CN109600232A - For attack verifying, means of defence and the device of SM2 signature algorithm - Google Patents
For attack verifying, means of defence and the device of SM2 signature algorithm Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
- H04L63/1408—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic by monitoring network traffic
- H04L63/1416—Event detection, e.g. attack signature detection
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- H04L63/1433—Vulnerability analysis
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/002—Countermeasures against attacks on cryptographic mechanisms
- H04L9/003—Countermeasures against attacks on cryptographic mechanisms for power analysis, e.g. differential power analysis [DPA] or simple power analysis [SPA]
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/002—Countermeasures against attacks on cryptographic mechanisms
- H04L9/004—Countermeasures against attacks on cryptographic mechanisms for fault attacks
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
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- H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
- H04L9/3252—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr schemes
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Abstract
The present invention discloses attack verifying, means of defence and the device for SM2 signature algorithm.The attack verification method carries out error injection attack in the addition position of SM2 signature algorithm, which protects the addition and subtraction process that random number k participates in.Attack verifying device for SM2 signature algorithm includes attack module, and the protective device for SM2 signature algorithm includes protection module.Present invention discover that safeguard procedures in the prior art have ignored the protection when calculating s to random number k; either original formula k-r*dA; or deformed formula r+k; all there is the addition and subtraction for thering is random number k to participate in; and existing guard technology does not all protect this place; so that current SM2 Encryption Algorithm, there are certain risk loophole, means of defence proposed by the present invention can effectively antagonize corresponding attack means, prevent information leakage.
Description
Technical field
The present invention relates to computer encryption technology fields, and in particular to a kind of attack verifying for SM2 signature algorithm, anti-
Maintaining method and device.
Background technique
1985, Neal Koblitz and Victor Miller, which are separately proposed, designed public affairs using elliptic curve
The problem of key cipher system.After nineteen ninety, elliptic curve cipher (Elliptic Curve Cryptography abbreviation ECC)
Start to obtain the approval of business circles, it is recognized that standardization body formulated elliptic curve crypto-protocol.ECC and RSA is to rely on
In the dyscalculia (abbreviation DLP problem) of discrete logarithm, if G is a limited ABEL module, it is assumed that some member that g is G,
A is arbitrary integer, if it is known that how g and ag, find out the problem that integer a comes and be mathematically known as discrete logarithm problem.From
Discrete logarithm problem can be subdivided into two classes again, and one kind is the discrete logarithm problem (RSA Algorithm) in some finite field；One kind is ellipse
Discrete logarithm problem (ECC algorithm) on curve.The two compares, and latter class problem solving is more more difficult.
The close SM2 ellipse curve public key cipher algorithm of state is asymmetric cryptographic algorithm, is the asymmetric calculation based on ECC algorithm
Method.It is issued by national Password Management office on December 17th, 2010.Currently, all trades and professions are all wideling popularize commercial national secret algorithm
Use, the industry especially to involve the interests of the state and the people in finance, social security etc., thus SM2 algorithm whether there is assailable loophole
And how security protection is carried out, it is the emphasis of those skilled in the art's research.
Currently, main attack method includes power analysis, fault injection attacks and attacks for block cipher failure
It hits.Wherein the basic thought of power analysis is to obtain its key by analyzing the energy consumption of encryption device.Substantially,
Two class energy consumption dependences: data dependency and operation dependency, the i.e. instantaneous energy of encryption device are utilized in this attack
The operation that consumption is carried out dependent on data and equipment handled by equipment.Power analysis is divided into simple energy analysis
(SPA) and differential power analysis (DPA).SPA is that one kind can be to the collected energy consumption of institute in cryptographic algorithm implementation procedure
The technology that information is directly analyzed, each of encryption device algorithm, which has, certain executes sequence.The behaviour that algorithm defines
It is translated into the instruction that equipment is supported.If attacker is detailed to being had by the specific implementation of cryptographic algorithm in attack equipment
Understanding, then the corresponding power consumption profile of each operational order can be distinguished from energy mark.That is SPA is attacked mainly along the time
Axis carrys out the energy consumption of analytical equipment.Attacker attempts to find certain mode in single energy mark or match with template.
If only executing some specific instruction when a certain bit of key is 1, while only being held when a certain bit of key is 0
Another instruction of row, then by checking instruction sequence embodied in energy mark, so that it may be inferred to key.
Fault injection attacks are that a few thing condition for changing crypto chip in the suitable time makes in chip operation
Between state change, and then cause output error or bypass leakage, attacker using these information implement analyze so that attacks
Hit key.Differential fault analysis DFA, security error analysis SEA and collision event are broadly divided into for block cipher fault attacks
Barrier analysis CFA and its invalid failures of extension analyze IFA.
In current SM2 signature algorithm, the calculating process of s are as follows: s=((1+dA) -1 (k-rdA)) modn；It realizes
The pseudocode for calculating s is as follows:
Temp1=r*dA；
Temp1=k-temp1；
Temp2=(1+dA) -1；
S=temp1*temp2.
