical method, adopt take the input of S box and round function output XOR value as the HW model (being the HD model of round function) of object of attack and be output as the HW model of object of attack with round function, the 1st of cryptographic calculation is taken turns analyze.

A) gather 1000 groups of waveforms to the plain text encryption computing, as shown in figure 11, the sampled energy consumption relevant to the SM4 cryptographic calculation is selected this part time point corresponding with crypto-operation between 7 μ s-11.7 μ s, obtain sampled energy absorption matrix W; Select the 1st XOR value of taking turns the input of S box and round function output as object of attack, set up the HW model; The 1st byte of conjecture round key obtains emulation energy absorption matrix H; The coefficient correlation of Calculation Simulation energy consumption matrix H and sampling energy consumption matrix W obtains correlation matrix R, selects conjecture key byte corresponding to maximum in R as the 1st byte of round key; Analyze successively other 3 bytes of round key, obtain the 1st and take turns round key rk ₁Analysis result is as shown in table 3, has enumerated when analyzing each round key byte the coefficient correlation of front 10 maximums and corresponding conjecture key byte thereof.For the 1st round key conjecture of taking turns, correct coefficient correlation corresponding to conjecture key byte is far longer than the coefficient correlation corresponding to conjecture key byte of other 9 mistakes.

Table 3: the round function output HD model that cryptographic calculation the 1st is taken turns carries out the CPA analysis result

Equally, to the energy mark of Figure 11, select the output of round function as object of attack, set up the HW model, take turns round key 0x 85 23 5C E2 according to above-mentioned steps analysis the 1st, analysis result sees Table 4.As known from Table 4, the coefficient correlation value difference of front 10 maximums is not atomic little, and adjacent both difference is all less than 0.015, thereby can't judicious round key, analyzes and obtains wrong round key 0x CB AC 38 55; And more corresponding than other conjecture keys at least maximum correlation coefficient of the coefficient correlation that in table 3, correct key is corresponding is large 0.4, thereby is easy to distinguish correct round key.

Table 4: the round function output HW model that cryptographic calculation the 1st is taken turns carries out the CPA analysis result

In addition, Figure 12, Figure 13 are respectively the coefficient correlation figure of corresponding all time points of correct round key byte when selecting two kinds of objects of attack to analyze.As shown in Figure 12, an obvious spike appears in the corresponding coefficient correlation of sampled point, and this spike shows: when the round key conjecture is correct, with the correlation of the sampling energy consumption leak point time point much larger than other; And Figure 13 is without obvious spike, when the round key conjecture is correct, can't distinguish real energy consumption leak point, and coefficient correlation corresponding to all time points is much smaller than the kurtosis of Figure 12.Therefore, be the input of S box and the conversion of round function output state when the energy of SM4 cryptographic algorithm computing consumes the leak point, adopt the side channel energy analytical method of the HD model of round function to be better than the side channel energy analytical method of the HW model of employing round function.

It is consistent that DPA analyzes the operation of analyzing in collecting energy mark, selection object of attack with CPA.The principle of analyzing according to above-mentioned DPA, in conjunction with to SM4 cryptographic algorithm construction analysis, the present invention is as follows to the concrete grammar that the S box of SM4 cryptographic algorithm carries out the DPA analysis:

For the cryptographic calculation of SM4 cryptographic algorithm, if expressly, analyzing front 4 of cryptographic algorithm, known encryption takes turns.Suppose to carry out N group cryptographic calculation expressly, make k that group expressly is input as

K ∈ 0 ..., and N-1}, the wheel of i wheel is input as

I is followed successively by 0,1, and 2,3.

(a) collecting energy mark.Expressly be encrypted computing to every group, gather the energy expenditure information (energy mark) of Measuring Time point correspondence, set up sampled energy absorption matrix W (N * T).

