CN103138917B - The Hamming distance model being input as basis with S box carries out SM4 cryptographic algorithm side channel energy analytical method - Google Patents

Abstract

The invention discloses and be input as with S box the method that basic Hamming distance model carries out the channel energy analysis of SM4 cryptographic algorithm side, its core is to carry out in the channel energy analytic process of SM4 cryptographic algorithm side, round function is selected to set up Hamming distance model as the point of attack, using the input of S box as the front and continued state v of Hamming distance model ₁, Hamming distance (HD (v ₁, v ₂)) the successor states v of model ₂it is round function input/output.The method can be applicable to the CPA/DPA side channel energy analysis of SM4 cryptographic algorithm.Utilize method of the present invention to improve the correct correlation guessed between key and energy information, enhance and analyze validity and success rate.

Description

The Hamming distance model being input as basis with S box carries out SM4 cryptographic algorithm side channel energy analytical method

Technical field

The invention belongs to 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; side channel energy analysis is carried out for the crypto module realizing SM4 cryptographic algorithm; obtain the Energy Analysis for High of shielded key information; that is, be input as basic Hamming distance model with S box and carry out SM4 cryptographic algorithm side channel energy analytical method.

Background technology

Along with the development of information technology, various cryptographic algorithm is just 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 analysis and research that cryptographic algorithm software and hardware realizes (crypto module) have great importance safely to protection information.In recent years, the multiple attack to crypto module is widely known by the people, and all these objects of attacking are all the keys in order to obtain in crypto module.Common attack pattern can be divided into intrusive mood to attack, half intrusive mood is attacked and non-intrusion type is attacked.In recent years, due to non-intrusion type attack in side Multiple Channel Analysis implement convenient, less expensive and be widely used.Side Multiple Channel Analysis can be subdivided into chronometric analysis, energy spectrometer and emi analysis.Side channel energy analysis is wherein one of method the most frequently used in numerous analysis means, and it breaches the analytical model of conventional cipher algorithm, and ability is powerful, implements relatively easy.Side channel energy analysis and utilization crypto module energy ezpenditure and data operation and the correlation between performing, the energy leakage function based on cryptographic algorithms' implementation sets up energy model, Using statistics 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, DPA principle is: for the enciphering/deciphering computing of N group plain/cipher text data, obtains N bar energy mark, and energy mark here refers to the energy consumption measurement vector collected in a Password Operations process; To each conjecture key K, produce corresponding median (object of attack), according to median determination choice function; By choice function, energy mark collection is divided into two subsets; Be averaged the energy ezpenditure that two sub-set pairs are answered respectively, and ask poor to two average energy consumption values, this equal value difference is that median that choice function is corresponding is to the impact effect of energy mark.According to statistical theory, if K conjecture is incorrect, when the number N convergence of energy mark is infinitely great, the equal value difference of two subsets will level off to zero; If when K conjecture is correct, certain sampling point in energy mark, will there will be the maximum sharpness (maximum absolute value value) of an equal value difference, can determine correct key by maximum sharpness.

CPA principle is: for the enciphering/deciphering computing of N group plain/cipher text data, obtains N bar energy mark; To each conjecture key K, produce corresponding median (object of attack); Energy model is set up according to median; By energy model, median is mapped as simulated energy consumption; Linearly dependent coefficient between computer sim-ulation energy ezpenditure 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 there is noise jamming in collecting energy mark process, maximum is less than 1, and conjecture key corresponding to this coefficient correlation maximum is correct key.

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 nonlinear iteration structure.

The structure of SM4 cryptographic algorithm is as follows:

If $(X_0,X_1,X_2,X_3)\∈{\left(Z_2^{32}\right)}^4$ For encrypting plaintext, $(X_i,X_{i+1},X_{i+2},X_{i+3})\∈{\left(Z_2^{32}\right)}^4$ Be the i-th algorithm input taken turns, be the i-th round key of taking turns, round function F is:

F(X _i,X _i+1,X _i+2,X _i+3,rk _i)＝X _i⊕T(X _i+1⊕X _i+2⊕X _i+3⊕rk _i)(1)

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

τ is made up of, as shown in Figure 2, if be input as 4 parallel S boxes output is $B=(b_0,b_1,b_2,b_3)\∈{\left(Z_2^8\right)}^4,$ Then:

(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 output is $C\∈Z_2^{32},$ Then:

C＝L(B)＝B⊕(B<<<2)⊕(B<<<10)⊕(B<<<18)⊕(B<<<24)(3)

Suppose A _ibe the i-th input taking turns S box, B _ibe the input of the i-th output taking turns S box, L displacement, C _ibe the i-th output taking turns L displacement.Meet as follows according to algorithm:

A _i＝(X _i+1⊕X _i+2⊕X _i+3⊕rk _i)(4)

B _i＝τ(A _i)(5)

C _i＝L(B _i)(6)

X _i+4＝X _i⊕C _i(7)

According to above formula (4), (5), (6), (7), the i-th+1 wheel input (X taken turns can be obtained _i+1, X _i+2, X _i+3, X _i+4), computing 32 is taken turns successively, namely can obtain exporting ciphertext $Y=(Y_0,Y,Y_2,Y_3)=(X_{35},X_{34},X_{33},X_{32})\&Element;{\left(Z_2^{32}\right)}^4,$ 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 similar, as Fig. 2, only linear transformation L shift function is inconsistent.Initial encryption key is made to be (MK ₀, MK ₁, MK ₂, MK ₃).

(K ₀,K ₁,K ₂,K ₃)＝(MK ₀⊕FK ₀,MK ₁⊕FK ₁,MK ₂⊕FK ₂,MK ₃⊕FK ₃)(8)

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

rk _i＝K _i+4＝K _i⊕T′(K _i+1⊕K _i+2⊕K _i+3⊕CK _i)＝K _i⊕L'(τ(K _i+1⊕K _i+2⊕K _i+3⊕CK _i))(9)

Wherein, τ function is consistent with the τ function in above-mentioned SM4 cipher algorithm encryption structure, rk _ibe the i-th encryption key of taking turns, i=0,1 ..., 31, CK _ifor known constant.

Linear transformation L' is:

L'(x)＝x⊕(x<<<13)⊕(x<<<23)(10)

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

Data deciphering is identical with the algorithm structure of data encryption, and just the use order of round key is contrary, and decryption round key is the backward of encryption round key.During deciphering, use round key sequence (rk ₃₁, rk ₃₀..., rk ₀).

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

Summary of the invention

In 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 object of the invention is to the realization character of network analysis SM4 cryptographic algorithm, creatively select the S box output of SM4 cryptographic algorithm, round function (successor states) as the point of attack respectively, innovatively propose the Hamming distance model using the input of S box as Hamming distance reference state (front and continued state), to energy leakage information different during the computing of SM4 cryptographic algorithm, this model improves the correlation between correct conjecture key and energy information, enhances validity and the success rate of analysis.