As it can be seen that only having used private key dA when calculating s in SM2 signature algorithm, calculates and there was only two in the equation of s
A unknown number, k and dA.When putting for k times of calculating, if do not protected k, SPA attacks the value of available k, then
Private key dA can be computed.Therefore, corresponding protection in the prior art are as follows: the k times of algorithm put is changed (such as by design
Dressing algorithm, calculated under Jacobi Coordinate system etc.), or mask protection is carried out to k, so that during putting for K times of calculating
Can not carry out SPA attack to k also can not just obtain private key to can not obtain the value of k when calculating s.Because k is a random
Number can not determine median so the value of k is all different when SM2 signs every time, so that DPA attack can not be carried out to k；
It can be seen that one multiplication is r*dA, and which results in typical DPA risks when calculating s.This process is same
There are the risks of error injection for sample.The last byte of dA is changed when signature, becomes dA ', then signs,
The r generated at this time is pair that s becomes s ', s '=(1+dA)-1* (k-r*dA '), when sign test, s ' G+t ' PA ≠ kG, s ' G+t ' PA
=(x1 ', y1 ')
S ' G+t ' PA=s ' G+ (r+s ') dA*G
=s ' (1+dA) G+r*dA*G
=(1+dA)-1*(k-r*dA’)*(1+dA)*G+r*dA*G
=kG+r* (dA-dA ') * G
=(x1 ', y1 ')
The gap of only one byte of dA and dA ', it is assumed that the last byte of dA is d1d0, then poor value range
Be the back section [0, d1d0] U [d1d0-ff, -1] be negative value, [p+d1d0-ff, p-1] is changed to, so the meeting on power consumption profile
There are two apparent sections, so as to obtain the value of interval border, traverse a byte and need 256 times, can find out correct
Difference, then repeatedly signed, statistical difference occur range, obtain boundary value, so that it may find out the last byte of dA.
To cope with prime formula s=(1+dA)-1The formula, is deformed by * typical DPA risk present in (k-r*dA) in the prior art
S=(1+dA)-1* (r+k)-r defends this attack, calculates s formula equivalent variations process as follows:
S=(1+dA)-1*(k-r*dA)mod N
=(1+dA)-1*k-(1+dA)-r*dA*(1+dA)-1mod N
=(1+dA)-1*k-r*(dA+1-1)*(1+dA)-1mod N
=(1+dA)-1*k-r+r*(1+dA)-1mod N
=(1+dA)-1*(k+r)-r mod N
At this point, k+r is random number, attacker does not know, so dA can not be deduced.For prevent attacker obtain it is any with
The relevant data of private key, manufacturer import private key dA when calculating s again, recalculate to the dA median for participating in calculating,
Whether identical compare two times result, is verified.As a result, in the prior art in SM2 signature s realization (band protection) process are as follows:
Temp1=r+k；
Temp2=(1+dA)-1；
Temp3=temp1*temp2；
S1=temp3-r；
Again dA is imported, dA2 is denoted as；
Temp4=(1+dA2)-1；
Temp5=temp1*temp4；
S2=temp5-r；
Do you compare s1?=s2, equal, output；It differs, returns to mistake.
Whether the SM2 algorithm after taking above-mentioned safeguard procedures to protect still has security breaches, and to that may be present
How loophole protects to promote cryptographic security, needs to continue the technical issues of solving for those skilled in the art.
Summary of the invention
In view of this, the purpose of the embodiment of the present invention is, propose that a kind of attack for SM2 signature algorithm is verified, is anti-
Maintaining method and device, further to promote the cryptographic security of SM2 algorithm.
Based on above-mentioned purpose, the first aspect of the embodiment of the present invention provides the attack verifying for SM2 signature algorithm
Method, comprising steps of
Error injection attack is carried out in the addition position of SM2 signature algorithm.
Optionally, SM2 signature algorithm addition position carry out error injection attack comprising steps of
Measurement obtains the energy mark of SM2 signature, i.e. power consumption waveform；
It is analyzed by SPA, finds position of the additive process for calculating temp1 on the power consumption waveform, record the position
Corresponding time point is as trigger time；
Laser injection is carried out in the trigger time, interferes the additive process；
Repeat laser injection in the trigger time, obtains the data of mistake.
Optionally, after the data for obtaining mistake, comprising steps of
The data of the mistake are analyzed, r will appear certain value in obtained wrong data, and the definite value is SM2
The cryptographic Hash e, i.e. r=e of plaintext needed for signature.
The second aspect of the embodiment of the present invention proposes that device is verified in a kind of attack for SM2 signature algorithm, comprising:
Module is attacked, for carrying out error injection attack in the addition position of SM2 signature algorithm.
