CN105227295A - A kind of Differential fault injection attacks for SMS4 cryptographic algorithm - Google Patents
A kind of Differential fault injection attacks for SMS4 cryptographic algorithm Download PDFInfo
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- CN105227295A CN105227295A CN201510652968.7A CN201510652968A CN105227295A CN 105227295 A CN105227295 A CN 105227295A CN 201510652968 A CN201510652968 A CN 201510652968A CN 105227295 A CN105227295 A CN 105227295A
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Abstract
The invention discloses a kind of Differential fault injection attacks for SMS4 cryptographic algorithm.This attack is by direct fault location in the rear four-wheel computing of SMS4 cipher algorithm encryption process, and after making ciphering process, four-wheel produces any mistake, and utilizes consequent wrong ciphertext to attack.Choose in wrong ciphertext, utilize correct ciphertext to compare, identical, that ciphertext is different and data message the is complete wrong ciphertext of plaintext is chosen out, in follow-up difference analysis.For when often taking turns attack, the wrong ciphertext adopted is identical, without the need to carrying out encrypt data classification according to needing of often taking turns.This method solve the special byte of present stage directional induction to produce the infeasible problem of specific fault and need to re-start the problem of direct fault location for often taking turns attack.
Description
Technical field
The present invention relates to cryptographic algorithm analyzing and testing field, particularly relate to a kind of Differential fault injection attacks for SMS4 cryptographic algorithm.
Background technology
Generally, the hardware device or the software program that run cryptographic algorithm all can correctly perform various cryptographic algorithm, but in cases of a disturbance, may be there is register mistake or computing in crypto-operation module, utilize these misdeeds or information to be called code error analysis to the method recovering key.Encryption device mostly realizes based on electronic technology, and interface is also relatively simple, and be comparatively vulnerable to external interference, this makes direct fault location analysis become one of the most effective bypass analysis method.
Direct fault location is exactly the condition of work at some suitable time change crypto chip, and the intermediateness that crypto chip is run changes, and then the bypass producing mistake output or exception is revealed.May be there is register mistake or computing in crypto-operation module, utilize these misdeeds or information to be called code error analysis to the method recovering key.Encryption device mostly realizes based on electronic technology, and interface is also relatively simple, and be comparatively vulnerable to external interference, this makes error analysis become one of the most effective bypass analysis method.Invade the degree of encryption device interface and running environment according to assailant, direct fault location can be divided into non-intrusion type direct fault location, half intrusive mood direct fault location and intrusive mood direct fault location three kinds.Non-intrusion type direct fault location, by the mode of external interference, as clock, voltage or magnetic field etc., allows crypto chip perform and makes mistakes, have higher feasibility compared to other two kinds of modes.And non-intrusion type direct fault location is a kind of attack pattern of cheap and simple, uses such attack only to need to use external interface modification condition, normally implemented by voltage, clock signal upset etc.This attack pattern disguise is higher, is difficult to be found.
Differential fault attack (DFA) is a kind of attack method produced after fault injection attacks method and traditional differential cryptanalysis method combine, mainly utilize the mistake of same plaintext respectively after correct output under normal circumstances and direct fault location export between relation carry out key and crack.It is specifically expressed as follows: (1) determines a plaintext, and under correct key effect, obtain corresponding correct ciphertext; (2) for same plaintext, fault induction is carried out to ciphering process, and obtain corresponding wrong ciphertext; (3) correct ciphertext and wrong ciphertext are analyzed, assailant can obtain the candidate value set of each key, to the common factor that can obtain these cipher key sets after multiple ciphertext analysis, correct key is affirmed in common factor, by analyzing one by one multiple key and then realizing key recovery.
SMS4 cryptographic algorithm is the grouping symmetric cryptographic algorithm of China's designed, designed, and its fundamental property has: (1) block length and key length are all 128bit; (2) algorithms for encryption and decryption structure is the same, and just the order of respective loops use is contrary; (3) what cryptographic algorithm and key schedule all adopted is 32 takes turns nonlinear iteration structure, and its repeatability makes SMS4 algorithm can be used on a special chip ideally; (4) SMS4 algorithm uses the arithmetic sum logical operation of standard, and its effect number mostly is 32bit most, is therefore easy to realize by hardware technology.Below for the first run flow process of encryption and key schedule algorithm, introduce SMS4 algorithm.