Realizing above-mentioned purpose technical scheme of the present invention is, the Hamming distance model being input as basis with S box carries out SM4 cryptographic algorithm side channel energy analytical method, carry out in the channel energy analytic process of SM4 cryptographic algorithm side, S box or round function is selected to set up Hamming distance model as the point of attack, using the input of S box as the front and continued state v of Hamming distance model ₁.

When attacking S box, Hamming distance (HD (v ₁, v ₂)) the successor states v of model ₂that S box exports; When round function is attacked, Hamming distance (HD (v ₁, v ₂)) the successor states v of model ₂it is round function input/output.Above-mentioned to S box export before/end 4 take turns carry out attack adopt Hamming distance (HD (v ₁, v ₂)) model is equivalent to attack using S box constrained input XOR value as Hamming weight (HW) model of the point of attack; To before round function/end 4 take turns carry out attack adopt Hamming distance (HD (v ₁, v ₂)) model is equivalent to using the input of S box and the attack as Hamming weight (HW) model of the point of attack of the XOR value of round function input/output.

Above-mentioned with S box be input as basis Hamming distance model for the CPA/DPA side channel energy analysis to SM4 cryptographic algorithm.

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

(1) collecting energy mark, specifically often organizes plain/cipher text and is encrypted/decrypt operation, gathers the energy expenditure information that Measuring Time point is corresponding, is energy mark, sets up sampled energy absorption matrix; (2) choosing object of attack is S box or round function, determines Hamming distance algorithm challenge model; (3), after determining object of attack and model, conjecture round key, calculates the median determination median matrix of wheel computing; (4) median utilization walked and median matrix are mapped as simulated energy consumption figures and simulated energy absorption matrix; (5) linearly dependent coefficient of computer sim-ulation energy ezpenditure matrix and sampled energy absorption matrix, obtains correct conjecture key.

The concrete grammar utilizing CPA to carry out above-mentioned steps (3) is: known kth (k ∈ 0 ..., and N-1}) organize plain/cipher text input $X^k=(X_0^k,X_1^k,X_2^k,X_3^k)$ Or ciphertext/plaintext exports $X^k=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k)$ Time, round key is taken turns in conjecture i-th in byte rk _i,jconjecture value be respectively rk _{i, j, s}=s, s ∈ 0 ..., 255}, when before selecting S box to export/end 4 take turns and attack time, conjecture round key byte rk _{i, j, s}corresponding median is, $v_{i,j,s}^k=\mathrm{\&tau;}\left(\right(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}$ Wherein, encrypt/decrypt computing is taken turns, median corresponding when a conjecture jth key byte is s for carrying out kth group plain/cipher text i-th, x respectively _{i+1, j}, X _{i+2, j}, X _{i+3, j}be intermediate operations value a jth byte; When selection round function output front 4 is taken turns and the attack carried out is taken turns at end 4, conjecture round key byte rk _{i, j, s}corresponding median is respectively $\begin{array}{c}{v}_{i,j,s}^k={\left(L^{-1}{X}_{i+1}^k\right)}_j\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\right)\&CirclePlus;{\mathrm{rk}}_{i,j,s}\\ ={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(\right(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}\end{array}$ With $\begin{array}{c}{v}_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\\ ={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\end{array},$ Wherein, L ^-1(x) _jfor carry out L ^-1a jth byte after displacement, $\begin{array}{c}{L}^{-1}\left(x\right)=x\&CirclePlus;(x<<<2)\&CirclePlus;(x<<<4)\&CirclePlus;(x<<<8)\&CirclePlus;(x<<<12)\&CirclePlus;(x<<<14)\&CirclePlus;(x<<<16)\&CirclePlus;\\ (x<<<18)\&CirclePlus;(x<<<22)\&CirclePlus;(x<<<24)\&CirclePlus;(x<<<30)\end{array};$ To N group bright/ciphertext carry out enciphering/deciphering operation time, calculate 256 conjecture round key byte rk successively _{i, j, s}corresponding median determination median matrix $V(N\&times;256)=\left(\begin{array}{ccc}{v}_{i,j,0}^0& \mathrm{...}& v_{i,j,255}^0\\ .& & .\\ .& v_{i,j,s}^k& .\\ .& & .\\ v_{i,j,0}^{N-1}& \mathrm{...}& v_{i,j,255}^{N-1}\end{array}\right);$ The concrete grammar utilizing CPA to carry out step (4) is: the simulated energy consumption that (3) step median maps is: namely kth group expressly i-th takes turns simulated energy consumption corresponding to jth byte s conjecture key byte, and HW (x) is the number of 1 for bit place value in x, is encrypted/decryption oprerations, determines round key byte rk to N group plain/cipher text _{i, j, s}corresponding simulated energy absorption matrix is:

The concrete grammar utilizing CPA to carry out above-mentioned steps (5) is: to the sampled energy absorption matrix of step (1) $W(N\&times;T)=\left(\begin{array}{ccc}{s}_0^0& \mathrm{...}& s_{T-1}^0\\ .& & .\\ .& s_t^k& .\\ .& & .\\ s_0^{N-1}& \mathrm{...}& s_{T-1}^{N-1}\end{array}\right)$ The correlation coefficient ρ of both s row and t row is calculated respectively with the simulated energy absorption matrix H of step (4) _s,t: ${\mathrm{\&rho;}}_{s,t}\&ap;r_{s,t}=\frac{\underset{k=0}{\overset{N-1}{\&Sigma;}}\&lsqb;h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}\&rsqb;\&lsqb;s_t^k-\stackrel{\&OverBar;}{s_t^k}\&rsqb;}{\sqrt{\underset{k=0}{\overset{N-1}{\&Sigma;}}{\&lsqb;h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}\&rsqb;}^2\underset{k=0}{\overset{N-1}{\&Sigma;}}{\&lsqb;s_t^k-\stackrel{\&OverBar;}{s_t^k}\&rsqb;}^2}}$ Wherein, be expressed as a kth plain/cipher text, sampled energy consumption figures that a t time point is corresponding, T is the time point number in energy mark, for the mean value that matrix H s arranges, for the mean value that matrix W t arranges, ρ _s,trepresent s the conjecture double secret key simulated energy consumption of answering and t time point sampled energy consume between linearly dependent coefficient, r _s,tfor the approximate calculation value of this coefficient correlation, calculate the coefficient correlation between all row row, the correlation matrix obtaining simulated energy consumption and sampled energy consumption is $R(256\&times;T)=\left(\begin{array}{ccc}{r}_{0,0}& \mathrm{...}& r_{0,T-1}\\ .& & .\\ .& r_{s,t}& .\\ .& & .\\ r_{255,0}& \mathrm{...}& r_{255,T-1}\end{array}\right),$ Choose the maximum r in R _m,n=max (r _s,t), r _m,ncorresponding conjecture key rk _{i, j, m}for correct conjecture round key byte, namely obtain correct i-th and take turns a round key jth byte rk _i,j; Repeat (1)-(5) step, other 3 key bytes of round key can be obtained respectively, thus obtain i-th and take turns correct round key rk _i, take turns for front 4, use round key rk _icarry out i-th and take turns crypto-operation, obtain the i-th N group wheel of taking turns and export, be i.e. the i-th+1 wheel input taken turns obtain the front 4 encryption round key (rk taken turns successively 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-th and take turns crypto-operation, obtain the i-th-1 wheel of taking turns and export 4 encryption round key (the rk taken 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); Enciphering/deciphering key is obtained according to key schedule inverse operation.