(b) choose object of attack, determine the DPA choice function.Object of attack in the DPA analytical method is chosen with the CPA method in full accord.To the HD model of S box output, as shown in Figure 3, i wheel object of attack with the XOR value of S box input and output as a kind of novel object of attack.When carrying out the i wheel cryptographic calculation of k group plaintext input, the object of attack of j byte $v_{i,j}^k={(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k)}_j\&CirclePlus;\mathrm{\&tau;}({(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k)}_j\&CirclePlus;{\mathrm{rk}}_{i,j})$ The Hamming weight desired value

The definition choice function with expressly, the conjecture key is as parameter: $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& \mathrm{HW}\left(v_{i,j}^k\right)<4\\ 0& \mathrm{HW}\left(v_{i,j}^k\right)>4\end{array}\right.;$ To the HD model of round function output, as shown in Figure 4, i wheel object of attack with the XOR value of the input of S box and round function output as a kind of novel object of attack $v_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}).$ In like manner, the definition choice function with expressly, the conjecture key is as parameter, $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& \mathrm{HW}\left(v_{i,j}^k\right)<4\\ 0& \mathrm{HW}\left(v_{i,j}^k\right)>4\end{array}\right..$

(c) the conjecture round key, be divided into two subsets with average energy consumption.After determining object of attack and choice function, guess successively i wheel round key byte rk1 _{I, j}, rk _{I, j}The conjecture value be respectively rk _{I, j, s}=s, s ∈ 0 ..., 255}.Respectively the HD model of S box output and the HD model of round function output are calculated choice function: for 256 conjecture key rk _{I, j, s}, carry out respectively the cryptographic calculation that i takes turns, obtain 256 corresponding medians of attacking, with rk _{I, j, s}Substitution obtains corresponding choice function D (X ^k, j, rk _{I, j, s}).Successively the N group expressly is encrypted computing, conjecture round key byte rk _{I, j, s}Corresponding choice function D (X ^k, j, rk _{I, j, s})=1 o'clock, total number

rk _{I, j, s}Corresponding choice function D (X ^k, j, rk _{I, j, s})=0 o'clock, total number

For two kinds of different HD models, respectively according to choice function, for time point t in the energy mark, obtain two total power consumption averages of this point: With,

Wherein, For using conjecture round key byte rk _{I, j, s}Carry out the operation of N group encryption, D (X ^k, j, rk _{I, j, s})=0 o'clock, the n of corresponding time point t ₀The group energy consumes mean value;

For selecting D (X ^k, j, rk _{I, j, s})=1 o'clock, the n of corresponding time point t ₁The group energy consumes mean value, n ₀+ n ₁=N.All time points are asked the energy consumption average, obtain two energy consumption matrix D ₀(256 * T) and D ₁(256 * T), be respectively: $D_0(256\&times;T)=\left(\begin{array}{ccc}{d0}_{i,j,0}^0& ...& {d0}_{i,j,0}^{T-1}\\ .& & .\\ .& {d0}_{i,j,s}^t& .\\ .& & .\\ {d0}_{i,j,255}^0& ...& {d0}_{i,j,255}^{T-1}\end{array}\right)$ With,

$D_1(256\&times;T)=\left(\begin{array}{ccc}{d1}_{i,j,0}^0& ...& {d1}_{i,j,0}^{T-1}\\ .& & .\\ .& {d1}_{i,j,s}^t& .\\ .& & .\\ {d1}_{i,j,255}^0& ...& {d1}_{i,j,255}^{T-1}\end{array}\right).$

(d) calculate two average energy consumption subset difference, obtain correct conjecture key.Calculate average energy consumption matrix D ₀(256 * T) and D ₁(256 * T) poor, obtain matrix Δ D=D ₁-D ₀

If rk _{I, j, s}The conjecture mistake, for the N group cryptographic calculation of input expressly, choice function is that 0 and 1 probability respectively is about

The corresponding poor increase convergence 0 along with N of average energy consumption; If rk _{I, j, s}Conjecture is correct, and for the N group cryptographic calculation of input expressly, choice function is that 0 or 1 probability should be 1, and the corresponding poor increase along with N of average energy consumption trends towards the actual influence of energy consumption.Select the maximum equal value difference of energy consumption

Corresponding conjecture round key byte rk _{I, j, m}Be correct key byte, namely obtain j byte of correct i wheel round key.In like manner, according to above-mentioned (a)-(b) step, can obtain respectively other 3 key bytes of round key, thereby obtain the correct round key rk of i wheel _i

After i wheel crypto-operation is carried out DPA analysis end, obtain correct round key rk _i, use round key rk _iCarry out i wheel cryptographic calculation, obtain the N group wheel output of i wheel, i.e. the wheel input of i+1 wheel

K ∈ 0,1 ..., N-1}.According to above-mentioned (a)-(b) step analytical method, the round key of four-wheel before obtaining successively: (rk ₀, rk ₁, rk ₂, rk ₃)=(K ₄, K ₅, K ₆, K ₇).