The first run flow process of SMS4 cryptographic algorithm as shown in Figure 1.Suppose that input is expressly (X
0, X
1, X
2, X
3) ∈ (Z
2 32)
4, output ciphertext is (Y
0, Y
1, Y
2, Y
3) ∈ (Z
2 32)
4, round key is (rk
0, rk
1..., rk
31) ∈ (Z
2 32)
4, S box be input as S
in, export as S
out, the output of linear transformation L is L
out, then basic process is as follows the SMS4 cryptographic algorithm first round:
1）S
in=X
1⊕X
2⊕X
3⊕rk
0=(a
0，a
1，a
2，a
3)∈(Z
2 32)
4；
2）S
out=τ(S
in)
=(Sbox(a
0)，Sbox(a
1，Sbox(a
2)，Sbox(a
3))
=(b
0，b
1，b
2，b
3)∈(Z
2 32)
4；
3)L
out=L(S
out)
=S
out⊕(S
out<<<2)⊕(S
out<<<10)⊕(S
out<<<18)⊕(S
out<<<24)；
4)X
4=X
0⊕L
out；
Therefore the output of the first round is (X
1, X
2, X
3, X
4), all the other 32 steps of taking turns are identical with the first round, and just in the end one take turns and namely the 32nd take turns and also need to carry out an antitone mapping, as shown in Figure 2, finally exporting ciphertext is:
(Y
1，Y
2，Y
3，Y
4)=R(X
32，X
33，X
34，X
35)=(X
35，X
34，X
33，X
32)；
In SMS4 algorithm, the sub-key of cryptographic algorithm is generated by key schedule by primary key, and its flow process as shown in Figure 3.If primary key MK=is (MK
0, MK
1, MK
2, MK
3), i=0,1,2,3.Make K
i∈ Z
2 32, i=0,1,2 ..., 35, sub-key rk
i∈ Z
2 32, i=0,1,2 ..., 31, then sub-key generation method is as follows:
1）(K
0，K
1，K
2，K
3)=(MK
0⊕FK
0，MK
1⊕FK
1，MK
2⊕FK
2，MK
3⊕FK
3)
2）rk
i=K
i+4=K
i⊕Tˊ(K
i+3⊕K
i+2⊕K
i+1⊕CK
i)
Wherein, T ˊ conversion converts substantially identical with the T in enciphering transformation, but linear transformation must change to L ˊ, i.e. L ˊ (B)=B ⊕ (B<<<13) ⊕ (B<<<23).
The value of system parameters FK, adopts 16 systems to be expressed as:
FK
0=A3B1BAC6，FK
1=56AA3350，FK
2=677D9197，FK
3=B27022DC。
The obtaining value method of preset parameter CK is: establish ck
i,jfor CK
ijth byte (i=0,1,2 ..., 31; J=0,1,2,3), i.e. CK
i=(ck
i, 0, ck
i, 1, ck
i, 2, ck
i, 3) ∈ (Z
2 32), then ck
i,j=(4i+j) × 7 (mod256).32 preset parameter CK
ibe expressed as with 16 systems:
00070e15,1c232a31,383f464d,545b6269,70777e85,8c939aa1,a8afb6bd,c4cbd2d9,
e0e7eef5,fc030a11,181f262d,343b4249,50575e65,6c737a81,888f969d,a4abb2b9,
c0c7ced5,dce3eaf1,f8ff060d,141b2229,30373e45,4c535a61,686f767d,848b9299,
a0a7aeb5,bcc3cad1,d8dfe6ed,f4fb0209,10171e25,2c333a41,484f565d,646b727。
According to key schedule algorithm, the method for anti-release primary key is as follows:
1) known rear four respective loops rk
31, rk
30, rk
29, rk
28, then have:
rk
31=rk
35rk
30=rk
34rk
29=rk
33rk
28=rk
32
2) by rk
31=K
31⊕ T ˊ (K
34⊕ K
33⊕ K
32⊕ CK
31) can obtain: K
31=rk
31⊕ T ˊ (rk
30⊕ rk
29⊕ rk
28⊕ CK
31)
3) by rk
i=K
i+4can obtain: rk
27=K
31, this just obtains the reciprocal 5th and takes turns i.e. the 28th sub-key of taking turns.The like, each sub-key of taking turns and primary key can be recovered.
In the research of the differential fault attack for SMS4 cryptographic algorithm, Zhang Lei and Wu Wenling has carried out this kind of research at first in 2006, but the prerequisite of its success attack be to often wheel attack before, need the mistake producing byte in fixing position, and all produce premised on byte fault by a certain position in follow-up numerous document published, and suppose in this to be difficult to realize in actual attack.