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

A () collecting energy mark, specifically often organizes plain/cipher text and is encrypted/decrypt operation, gather the energy expenditure information that Measuring Time point is corresponding, be energy mark, set up sampled energy absorption matrix; B () chooses object of attack is S box or round function, determines DPA choice function; Known i-th takes turns round key jth (j ∈ { 0,1,2,3}) individual byte rk _i,jcorresponding object of attack with plain/cipher text and conjecture key byte rk _i,jas parameter, and desired value here the choice function defined is $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& HW\left(v_{i,j}^k\right)<4\\ 0& HW\left(v_{i,j}^k\right)>4\end{array}\right.;$ C () conjecture round key, is divided into two average energy mouse collection matrixes by average energy consumption; D two average energy mouse collection that () obtains according to (c) step ask poor, determine correct conjecture key.

The concrete grammar utilizing DPA to carry out step (c) is: known kth group plain/cipher text input $X^k=(X_0^k,X_1^k,X_2^k,X_3^k)$ Or ciphertext/plaintext exports $X^k=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k)$ Time, round key rk is taken turns in conjecture i-th _iin byte rk _i,j, rk _i,jconjecture 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}during)=1, then total number rk _{i, j, s}corresponding choice function D (X ^k, j, rk _{i, j, s}during)=0, then total number for time point t in energy mark, obtain the total power consumption average of this point two: $d{0}_{i,j,s}^t=\frac{\underset{k=0}{\overset{N-1}{\&Sigma;}}(1-D(X^k,j,{\mathrm{rk}}_{i,j,s}\left)\right)s_t^k}{n_0}$ With $d{1}_{i,j,s}^t=\frac{\underset{k=0}{\overset{N-1}{\&Sigma;}}D(X^k,j,{\mathrm{rk}}_{i,j,s})s_t^k}{n_1},$ 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 time point t corresponding to 0 ₀group energy ezpenditure mean value; for choice function equals the n of time point t corresponding to 1 ₁group energy ezpenditure mean value, n ₀+ n ₁=N, asks energy consumption average by above formula to all time points, obtains two energy consumption matrix D ₀(256 × T) and D ₁(256 × T), is respectively: $D_0(256\&times;T)=\left(\begin{array}{ccc}d{0}_{i,j,0}^0& \mathrm{...}& d{0}_{i,j,0}^{T-1}\\ .& & .\\ .& d{0}_{i,j,s}^t& .\\ .& & .\\ d{0}_{i,j,255}^0& \mathrm{...}& d{0}_{i,j,255}^{T-1}\end{array}\right)$ With $D_1(256\&times;T)=\left(\begin{array}{ccc}d{1}_{i,j,0}^0& \mathrm{...}& d{1}_{i,j,0}^{T-1}\\ .& & .\\ .& d{1}_{i,j,s}^t& .\\ .& & .\\ d{1}_{i,j,255}^0& \mathrm{...}& d{1}_{i,j,255}^{T-1}\end{array}\right);$ The concrete grammar utilizing DPA to carry out step (d) is: the average energy consumption matrix D that calculation procedure (c) obtains ₀(256 × T) and D ₁the poor matrix △ D=D of (256 × T) ₁-D ₀, select the equal value difference of maximum energy consumption then corresponding conjecture round key byte rk _{i, j, m}for correct key byte, namely obtain the jth byte that correct i-th takes turns round key, repeat (a)-(d) step, other 3 key bytes of round key can be obtained respectively, thus obtain i-th and take turns correct round key rk _i, take turns for front 4, use round key rk _icarry out i-th and take turns crypto-operation, obtain the i-th N group wheel of taking turns and export, be i.e. the i-th+1 wheel input taken turns obtain the front 4 encryption round key (rk taken turns successively 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-th and take turns crypto-operation, obtain the i-th-1 wheel of taking turns and export 4 encryption round key (the rk taken 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); Enciphering/deciphering key is obtained according to key schedule inverse operation.

Above-mentioned when choosing object of attack, before selecting S box to export/end 4 is taken turns and is carried out attacking the Hamming distance (HD (v adopted ₁, v ₂)) the front and continued state v of model ₁the input of S box, successor states v ₂be that S box exports, it is equivalent to the attack using the XOR value that S box inputs and S box exports as Hamming weight (HW) model of object of attack, namely $v_{i,j}^k={(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k)}_j\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;\mathrm{\&tau;}({\left(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k\right)}_j\&CirclePlus;{\mathrm{rk}}_{i,j});$ When selecting before round function/Hamming distance (HD (v that the attack carried out adopts is taken turns at end 4 ₁, v ₂)) the front and continued state v of model ₁the input of S box, successor states v ₂be round function input/output, its XOR value being equivalent to the input of S box and wheel input/output adopts the attack of Hamming weight (HW) model as object of attack, namely $\begin{array}{c}{v}_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;{\left(L^{-1}{X}_{i+4}^k\right)}_j\\ =X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j})\end{array}$ Or $\begin{array}{c}{v}_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;{\left(L^{-1}{X}_i^k\right)}_j\\ =X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j})\end{array},,$ Here the i-th wheel input taken turns, be that the i-th wheel of taking turns exports, i is followed successively by 0,1,2,3 or 31, and 30,29,28.

Technical scheme of the present invention has the following advantages, and (1) existing energy leakage analysis site to SM4 cryptographic algorithm is single, can not adapt to the realization of various types of SM4 cryptographic algorithm well.The present invention is directed to the specific implementation of SM4 cryptographic algorithm, innovatively propose two kinds of novel Hamming distance models, the new method using the present invention to propose more effectively, all sidedly can carry out side channel energy analysis to SM4 cryptographic algorithms' implementation; (2) energy ezpenditure mainly comprises the dynamic power consumption that front and continued and follow-up two status bits 0 → 1,1 → 0 are changed, and the power consumption values of HD model hypothesis these two kinds conversion is equal, thus sets up the proportional relation between a conversion quantity and energy consumption.And HW model essence is a special case of HD model, all bits of its hypothesis front and continued output state are all 0, and energy ezpenditure is only relevant to succeeding state numerical value, simpler than HD model, and therefore HD model is portrayed the accuracy emulating energy consumption and is far longer than HW model.For the hardware implementing of SM4 cryptographic algorithm, register is triggered by clock signal, therefore in each clock cycle, register previously and current state only change once, carry out side channel energy analysis by the Hamming distance adopting register in the continuous clock cycle to store numerical value, the validity analyzing hard-wired crypto module can be strengthened.The present invention can analyze SM4 cryptographic algorithm effectively, obtains key information, extends the side channel energy analytical method to SM4 cryptographic algorithm.