By the inverse operation of cryptographic algorithm cipher key spreading, obtain the key (MK of SM4 cryptographic algorithm cryptographic calculation ₀, MK ₁, MK ₂, MK ₃).

If the known encryption ciphertext is analyzed the end 4 of SM4 cryptographic algorithm and taken turns cryptographic operation, the selection of object of attack and CPA end 4 are taken turns in full accord.

When supposing to carry out the computing of N group encryption, the ciphertext of k group is output as $Y^k=(Y_0^k,Y_1^k,Y_2^k,Y_3^k)=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k),$ Order

Be the SM4 cryptographic algorithm wheel output of i wheel, i is followed successively by 31,30, and 29,28.As shown in Figure 3, the object of attack of the HD model of S box output and CPA end 4 are taken turns consistent, be the input and output XOR value of S box; As shown in Figure 4, the object of attack of the HD model of round function input and CPA end 4 being taken turns consistent, is the XOR value that the input of S box and round function are inputted.According to the above-mentioned the 1st)-4) analytical method in step, obtain successively the end and 4 take turns correct round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂), obtain the key of SM4 cryptographic algorithm cryptographic calculation according to key schedule inverse operation successful analysis.

For the decrypt operation of SM4 cryptographic algorithm, can use equally above-mentioned DPA analytical method to obtain decruption key.If known ciphertext is analyzed front 4 of SM4 cryptographic algorithm decrypt operation and taken turns, it is identical that analytical method and front 4 of analysis SM4 cryptographic algorithm cryptographic calculation are taken turns, and obtains successively round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈), inverse operation obtains decruption key according to key schedule; In like manner, if known-plaintext is analyzed the end 4 of SM4 cryptographic algorithm decrypt operation and taken turns, it is identical that take turns at attack method and the end 4 of analysis SM4 cryptographic algorithm cryptographic calculation, obtains successively round key (rk ₀, rk ₁, rk ₂, rk ₃), inverse operation obtains decruption key according to key schedule.

Technique scheme has only embodied the optimal technical scheme of technical solution of the present invention, and some changes that those skilled in the art may make some part have wherein all embodied principle of the present invention, within belonging to protection scope of the present invention.

Claims (10)

1. be input as the Hamming distance model on basis in the application of SM4 cryptographic algorithm side channel energy analysis with the S box, it is characterized in that, carry out in SM4 cryptographic algorithm side channel energy analytic process, select S box or round function to set up the Hamming distance model as the point of attack, with the input of the S box front and continued state v as the Hamming distance model ₁

2. the Hamming distance model on basis that is input as with the S box according to claim 1 in the application of SM4 cryptographic algorithm side channel energy analysis, is characterized in that, when the S box is attacked, and Hamming distance (HD (v ₁, v ₂)) the follow-up state v of model ₂The output of S box; When round function is attacked, Hamming distance (HD (v ₁, v ₂)) the follow-up state v of model ₂It is the round function input/output.

3. the Hamming distance model on basis that is input as with the S box according to claim 2 in the application of SM4 cryptographic algorithm side channel energy analysis, is characterized in that, before the S box is exported/and the Hamming distance (HD (v that attacks employing is taken turns at end 4 ₁, v ₂)) model is equivalent to S box input and the attack of output XOR value as Hamming weight (HW) model of the point of attack; To before round function/Hamming distance (HD (v that attacks employing 4 is taken turns in the end ₁, v ₂)) model is equivalent to the attack as Hamming weight (HW) model of the point of attack of the XOR value of S box input and round function input/output.

4. according to claim 1, the 2 or 3 described Hamming distance models on basis that are input as with the S box are in the application of SM4 cryptographic algorithm side channel energy analysis, it is characterized in that, be input as the Hamming distance model on basis with the S box for the CPA/DPA side channel energy analysis to the SM4 cryptographic algorithm.

5. the Hamming distance model on basis that is input as with the S box according to claim 4 is in the application of SM4 cryptographic algorithm side channel energy analysis, it is characterized in that, the Hamming distance model that is input as the basis with the S box is as follows to the CPA side channel energy analytical procedure of SM4 cryptographic algorithm:

(1) collecting energy mark specifically carries out every group of plain/cipher text and is encrypted/decrypt operation, gathers energy expenditure information corresponding to Measuring Time point, is the energy mark, sets up the sampled energy absorption matrix;

(2) choosing object of attack is S box or round function, determines the Hamming distance attack model;

(3) determine object of attack and model after, the conjecture round key calculates the median of wheel computing and determines the median matrix;

(4) in utilization, median and the median matrix in step are mapped as emulation energy consumption values and emulation energy absorption matrix;

(5) linearly dependent coefficient of Calculation Simulation energy absorption matrix and sampled energy absorption matrix obtains correct conjecture key.