Summary of the invention
The object of this invention is to provide a kind of differential fault attack method for SMS4 cryptographic algorithm, to solve two practical problems: (1) cannot induce some special byte of certain intermediateness to produce the problem of specific fault, namely the theoretical research of present stage all adopts the random fault model of byte-oriented, and success attack has a precondition supposed, require that some specified byte of certain median of induction convert exactly, and this hypothesis is difficult to control in the fault induction of reality.(2) when attacking round key, must carry out special direct fault location for the requirement often taken turns, often attack one and take turns and again will carry out direct fault location as requested, process is loaded down with trivial details.The present invention has creatively carried out Arbitrary Fault injection to four-wheel after SMS4 cryptographic algorithm, do not need to carry out failure and special induction, and the fault data to adopt for the attack often taken turns is all identical, also without the need to refilling fault, this make actual carry out fault injection attacks time, direct fault location implements very easy.
For solving the problem, the invention provides a kind of Differential fault injection attacks for SMS4 cryptographic algorithm, specifically comprising the following steps:
S1: determine one group of expressly X, and obtain this group expressly X correct ciphertext Y in normal state, and the wrong ciphertext Y ˊ under direct fault location state.
S11: determine one group of expressly X, and obtain this group expressly correct ciphertext Y of X under correct key K effect.
S12: input phase isolog X, and Arbitrary Fault injection is carried out to the rear four-wheel of SMS4 cipher algorithm encryption process, obtain the expressly wrong ciphertext Y ˊ of X under direct fault location state, as shown in Figure 4.
S13: utilize expressly X and correct ciphertext Y, compare with the wrong ciphertext Y ˊ under malfunction, chooses out, for follow-up difference analysis by complete for data return value (comprising plaintext and ciphertext), expressly identical, that ciphertext is different wrong ciphertext.
S2: difference analysis is carried out to the correct ciphertext Y got and wrong ciphertext Y ˊ, attacks out the sub-key rk that SMS4 cryptographic algorithm the 32nd is taken turns
32.Then the sub-key rk that identical correct ciphertext Y, mistake ciphertext Y ˊ and the 32nd take turns is utilized
32attack out the 31st sub-key rk taken turns
31.In like manner, attack out the 30th successively and take turns the sub-key rk taken turns with 29
30and rk
29.
S21: according to antitone mapping, calculates reverse for ciphertext the input value entering antitone mapping R, i.e. the 32nd output valve of taking turns, and wherein correct output valve is designated as XX4, XX3, XX2, XX1, and erroneous output value is Xx4, Xx3, Xx2, Xx1;
S22: calculate the difference value of S box input and the difference value of S box output, be designated as Sin_differ and Sout_differ respectively, then have:
Sin_differ=XX3⊕Xx3⊕XX2⊕Xx2⊕XX1⊕Xx1；
Sout_differ=invT1(XX4⊕Xx4)；
Wherein invT1 is the inverse transformation of L conversion.
Remember that the corresponding Sout_differ of four S boxes is S
a[i], i value is 0,1,2,3, represents four S boxes from left to right, then has:
S
a[i]=Sout_differ>>(8*i)＆0xFF；
S23: calculate S box and export, the output that wherein correct data enters S box is designated as S
b, the output that misdata enters S box is designated as S
c, then have for four S boxes:
S
b[i]=S(XX3⊕XX2⊕XX1⊕M)>>(8*i)＆0xFF；
S
c[i]=S(XX3⊕XX2⊕XX1⊕M⊕Sin_differ)>>(8*i)＆0xFF；
Wherein, M is 256 kinds of candidate's sub-keys.
S24: 256 kinds of candidate's sub-key M are taken turns in the formula of S23, and judges S
a[i] and S
b[i] ⊕ S
cwhether [i] be identical, if identical, is then possible correct sub-key.
S25: the 32nd sub-key rk taken turns can be obtained by S24
32, utilize rk
32computing is decrypted to correct ciphertext and wrong ciphertext, obtains the 31st correct wheel output valve of taking turns and mistake wheel output valve, and then carry out the computing of S22 to S24, finally attack out the 31st sub-key rk taken turns
31.Repeat this process, so obtain the 30th taking turns, the 29th sub-key rk taken turns
30and rk
29.