Accompanying drawing explanation

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 that S box exports;

Fig. 44 takes turns object of attack before the HD model that exports of round function;

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

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 to the 1st to export HD model analysis, the coefficient correlation waveform that correct round key is corresponding, corresponding 4 S boxes respectively;

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

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 to the 1st, the coefficient correlation waveform that correct round key is corresponding, respectively corresponding 4 S boxes;

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

Embodiment

Below technical scheme of the present invention is specifically described, first carries out CPA for the round function of SM4 cryptographic algorithm and analyze, technical scheme of the present invention is described.Fig. 6 is CPA analysis process figure.For the cryptographic calculation of SM4 cryptographic algorithm, if known encryption expressly, analyze cryptographic algorithm front 4 take turns.Suppose to carry out N group cryptographic calculation expressly, make kth group expressly be input as k ∈ 0 ..., N-1}, the i-th wheel of taking turns is input as i is followed successively by 0,1,2,3, and its step is as follows: (1) collecting energy mark, being expressly encrypted computing, gathering the energy expenditure information that Measuring Time point is corresponding, being energy mark, setting up sampled energy absorption matrix W (N × T) often organizing:

$W(N\&times;T)=\left(\begin{array}{ccc}{s}_0^0& \mathrm{...}& s_{T-1}^0\\ .& & .\\ .& s_t^k& .\\ .& & .\\ s_0^{N-1}& \mathrm{...}& s_{T-1}^{N-1}\end{array}\right)$

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

(2) choose object of attack, determine algorithm challenge model; Front and continued state v using the input of S box as Hamming distance ₁, the output of the output and round function that have chosen two point of attack S boxes is respectively as successor states v ₂, establish two Hamming distance (HD) models.HD (v ₁, v ₂) be v ₁and v ₂hamming distance, namely in two states bit 0 → 1,1 → 0 change number, HW (v) for bit in v be the number of 1, then: HD (v ₁, v ₂)=HW (v ₁⊕ v ₂), i.e. front and continued state v ₁with successor states v ₂hamming distance HD (v ₁, v ₂) be equivalent to the Hamming weight HW (v after both XORs ₁⊕ v ₂), therefore HD model is actual is Hamming weight (HW) model using the data after front and continued state and successor states XOR as the point of attack.Therefore, using the input of S box as front and continued state, it is HW model using S box constrained input XOR value as the point of attack that S box exports actual as the HD model of succeeding state; Using the input of S box as front and continued state, it be HW model using the XOR value that S box inputs and round function exports as the point of attack that round function exports actual as the HD model of succeeding state.

To S box export HD model based on hypothesis: suppose the S box input value v collecting SM4 crypto module ₁with S box output valve v ₂, energy leakage point is two state v ₁, v ₂bit reversal.According to the cryptographic structure of SM4 cryptographic algorithm, 4 S boxes are separate, and L shift operation is reversible, then be also independently to the wheel computing of 4 bytes of round key, therefore, can select the object of attack that each key byte of round key is corresponding respectively.Be HW model by HD model conversation, then i-th take turns round key rk _ibyte rk _i,jcorresponding object of attack is: $v_{i,j}^k=\mathrm{\&tau;}\left(\right(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j},$ As shown in Figure 3.

To round function export HD model based on hypothesis: suppose S box input value v ₁with round function output valve v ₂be stored in same register, energy leakage point is two state v ₁, v ₂bit reversal, the HD model of same register output state flip can be adopted.After being Hamming weight model according to Hamming distance model conversation, i-th takes turns round key rk _ibyte rk _i,jcorresponding object of attack is: $\begin{array}{c}{v}_{i,j}^k={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\right)\&CirclePlus;{\mathrm{rk}}_{i,j}\\ ={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(\right(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j}\end{array},$ Concrete object of attack as shown in Figure 4.

(3) guess round key, calculate the median of wheel computing.After determining object of attack and model, round key rk is taken turns in conjecture i-th _ijth (j ∈ 0,1,2,3}) individual byte rk _i,j, j is followed successively by 0, and 1,2,3.Rk _i,jconjecture value be respectively rk _{i, j, s}=s, s ∈ 0 ..., 255}.

For 256 conjecture key byte rk _{i, j, s}, carry out the i-th encryption round computing taken turns respectively.

To the HD model that S box exports, conjecture round key byte rk _{i, j, s}corresponding median is: $v_{i,j,s}^k=\mathrm{\&tau;}\left(\right(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}.$

To the HD model that round function exports, conjecture round key byte rk _{i, j, s}corresponding median is $v_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(\right(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k)\&CirclePlus;{\mathrm{rk}}_{i,j,s}.$

According to the median of front formula, when being expressly encrypted operation to N group, calculate 256 conjecture round key byte rk successively _{i, j, s}corresponding median, obtains median matrix V (N × 256) respectively: $V(N\&times;256)=\left(\begin{array}{ccc}{v}_{i,j,0}^0& \mathrm{...}& v_{i,j,255}^0\\ .& & .\\ .& v_{i,j,s}^k& .\\ .& & .\\ v_{i,j,0}^{N-1}& \mathrm{...}& v_{i,j,256}^{N-1}\end{array}\right).$

(4) median is mapped as simulated energy absorption matrix.According to the determined energy model of (3) step, the simulated energy consumption that median maps is for expressly i-th cryptographic calculation is taken turns, simulated energy consumption corresponding when a conjecture jth key byte is s for carrying out kth group.Expressly operation is encrypted to N group, 256 conjecture round key byte rk _{i, j, s}corresponding simulated energy absorption matrix is:

(5) linearly dependent coefficient of computer sim-ulation energy ezpenditure and energy mark, obtains correct conjecture key byte.