6. the Hamming distance model on basis that is input as with the S box according to claim 5 is in the application of SM4 cryptographic algorithm side channel energy analysis, it is characterized in that, the concrete grammar that utilizes CPA to carry out step (3) is: (k ∈ { 0 as input k, ..., N-1}) the bright ciphertext I/O of group plaintext is

Or

The time, conjecture i wheel round key

In byte

rk _{I, j}The conjecture value be respectively rk _{I, j, s}=s, s ∈ 0 ..., 255}, before selecting the output of S box/when end 4 is taken turns and is attacked, conjecture round key byte rk _{I, j, s}Corresponding median is,

Wherein,

For carrying out the computing of k group plain/cipher text i wheel encrypt/decrypt, guess j key byte corresponding median when being s,

Difference X _{I+1, j}, X _{I+2, j}, X _{I+3, j}Be the intermediate operations value J the known constant of byte; Select round function output front 4 to take turns or end 4 when taking turns the attack of carrying out, guess round key byte rk _{I, j, s}Corresponding median

Be respectively

With

Wherein, L ^-1(x) _jFor

Carry out L ^-1J byte after displacement,

When bright/the ciphertext of N group is carried out the enciphering/deciphering operation, calculate successively 256 conjecture round key byte rk _{I, j, s}Corresponding median is determined the median matrix

The concrete grammar that utilizes CPA to carry out step (4) is: the emulation energy consumption of median mapping of (3) step is:

I.e. expressly emulation energy consumption corresponding to s conjecture key byte of j byte of i wheel of k group, HW (x) is 1 number for bit place value in x, and N group plain/cipher text is encrypted/decryption oprerations, determines round key byte rk _{I, j, s}Corresponding emulation energy absorption matrix is:

7. be input as the Hamming distance model on basis in the application of SM4 cryptographic algorithm side channel energy analysis with the S box according to claim 5, it is characterized in that, the concrete grammar that utilizes CPA to carry out step (5) is: to the sampled energy absorption matrix of step (1) And the emulation energy absorption matrix H of step (4) calculates respectively the correlation coefficient ρ of both s row and t row _{S, t}:

Wherein, Be expressed as k plain/cipher text, sampled energy consumption figures that a t time point is corresponding, T is the time point number in the energy mark,

Be the mean value of matrix H s row,

Be the mean value of matrix W t row, ρ _{S, t}Represent s emulation energy corresponding to conjecture key consume with t time point sampled energy consumption between linearly dependent coefficient, r _{S, t}Be the approximate calculation value of this coefficient correlation, calculate the coefficient correlation between all row row, the correlation matrix that obtains the consumption of emulation energy and sampled energy consumption is

Choose the maximum r in R _{M, n}=max (r _{S, t}), r _{M, n}Corresponding conjecture key rk _{I, j, m}Be correct conjecture round key byte, namely obtain correct j byte rk of i wheel round key _{I, j}Repeat (1)-(5) step, can obtain respectively other 3 key bytes of round key, thereby obtain the correct round key rk of i wheel _i, take turns for front 4, use round key rk _iCarry out i wheel crypto-operation, obtain the N group wheel output of i wheel, i.e. the wheel input of i+1 wheel Obtain successively the front 4 encryption round key (rk that take turns ₀, rk ₁, rk ₂, rk ₃)=(K ₄, K ₅, K ₆, K ₇) or decryption round key (rk ₀, rk ₁, rk ₂, rk ₃)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂); Take turns for rear 4, use round key rk _iCarry out i wheel crypto-operation, obtain the wheel output of i-1 wheel

4 encryption round key (the rk that take turns after obtaining successively ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂) or decryption round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₄, K ₅, K ₆, K ₇); Inverse operation obtains the enciphering/deciphering key according to key schedule.