S3: utilize the rk obtained
32, rk
31, rk
30, rk
29in conjunction with the inverse operation of SMS4 key schedule algorithm, each sub-key of taking turns and primary key can be recovered.
Accompanying drawing explanation
Fig. 1 is SMS4 cryptographic algorithm first run flow chart.
Fig. 2 is SMS4 cryptographic algorithm antitone mapping R.
Fig. 3 is SMS4 cipher key spreading flow chart.
Fig. 4 is direct fault location schematic diagram.
Fig. 5 is the Differential fault injection attacks basic flow sheet for SMS4 cryptographic algorithm.
Embodiment
Below the specific embodiment of the present invention is described; so that those skilled in the art understand the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various change to limit and in the spirit and scope of the present invention determined, these conversion are apparent, and all innovation and creation utilizing the present invention to conceive are all at the row of protection in appended claim.
For the fault injection attacks method of SMS4 cryptographic algorithm, specifically comprise the following steps:
S1: determine one group of expressly X, and obtain this group expressly X correct ciphertext Y in normal state, and the wrong ciphertext Y ˊ under direct fault location state.
S11: determine one group of expressly X, and obtain this group expressly correct ciphertext Y of X under correct key K effect.
S12: input phase isolog X, and Arbitrary Fault injection is carried out to the rear four-wheel of SMS4 cipher algorithm encryption process, obtain the expressly wrong ciphertext Y ˊ of X under direct fault location state.
S13: utilize expressly X and correct ciphertext Y, compare with the wrong ciphertext Y ˊ under malfunction, chooses out, for follow-up difference analysis by complete for data return value (comprising plaintext and ciphertext), expressly identical, that ciphertext is different wrong ciphertext.
S2: difference analysis is carried out to the correct ciphertext Y got and wrong ciphertext Y ˊ, attacks out the sub-key rk that SMS4 cryptographic algorithm the 32nd is taken turns
32.Then the sub-key rk that identical correct ciphertext Y, mistake ciphertext Y ˊ and the 32nd take turns is utilized
32attack out the 31st sub-key rk taken turns
31.In like manner, attack out the 30th successively and take turns the sub-key rk taken turns with 29
30and rk
29.
S21: according to antitone mapping, calculates reverse for ciphertext the input value entering antitone mapping R, i.e. the 32nd output valve of taking turns, and wherein correct output valve is designated as XX4, XX3, XX2, XX1, and erroneous output value is Xx4, Xx3, Xx2, Xx1;
S22: calculate the difference value of S box input and the difference value of S box output, be designated as Sin_differ and Sout_differ respectively, then have:
Sin_differ=XX3⊕Xx3⊕XX2⊕Xx2⊕XX1⊕Xx1；
Sout_differ=invT1(XX4⊕Xx4)；
Wherein invT1 is the inverse transformation of L conversion.
Remember that the corresponding Sout_differ of four S boxes is S
a[i], i value is 0,1,2,3, represents four S boxes from left to right, then has:
S
a[i]=Sout_differ>>(8*i)＆0xFF；
S23: calculate S box and export, the output that wherein correct data enters S box is designated as S
b, the output that misdata enters S box is designated as S
c, then have for four S boxes:
S
b[i]=S(XX3⊕XX2⊕XX1⊕M)>>(8*i)＆0xFF；
S
c[i]=S(XX3⊕XX2⊕XX1⊕M⊕Sin_differ)>>(8*i)＆0xFF；
Wherein, M is 256 kinds of candidate's sub-keys.
S24: 256 kinds of candidate's sub-key M are taken turns in the formula of S23, and judges S
a[i] and S
b[i] ⊕ S
cwhether [i] be identical, if identical, is then possible correct sub-key.
S25: the 32nd sub-key rk taken turns can be obtained by S24
32, utilize rk
32computing is decrypted to correct ciphertext and wrong ciphertext, obtains the 31st correct wheel output valve of taking turns and mistake wheel output valve, and then carry out the computing of S22 to S24, finally attack out the 31st sub-key rk taken turns
31.Repeat this process, so obtain the 30th taking turns, the 29th sub-key rk taken turns
30and rk
29.
S3: utilize the rk obtained
32, rk
31, rk
30, rk
29in conjunction with the inverse operation of SMS4 key schedule algorithm, each sub-key of taking turns and primary key can be recovered.