To sampled energy absorption matrix W and simulated energy absorption matrix H, the coefficient correlation of s row and t row both calculating respectively ${\mathrm{\&rho;}}_{s,t}:{\mathrm{\&rho;}}_{s,t}\&ap;r_{s,t}=\frac{\underset{k=0}{\overset{N-1}{\&Sigma;}}\&lsqb;h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}\&rsqb;\&lsqb;s_t^k-\stackrel{\&OverBar;}{s_t^k}\&rsqb;}{\sqrt{\underset{k=0}{\overset{N-1}{\&Sigma;}}{\&lsqb;h_{i,j,s}^k-\stackrel{\&OverBar;}{h_{i,j,s}^k}\&rsqb;}^2\underset{k=0}{\overset{N-1}{\&Sigma;}}{\&lsqb;s_t^k-\stackrel{\&OverBar;}{s_t^k}\&rsqb;}^2}},$ Wherein, for the mean value that matrix H s arranges, for the mean value that matrix W t arranges.ρ _s,trepresent s the conjecture double secret key simulated energy consumption of answering and t time point sampled energy consume between linearly dependent coefficient, r _s,tfor the approximate calculation value of this coefficient correlation.Calculate the coefficient correlation between all row row, the correlation matrix obtaining simulated energy consumption and sampled energy consumption is: $R(256\&times;T)=\left(\begin{array}{ccc}{r}_{0,0}& \mathrm{...}& r_{0,T-1}\\ .& & .\\ .& r_{s,t}& .\\ .& & .\\ r_{255,0}& \mathrm{...}& r_{255,T-1}\end{array}\right),$ R _s,tlarger, then arrange s larger with the matching degree of row t, corresponding conjecture key rk _{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,ncorresponding conjecture key rk _{i, j, m}for correct conjecture round key byte, namely obtain correct i-th and take turns a round key jth byte.In like manner, according to above-mentioned (1)-(5) step, obtain other 3 key bytes of round key respectively, thus obtain i-th and take turns correct round key rk _i.

To i-th take turns crypto-operation carry out CPA analyze terminate after, obtain correct round key rk _i, use round key rk _icarry out i-th and take turns cryptographic calculation, obtain the i-th N group wheel of taking turns and export, be i.e. the i-th+1 wheel input taken turns 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'(τ (K _i+1⊕ K _i+2⊕ K _i+3⊕ CK _i)) ⊕ K _i+4, (MK ₀, MK ₁, MK ₂, MK ₃)=(K ₀⊕ FK ₀, K ₁⊕ FK ₁, K ₂⊕ FK ₂, K ₃⊕ FK ₃), determine the key (MK of SM4 cipher algorithm encryption computing ₀, MK ₁, MK ₂, MK ₃).

If known encryption ciphertext, then analyze end 4 and take turns cryptographic operation, analytical method and front 4 is taken turns roughly the same, only slightly different in selection object of attack.

When supposing to carry out the computing of N group encryption, the ciphertext of kth group exports and is order be the wheel output of the SM4 cryptographic algorithm that i-th takes turns, i is followed successively by 31, and 30,29,28.To the analytical method of two kinds of Hamming distance models be: take turns analytical method to the HD model end 4 that S box exports, its analytical method and front 4 is taken turns identical.HD model conversation is after HW model, and object of attack is the input and output XOR value of the S box that this is taken turns, as shown in Figure 3.Conjecture round key byte rk _{i, j, s}corresponding attack median and front 4 is taken turns completely the same.Obtain end 4 successively and take turns correct round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂), the key of SM4 cipher algorithm encryption computing is obtained by key schedule inverse operation successful analysis.

The HD model end four-wheel analytical method of round function input, its analytical method and front 4 is taken turns identical, only slightly different to the selection of object of attack.HD model conversation is after HW model, and the object of attack that end 4 is taken turns as shown in Figure 5.Conjecture round key byte rk _{i, j, s}corresponding attack median is: $\begin{array}{c}{v}_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s}\right)\\ ={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\&CirclePlus;(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s})\end{array},$

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

For the decrypt operation of SM4 cryptographic algorithm, above-mentioned CPA analytical method can be used equally to obtain decruption key.If known ciphertext, analyze SM4 cryptographic algorithm decrypt operation front 4 take turns, and analytical method and analyze the computing of SM4 cipher algorithm encryption front 4 is taken turns identical, obtains round key (rk successively ₃₁, rk ₃₀, rk ₂₉, rk ₂₈), obtain decruption key according to key schedule inverse operation; If known-plaintext, the end 4 analyzing SM4 cryptographic algorithm decrypt operation is taken turns, and attack method is taken turns identical with the end 4 analyzing the computing of SM4 cipher algorithm encryption, obtains round key (rk successively ₀, rk ₁, rk ₂, rk ₃), obtain decruption key according to key schedule inverse operation.

According to above-mentioned CPA analytical method, adopt with the S box input and output XOR value HW model (i.e. the HD model of S box) that is object of attack respectively and to export with S box be the HW model of object of attack, take turns the 1st of cryptographic calculation and analyze, it is 0x85235CE2 that known this takes turns round key.

Gather 1000 groups of waveforms to plain text encryption computing, i.e. energy mark, as shown in Figure 8, totally 5000 time points, wherein, the sampled energy consumption relevant to SM4 cryptographic calculation between 43 μ s-50 μ s, the time point corresponding with crypto-operation totally 408, then sampled energy absorption matrix W (1000 × 408); Select the 1st to take turns the XOR value of the input and output of S box as object of attack, set up HW model; Conjecture round key the 1st byte, obtains simulated energy absorption matrix H (1000 × 256); Computer sim-ulation energy consumption matrix H and the coefficient correlation of sampling energy consumption matrix W, obtain correlation matrix R, the conjecture key byte selecting the maximum in R corresponding is as the 1st byte of round key; Analyze other 3 bytes of round key successively, obtain the 1st and take turns round key rk ₁.

Analysis result is as shown in table 1, when listing conjecture 4 round key bytes respectively, and the conjecture key byte of front 10 maximum coefficient correlations and correspondence thereof.Take turns for the 1st, the coefficient correlation that correct conjecture key byte is corresponding is far longer than coefficient correlation corresponding to other 9 wrong conjecture key bytes.

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

Equally, to the energy mark of Fig. 8, select the output of S box as object of attack, set up HW model, take turns round key 0x85235CE2 according to above-mentioned steps analysis the 1st, analysis result is in table 2.As known from Table 2, front 10 maximum correlation coefficient value difference are small, and adjacent both are all less than 0.02, cannot judicious round key, analyze the round key 0x830A5082 obtaining mistake; And the maximum correlation coefficient at least large 0.45 that the coefficient correlation that in table 1, correct double secret key is answered is answered than other conjecture double secret key, thus be easy to distinguish correct round key.

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

In addition, Fig. 9, Figure 10 are respectively the coefficient correlation figure of correct round key byte corresponding all time points when selection two kinds of objects of attack are analyzed.As shown in Figure 9, there is an obvious spike in the coefficient correlation that sampled point is corresponding, this spike shows: when round key conjecture is correct, with the correlation of sampling energy consumption leak point much larger than other time point; And Figure 10 is without obvious spike, when round key conjecture is correct, real energy consumption leak point cannot be distinguished, and coefficient correlation corresponding to all time points is much smaller than the kurtosis of Fig. 9.Therefore, when the energy ezpenditure leak point of SM4 cryptographic algorithm computing is the conversion of the constrained input state of S box, 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 adopting S box.