8. the Hamming distance model on basis that is input as with the S box according to claim 4 is in the application of SM4 cryptographic algorithm side channel energy analysis, it is characterized in that, the Hamming distance model that is input as the basis with the S box is as follows to the DPA side channel energy analytical procedure of SM4 cryptographic algorithm:

(a) collecting energy mark specifically carries out every group of plain/cipher text and is encrypted/decrypt operation, gathers energy expenditure information corresponding to Measuring Time point, is the energy mark, sets up the sampled energy absorption matrix;

(b) choosing object of attack is S box or round function, determines the DPA choice function; Known i wheel round key j (j ∈ 0,1,2,3}) individual byte rk _{I, j}Corresponding object of attack

With plain/cipher text and conjecture key byte rk _{I, j}As parameter, and desired value

Here the choice function of definition is

(c) conjecture round key is divided into two average energy mouse collection matrixes with average energy consumption;

(d) two average energy mouse collection that obtain according to (c) step ask poor, determine correct conjecture key.

9. be input as the Hamming distance model on basis in the application of SM4 cryptographic algorithm side channel energy analysis with the S box according to claim 8, it is characterized in that, the concrete grammar that utilizes DPA to carry out step (c) is: the input of known k group plain/cipher text

Or ciphertext/plaintext output

The time, conjecture i wheel round key rk _iIn byte rk _{I, j}, rk _{I, j}The conjecture value be respectively rk _{I, j, s}=s, s ∈ 0 ..., 255}, conjecture round key byte rk _{I, j, s}Corresponding choice function D (X ^k, j, rk _{I, j, s})=1 o'clock, total number

rk _{I, j, s}Corresponding choice function D (X ^k, j, rk _{I, j, s})=0 o'clock, total number

For time point t in the energy mark, obtain the total power consumption average of two of this points: With Wherein,

For using conjecture round key byte rk _{I, j, s}When carrying out N group encryption/decryption oprerations, choice function equals the n of 0 corresponding time point t ₀The group energy consumes mean value;

Equal the n of 1 corresponding time point t by choice function ₁The group energy consumes mean value, n ₀+ n ₁=N asks the energy consumption average by following formula to all time points, obtains two energy consumption matrix D ₀(256 * T) and D ₁(256 * T), be respectively:

With

The concrete grammar that utilizes DPA to carry out step (d) is: the average energy consumption matrix D that calculation procedure (c) obtains ₀(256 * T) and D ₁(256 * T) poor matrix Δ D=D ₁-D ₀, select the maximum equal value difference of energy consumption

Corresponding conjecture round key byte rk _{I, j, m}Be correct key byte, namely obtain j byte of correct i wheel round key, repeat (a)-(d) step, can obtain respectively other 3 key bytes of round key, thereby obtain the correct round key rk of i wheel _i, take turns for front 4, use round key rk _iCarry out i wheel crypto-operation, obtain the N group wheel output of i wheel, i.e. the wheel input of i+1 wheel

Obtain successively the front 4 encryption round key (rk that take turns ₀, rk ₁, rk ₂, rk ₃)=(K ₄, K ₅, K ₆, K ₇) or decryption round key (rk ₀, rk ₁, rk ₂, rk ₃)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂); Take turns for rear 4, use round key rk _iCarry out i wheel crypto-operation, obtain the wheel output of i-1 wheel 4 encryption round key (the rk that take turns after obtaining successively ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂) or decryption round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₄, K ₅, K ₆, K ₇); Inverse operation obtains the enciphering/deciphering key according to key schedule.

10. the according to claim 5 or 8 described Hamming distance models on basis that are input as with the S box are in the application of SM4 cryptographic algorithm side channel energy analysis, it is characterized in that, when choosing object of attack, before selecting the output of S box/Hamming distance (HD (v that attacks employing is taken turns at end 4 ₁, v ₂)) the front and continued state v of model ₁The input of S box, follow-up state v ₂Be S box output, it is equivalent to the XOR value exported with the input of S box and S box as the attack of Hamming weight (HW) model of object of attack, namely

Before selecting round function/Hamming distance (HD (v of the attack employing of carrying out is taken turns at end 4 ₁, v ₂)) the front and continued state v of model ₁The input of S box, follow-up state v ₂Be the round function input/output, it is equivalent to the input of S box and adopts the attack of Hamming weight (HW) model as object of attack with the XOR value of taking turns input/output, namely

Or

Here The wheel input of i wheel,

Be the wheel output of i wheel, i is followed successively by 0,1, and 2,3 or 31,30,29,28.

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