Claims (3)
1., for the Differential fault injection attacks of SMS4 cryptographic algorithm, using the rear four-wheel of SMS4 algorithm for encryption process as target, it is characterized in that said method comprising the steps of:
S1: determine one group of expressly X, and obtain the wrong ciphertext Y ˊ of this group expressly under X correct ciphertext Y in normal state and direct fault location state;
S2: difference analysis is carried out to the correct ciphertext Y got and wrong ciphertext Y ˊ, attacks out the sub-key rk that SMS4 cryptographic algorithm the 32nd is taken turns
32, then utilize the sub-key rk that identical correct ciphertext Y, mistake ciphertext Y ˊ and the 32nd take turns
32attack out the 31st sub-key rk taken turns
31, in like manner, attack out the 30th successively and take turns the sub-key rk taken turns with 29
30and rk
29;
S3: utilize the rk obtained
32, rk
31, rk
30, rk
29in conjunction with the inverse operation of SMS4 key schedule algorithm, each sub-key of taking turns and primary key can be recovered.
2. method according to claim 1, is characterized in that S1 specifically comprises the following steps:
S11: determine one group of expressly X, and obtain this group expressly correct ciphertext Y of X under correct key K effect;
S12: input phase isolog X, and Arbitrary Fault injection is carried out to the rear four-wheel of SMS4 cipher algorithm encryption process, obtain the expressly wrong ciphertext Y ˊ of X under direct fault location state;
S13: utilize expressly X and correct ciphertext Y, compare with the wrong ciphertext Y ˊ under malfunction, chooses out, for follow-up difference analysis by complete for data return value (comprising plaintext and ciphertext), expressly identical, that ciphertext is different wrong ciphertext.
3. method according to claim 1, is characterized in that S2 specifically comprises the following steps:
S21: according to antitone mapping, calculates reverse for ciphertext the input value entering antitone mapping R, i.e. the 32nd output valve of taking turns, and wherein correct output valve is designated as XX4, XX3, XX2, XX1, and erroneous output value is Xx4, Xx3, Xx2, Xx1;
S22: calculate the difference value of S box input and the difference value of S box output, be designated as Sin_differ and Sout_differ respectively, then have:
Sin_differ=XX3⊕Xx3⊕XX2⊕Xx2⊕XX1⊕Xx1；
Sout_differ=invT1(XX4⊕Xx4)；
Wherein invT1 is the inverse transformation of L conversion;
Remember that the corresponding Sout_differ of four S boxes is S
a[i], i value is 0,1,2,3, represents four S boxes from left to right, then has:
S
a[i]=Sout_differ>>(8*i)＆0xFF；
S23: calculate S box and export, the output that wherein correct data enters S box is designated as S
b, the output that misdata enters S box is designated as S
c, then have for four S boxes:
S
b[i]=S(XX3⊕XX2⊕XX1⊕M)>>(8*i)＆0xFF；
S
c[i]=S(XX3⊕XX2⊕XX1⊕M⊕Sin_differ)>>(8*i)＆0xFF；
Wherein, M is 256 kinds of candidate's sub-keys;
S24: 256 kinds of candidate's sub-key M are taken turns in the formula of S23, and judges S
a[i] and S
b[i] ⊕ S
cwhether [i] be identical, if identical, is then possible correct sub-key;
S25: the 32nd sub-key rk taken turns can be obtained by S24
32, utilize rk
32computing is decrypted to correct ciphertext and wrong ciphertext, obtains the 31st correct wheel output valve of taking turns and mistake wheel output valve, and then carry out the computing of S22 to S24, finally attack out the 31st sub-key rk taken turns
31, repeat this process, so obtain the 30th taking turns, the 29th sub-key rk taken turns
30and rk
29.
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| CN112464294A (en) * | 2020-12-11 | 2021-03-09 | 北京智慧云测信息技术有限公司 | Fault injection attack method and device and electronic equipment |
| CN113206734A (en) * | 2021-04-30 | 2021-08-03 | 桂林电子科技大学 | Method for detecting and resisting differential fault attack |
| CN113434332A (en) * | 2021-05-27 | 2021-09-24 | 国家信息技术安全研究中心 | Fault propagation-based key recovery method for DES/3DES middle wheel attack |
| CN114124353A (en) * | 2021-11-19 | 2022-03-01 | 东华大学 | Secret key leakage detection method for authentication encryption algorithm SILC |
| CN114124353B (en) * | 2021-11-19 | 2024-03-29 | 东华大学 | Key leakage detection method for authentication encryption algorithm SILC |
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