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

A) gather 1000 groups of waveforms to plain text encryption computing, as shown in figure 11, the sampled energy consumption relevant to SM4 cryptographic calculation, between 7 μ s-11.7 μ s, is selected the time point that this part is corresponding with crypto-operation, is obtained sampled energy absorption matrix W; Select the 1st to take turns XOR value that the input of S box exports with round function, as object of attack, sets up HW model; Conjecture round key the 1st byte, obtains simulated energy absorption matrix H; Computer sim-ulation energy consumption matrix H and the coefficient correlation of sampling energy consumption matrix W, obtain correlation matrix R, the conjecture key byte selecting the maximum in R corresponding is as the 1st byte of round key; Analyze other 3 bytes of round key successively, obtain the 1st and take turns round key rk ₁.Analysis result is as shown in table 3, enumerates when analyzing each round key byte, the conjecture key byte of front 10 maximum coefficient correlations and correspondence thereof.For the round key conjecture that the 1st takes turns, the coefficient correlation that correct conjecture key byte is corresponding is far longer than coefficient correlation corresponding to other 9 wrong conjecture key bytes.

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

Equally, to the energy mark of Figure 11, select the output of round function as object of attack, set up HW model, take turns round key 0x85235CE2 according to above-mentioned steps analysis the 1st, analysis result is in table 4.As known from Table 4, front 10 maximum correlation coefficient value difference are atomic little, and both difference adjacent is all less than 0.015, thus cannot judicious round key, analyze the round key 0xCBAC3855 obtaining mistake; And the coefficient correlation that in table 3, correct double secret key is answered is at least than the maximum correlation coefficient large 0.4 that other conjecture double secret key are answered, thus be easy to distinguish correct round key.

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

In addition, Figure 12, Figure 13 are respectively the coefficient correlation figure of correct round key byte corresponding all time points when selection two kinds of objects of attack are analyzed.As shown in Figure 12, there is an obvious spike in the corresponding coefficient correlation of sampled point, this spike shows: when 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 round key conjecture is correct, real energy consumption leak point cannot be distinguished, and coefficient correlation corresponding to all time points is much smaller than the kurtosis of Figure 12.Therefore, when the energy ezpenditure leak point of SM4 cryptographic algorithm computing is the input of S box and the conversion of round function output state, 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 adopting round function.

DPA analysis is analyzed at collecting energy mark with CPA, is selected the operation of object of attack to be consistent.According to the principle that above-mentioned DPA analyzes, in conjunction with the analysis to SM4 cryptographic algorithm structure, the concrete grammar that the S box of the present invention to SM4 cryptographic algorithm carries out DPA analysis is as follows:

For the cryptographic calculation of SM4 cryptographic algorithm, if known encryption expressly, analyze cryptographic algorithm front 4 take turns.Suppose to carry out N group cryptographic calculation expressly, make kth group expressly be input as k ∈ 0 ..., N-1}, the i-th wheel of taking turns is input as i is followed successively by 0, and 1,2,3.

(a) collecting energy mark.Expressly being encrypted computing to often organizing, gathering the energy expenditure information (energy mark) that Measuring Time point is corresponding, setting up sampled energy absorption matrix W (N × T).

B () chooses object of attack, determine DPA choice function.Object of attack in DPA analytical method is chosen with CPA method completely the same.To the HD model that S box exports, as shown in Figure 3, i-th takes turns object of attack using the XOR value of S box input and output as a kind of novel object of attack.When carry out the input of kth group plaintext i-th takes turns cryptographic calculation, the object of attack of a jth byte $v_{i,j}^k={(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k)}_j\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;\mathrm{\&tau;}({\left(X_{i+1}^k\&CirclePlus;X_{i+2}^k\&CirclePlus;X_{i+3}^k\right)}_j\&CirclePlus;{\mathrm{rk}}_{i,j})$ Hamming weight desired value define choice function using plaintext, conjecture key as parameter, then: $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& HW\left(v_{i,j}^k\right)<4\\ 0& HW\left(v_{i,j}^k\right)>4\end{array}\right.;$ To the HD model that round function exports, as shown in Figure 4, i-th object of attack is taken turns using the XOR value that S box inputs and round function exports 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, choice function is defined using plaintext, conjecture key as parameter, then $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& HW\left(v_{i,j}^k\right)<4\\ 0& HW\left(v_{i,j}^k\right)>4\end{array}\right..$

C () conjecture round key, is divided into two subsets by average energy consumption.After determining object of attack and choice function, guess that i-th takes turns round key byte rk successively _i,j, rk _i,jconjecture value be respectively rk _{i, j, s}=s, s ∈ 0 ..., 255}.Respectively choice function is calculated to the HD model that HD model and the round function of the output of S box export: guess key rk for 256 _{i, j, s}, carry out the i-th cryptographic calculation of taking turns respectively, obtain 256 and attack median accordingly, by rk _{i, j, s}substitution obtains corresponding choice function D (X ^k, j, rk _{i, j, s}).Successively expressly computing is encrypted to N group, conjecture round key byte rk _{i, j, s}corresponding choice function D (X ^k, j, rk _{i, j, s}during)=1, then total number rk _{i, j, s}corresponding choice function D (X ^k, j, rk _{i, j, s}during)=0, then total number for two kinds of different HD models, respectively according to choice function, for time point t in energy mark, obtain this point two total power consumption averages: 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}during)=0, the n of corresponding time point t ₀group energy ezpenditure mean value; for selecting D (X ^k, j, rk _{i, j, s}during)=1, the n of corresponding time point t ₁group energy ezpenditure mean value, n ₀+ n ₁=N.Energy consumption average is asked to all time points, obtains two energy consumption matrix D ₀(256 × T) and D ₁(256 × T), is respectively: $D_0(256\&times;T)=\left(\begin{array}{ccc}d{0}_{i,j,0}^0& \mathrm{...}& d{0}_{i,j,0}^{T-1}\\ .& & .\\ .& d{0}_{i,j,s}^t& .\\ .& & .\\ d{0}_{i,j,255}^0& \mathrm{...}& d{0}_{i,j,255}^{T-1}\end{array}\right)$ With, $D_1(256\&times;T)=\left(\begin{array}{ccc}d{1}_{i,j,0}^0& \mathrm{...}& d{1}_{i,j,0}^{T-1}\\ .& & .\\ .& d{1}_{i,j,s}^t& .\\ .& & .\\ d{1}_{i,j,255}^0& \mathrm{...}& d{1}_{i,j,255}^{T-1}\end{array}\right).$

D () calculates two average energy consumption subset difference, obtain correct conjecture key.Calculate average energy consumption matrix D ₀(256 × T) and D ₁the difference of (256 × T), obtains matrix △ D=D ₁-D ₀.

If rk _{i, j, s}conjecture mistake, then for the cryptographic calculation that N group expressly inputs, choice function be 0 and 1 probability be respectively about corresponding average energy consumption difference is along with the increase convergence 0 of N; If rk _{i, j, s}conjecture is correct, then for the cryptographic calculation of N group expressly input, choice function be 0 or 1 probability should be 1, the average energy consumption difference of correspondence trends towards the actual influence of energy consumption along with the increase of N.Select the maximum equal value difference of energy consumption then corresponding conjecture round key byte rk _{i, j, m}for correct key byte, namely obtain the jth byte that correct i-th takes turns round key.In like manner, according to above-mentioned (a)-(b) step, other 3 key bytes of round key can be obtained respectively, thus obtain i-th and take turns correct round key rk _i.

To i-th take turns crypto-operation carry out DPA analyze terminate after, obtain correct round key rk _i, use round key rk _icarry out i-th and take turns cryptographic calculation, obtain the i-th N group wheel of taking turns and export, be i.e. the i-th+1 wheel input taken turns 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).

The inverse operation expanded by crypt algorithm keys, obtains the key (MK of SM4 cipher algorithm encryption computing ₀, MK ₁, MK ₂, MK ₃).

If known encryption ciphertext, then cryptographic operation is taken turns at the end 4 analyzing SM4 cryptographic algorithm, and selection and the CPA end 4 of object of attack are taken turns completely the same.

When supposing to carry out the computing of N group encryption, the ciphertext of kth group exports and is $Y^k=(Y_0^k,Y_1^k,Y_2^k,Y_3^k)=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k),$ Order be that the i-th SM4 cryptographic algorithm wheel of taking turns exports, i is followed successively by 31, and 30,29,28.As shown in Figure 3, taking turns consistent to the object of attack of the HD model that S box exports with CPA end 4, is the input and output XOR value of S box; As shown in Figure 4, taking turns consistent to the object of attack of the HD model of round function input with CPA end 4, is the XOR value that the input of S box inputs with round function.According to the above-mentioned 1st) ~ 4) analytical method of step, obtain end 4 successively and take turns correct round key (rk ₃₁, rk ₃₀, rk ₂₉, rk ₂₈)=(K ₃₅, K ₃₄, K ₃₃, K ₃₂), the key of SM4 cipher algorithm encryption computing is obtained according to key schedule inverse operation successful analysis.

For the decrypt operation of SM4 cryptographic algorithm, above-mentioned DPA analytical method can be used equally to obtain decruption key.If known ciphertext, analyze SM4 cryptographic algorithm decrypt operation front 4 take turns, and analytical method and analyze the computing of SM4 cipher algorithm encryption front 4 is taken turns identical, obtains round key (rk successively ₃₁, rk ₃₀, rk ₂₉, rk ₂₈), obtain decruption key according to key schedule inverse operation; In like manner, if known-plaintext, the end 4 analyzing SM4 cryptographic algorithm decrypt operation is taken turns, and attack method is taken turns identical with the end 4 analyzing the computing of SM4 cipher algorithm encryption, obtains round key (rk successively ₀, rk ₁, rk ₂, rk ₃), obtain decruption key according to key schedule inverse operation.

Technique scheme only embodies the optimal technical scheme of technical solution of the present invention, and those skilled in the art all embody principle of the present invention to some variations that wherein some part may be made, and belong within protection scope of the present invention.

Claims (10)

1. be input as basic Hamming distance model with S box and carry out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, carry out in the channel energy analytic process of SM4 cryptographic algorithm side, select round function to set up Hamming distance model as the point of attack with the input of S box and round function output; The input of S box is now as the front and continued state v of Hamming distance model ₁.

2. according to claim 1 with S box be input as basis Hamming distance model carry out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, when round function is attacked, Hamming distance (HD (v ₁, v ₂)) the successor states v of model ₂it is round function input/output.

3. according to claim 2 with S box be input as basis Hamming distance model carry out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, to before round function/end 4 take turns carry out attack adopt Hamming distance (HD (v ₁, v ₂)) model is equivalent to using the input of S box and the attack as Hamming weight (HW) model of the point of attack of the XOR value of round function input/output.

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

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

(1) collecting energy mark, specifically often organizes plain/cipher text and is encrypted/decrypt operation, gathers the energy expenditure information that Measuring Time point is corresponding, is energy mark, sets up sampled energy absorption matrix;

(2) choosing object of attack is round function, determines Hamming distance challenge model;

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

(4) median utilization walked and median matrix are mapped as simulated energy consumption figures and simulated energy absorption matrix;

(5) linearly dependent coefficient of computer sim-ulation energy ezpenditure matrix and sampled energy absorption matrix, obtains correct conjecture key.

6. according to claim 5 with S box be input as basis Hamming distance model carry out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, the concrete grammar utilizing CPA to carry out step (3) is: when to N (k ∈ { 0,1,, N-1}) organize plain/cipher text and be encrypted/decryption oprerations time, known kth (k ∈ { 0, ..., N-1}) the plain/cipher text input organized or the output of ciphertext/is plaintext respectively $X^k=(X_0^k,X_1^k,X_2^k,X_3^k),$ $X^k=(X_{35}^k,X_{34}^k,X_{33}^k,X_{32}^k)$ Time, round key is taken turns in conjecture i-th in byte wherein Z ₂ ⁸, Z ₂ ³²for with 0,1} be element 8 dimension and 32 gt, rk _i,jconjecture value be respectively rk _{i, j, s}=s, s ∈ 0 ..., and 255}, when selection round function output front 4 is taken turns or the attack carried out is taken turns at end 4, conjecture round key byte rk _{i, j, s}corresponding median be respectively:

$\begin{array}{c}{v}_{i,j,s}^k={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\right)\&CirclePlus;{\mathrm{rk}}_{i,j,s}\\ ={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\right)\&CirclePlus;{\mathrm{rk}}_{i,j,s}\right)\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\right)\&CirclePlus;{\mathrm{rk}}_{i,j,s}\end{array}$ With $\begin{array}{c}{v}_{i,j,s}^k={\left(L^{-1}{X}_i^k\right)}_j\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s}\right)\\ ={\left(L^{-1}{X}_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s}\right)\&CirclePlus;\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j,s}\right)\end{array},$ Wherein, L ^-1(x) _jfor carry out L ^-1a jth byte after displacement, $\begin{array}{c}{L}^{-1}\left(x\right)=x\&CirclePlus;\left(x<<<2\right)\&CirclePlus;\left(x<<<4\right)\&CirclePlus;\left(x<<<8\right)\&CirclePlus;\left(x<<<12\right)\&CirclePlus;\left(x<<<14\right)\&CirclePlus;\left(x<<<16\right)\&CirclePlus;\\ \left(x<<<18\right)\&CirclePlus;\left(x<<<22\right)\&CirclePlus;\left(x<<<24\right)\&CirclePlus;\left(x<<<30\right)\end{array};$ τ is made up of, if be input as 4 parallel S boxes $A=(a_0,a_1,a_2,a_3)\&Element;{\left(Z_2^8\right)}^4,$ Output is $B=(b_0,b_1,b_2,b_3)\&Element;{\left(Z_2^8\right)}^4,$ Then: (b ₀, b ₁, b ₂, b ₃)=τ (A)=(Sbox (a ₀), Sbox (a ₁), Sbox (a ₂), Sbox (a ₃)); To N group bright/ciphertext carry out enciphering/deciphering operation time, calculate 256 conjecture round key byte rk successively _{i, j, s}corresponding median determination median matrix the concrete grammar utilizing CPA to carry out step (4) is: the simulated energy consumption that (3) step median maps is: namely kth group expressly i-th takes turns simulated energy consumption corresponding to jth byte s conjecture key byte, and HW (x) is the number of 1 for bit place value in x, is encrypted/decryption oprerations, determines round key byte rk to N group plain/cipher text _{i, j, s}corresponding simulated energy absorption matrix is:

7. the Hamming distance model being input as basis according to claim 5 with S box carries out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, the concrete grammar utilizing CPA to carry out step (5) is: to the sampled energy absorption matrix of step (1) the correlation coefficient ρ of both s row and t row is calculated respectively with the simulated energy absorption matrix H of step (4) _s,t: wherein, be expressed as a kth plain/cipher text, sampled energy consumption figures that a t time point is corresponding, T is the time point number in energy mark, for the matrix element in simulated energy absorption matrix, namely kth group expressly i-th takes turns simulated energy consumption corresponding to jth byte s conjecture key byte, for the mean value that matrix H s arranges, for the mean value that matrix W t arranges, ρ _s,trepresent s the conjecture double secret key simulated energy consumption of answering and t time point sampled energy consume between linearly dependent coefficient, r _s,tfor the approximate calculation value of this coefficient correlation, calculate the coefficient correlation between all row row, the correlation matrix obtaining simulated energy consumption and sampled energy consumption is choose the maximum r in R _m,n=max (r _s,t), r _m,ncorresponding conjecture key rk _{i, j, m}for correct conjecture round key byte, namely obtain correct i-th and take turns a round key jth byte rk _i,j; Repeat (1)-(5) step, other 3 key bytes of round key can be obtained respectively, thus obtain i-th and take turns correct round key rk _i, take turns for front 4, use round key rk _icarry out i-th and take turns crypto-operation, obtain the i-th N group wheel of taking turns and export, be i.e. the i-th+1 wheel input taken turns obtain the front 4 encryption round key (rk taken turns successively 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-th and take turns crypto-operation, obtain the i-th-1 wheel of taking turns and export 4 encryption round key (the rk taken 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); Enciphering/deciphering key is obtained according to key schedule inverse operation.

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

A () collecting energy mark, specifically often organizes the computing of plain/cipher text encrypt/decrypt, gather the energy expenditure information that Measuring Time point is corresponding, be energy mark, set up sampled energy absorption matrix;

B () chooses object of attack is round function, determines DPA choice function; Known i-th takes turns round key jth (j ∈ { 0,1,2,3}) individual byte rk _i,jcorresponding object of attack is with plain/cipher text and conjecture key byte rk _i,jas parameter, and its desired value here the choice function defined is $D(X^k,j,{\mathrm{rk}}_{i,j})=\left\{\begin{array}{cc}1& HW\left(v_{i,j}^k\right)<4\\ 0& HW\left(v_{i,j}^k\right)>4\end{array}\right.,$ Wherein HW (x) represent in x Bit String be 1 number;

C () conjecture round key, is divided into two average energy mouse collection matrixes by average energy consumption;

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

9. be input as basic Hamming distance model with S box according to claim 8 and carry out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, the concrete grammar utilizing DPA to carry out step (c) is: known kth group plain/cipher text input or ciphertext/plaintext exports time, round key rk is taken turns in conjecture i-th _iin byte rk _i,j, rk _i,jconjecture 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}during)=1, then total number rk _{i, j, s}corresponding choice function D (X ^k, j, rk _{i, j, s}during)=0, then total number for time point t in energy mark, obtain the total power consumption average of this point two: 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 time point t corresponding to 0 ₀group energy ezpenditure mean value; for choice function equals the n of time point t corresponding to 1 ₁group energy ezpenditure mean value, n ₀+ n ₁=N, N are encrypted the/group number of decryption oprerations, ask energy consumption average, obtain two energy consumption matrix D by above formula to all time points ₀(256 × T) and D ₁(256 × T), is respectively:

with

The concrete grammar utilizing DPA to carry out step (d) is: the average energy consumption matrix D that calculation procedure (c) obtains ₀(256 × T) and D ₁the poor matrix △ D=D of (256 × T) ₁-D ₀, select the equal value difference of maximum energy consumption then corresponding conjecture round key byte rk _{i, j, m}for correct key byte, namely obtain the jth byte that correct i-th takes turns round key, repeat (a)-(d) step, other 3 key bytes of round key can be obtained respectively, thus obtain i-th and take turns correct round key rk _i, take turns for front 4, use round key rk _icarry out i-th and take turns crypto-operation, obtain the i-th N group wheel of taking turns and export, be i.e. the i-th+1 wheel input taken turns obtain the front 4 encryption round key (rk taken turns successively 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-th and take turns crypto-operation, obtain the i-th-1 wheel of taking turns and export 4 encryption round key (the rk taken 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); Enciphering/deciphering key is obtained according to key schedule inverse operation.

10. the Hamming distance model being input as basis with S box according to claim 6 carries out SM4 cryptographic algorithm side channel energy analytical method, it is characterized in that, when selecting before round function/and the Hamming distance (HD (v that the attack carried out adopts is taken turns at end 4 ₁, v ₂)) the front and continued state v of model ₁the input of S box, successor states v ₂be round function input/output, its XOR value being equivalent to the input of S box and wheel input/output adopts the attack of Hamming weight (HW) model as object of attack, namely $\begin{array}{c}{v}_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;{\left(L^{-1}{X}_{i+4}^k\right)}_j\\ =X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_i^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\right)\end{array}$ Or $\begin{array}{c}{v}_{i,j}^k=X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;{\left(L^{-1}{X}_i^k\right)}_j\\ =X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\&CirclePlus;L^{-1}{\left(X_{i+4}^k\right)}_j\&CirclePlus;\mathrm{\&tau;}\left(X_{i+1,j}^k\&CirclePlus;X_{i+2,j}^k\&CirclePlus;X_{i+3,j}^k\&CirclePlus;{\mathrm{rk}}_{i,j}\right)\end{array},$ Here the i-th wheel input taken turns, be that the i-th wheel of taking turns exports, i is followed successively by 0,1,2,3 or 31, and 30,29,28.