Optionally, module is attacked, comprising:
Measuring unit obtains the energy mark of SM2 signature, i.e. power consumption waveform for measuring；
Analytical unit finds position of the additive process for calculating temp1 on the power consumption waveform for analyzing by SPA
It sets, records the position corresponding time point as trigger time；
Unit is interfered, for carrying out laser injection in the trigger time, interferes the additive process；And in the touching
Hair time point repeats laser injection, obtains the data of mistake.
In terms of the third of the embodiment of the present invention, it is also proposed that a kind of means of defence for SM2 signature algorithm, including step
It is rapid:
The addition and subtraction process participated in random number k is protected.
It is optional:
The addition and subtraction process participated in random number k is protected, comprising steps of after signature result s has been calculated, from interior
Again random number k and private key dA are imported in depositing, and are carried out second of the calculating of signature result s, calculated result will be compared twice
Verification；
And/or the addition and subtraction process participated in random number k is protected, comprising steps of directly being carried out after having signed
Sign test verification, is leaked private key dA not；
And/or to random number k participate in addition and subtraction process protect, comprising steps of for register value not by
The case where covering, makes the register for storing addition and subtraction result store random number before calculating addition and subtraction.
Optionally, after signature result s has been calculated, random number k and private key dA is imported again from memory, is signed
As a result second of the calculating of s, calculated result will compare verification twice, specifically include:
(1) M=ZA//M is set；
(2) e=Hv (M) is calculated；
(3) random number k ∈ [1, n-1] is generated with randomizer；
(4) elliptic curve point (x1, y1)=[k] G is calculated；
(5) r=(e+x1) modn is calculated, (3) are returned if r=0 or r+k=n；
(6) s=(1+dA) is calculated-1(k+r)-r modn returns to (3) if s=0；
(7) k and dA is imported from memory again, is denoted as k ' and dA ', it calculates again
S '=(1+dA ')-1·(k’+r)-r modn
(8) compare whether s is equal to s ':
If s=s ', sign successfully, output<r, s>；
If s ≠ s ', signature failure returns to mistake.
Optionally, sign test verification is directly carried out after having signed, and is leaked private key dA not, is specifically included:
SM2 signature is carried out, signature result r ', s ' are obtained；
T=(r '+s ') mod n is calculated to verify and do not pass through if t=0；
Calculate elliptic curve point (x '1, y '1)=[s '] G+ [t] PA；
Calculate R=(e '+x1') modn, whether checking R=r ' is true, is verified if setting up；Otherwise it verifies obstructed
It crosses.
4th aspect of the embodiment of the present invention, it is also proposed that a kind of protective device for SM2 signature algorithm, including protection
Module, the addition and subtraction process for participating in random number k are protected.
From the above it can be seen that the embodiment of the present invention proposes a kind of attack verifying, protection for SM2 signature algorithm
Method and device.Present invention discover that safeguard procedures in the prior art have ignored the protection when calculating s to random number k, no matter
It is original formula k-r*dA or deformed formula r+k, all there is the addition and subtraction for having random number k to participate in, and it is existing
Guard technology all this place is not protected, when using attack method proposed by the present invention attacked when, that is, exist
Additional calculation position carries out error injection attack, and addition is easy to be skipped, and the value of the register of corresponding storage addition results is not
It can change, be still the last value, and this mistake will not be found, it can by verification, thus demonstrate
SM2 algorithm after prior art protection still has loophole；For the loophole, the invention also provides corresponding means of defence,
Further improve the cryptographic security of SM2 algorithm.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, the attached drawing to embodiment is simply situated between below
It continues, it should be apparent that, the accompanying drawings in the following description merely relates to some embodiments of the present invention, rather than limitation of the present invention.
Fig. 1 is a kind of flow diagram of one embodiment of the attack verification method for SM2 signature algorithm of the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
Attached drawing, the technical solution of the embodiment of the present invention is clearly and completely described.Obviously, described embodiment is this hair
Bright a part of the embodiment, instead of all the embodiments.Based on described the embodiment of the present invention, ordinary skill
Personnel's every other embodiment obtained under the premise of being not necessarily to creative work, shall fall within the protection scope of the present invention.
Embodiment 1
The embodiment of the present invention 1 provides a kind of attack verification method for SM2 signature algorithm, comprising steps of signing in SM2
The addition position of name algorithm carries out error injection attack.
Error injection attack is carried out in additional calculation position, addition is easy to be skipped, and corresponding storage addition results are posted
The value of storage will not change, and be still the last value.And this mistake will not be found, it can pass through verification.
This illustrates the SM2 Encryption Algorithm after protecting in the prior art, and there are security risks.
Embodiment 2
The embodiment of the present invention 2 provides a preferred embodiment of the attack verification method for SM2 signature algorithm.Referring to figure
Shown in 1, in this embodiment, attack verification method comprising steps of
S201, measurement obtain the energy mark of SM2 signature, i.e. power consumption waveform；
S202 is analyzed by SPA, finds the time location for calculating temp1=k+r on power consumption waveform；
S203 carries out the error injection of laser in this time location；
S204 is repeatedly injected in the same time, obtains the data of mistake.
Preliminary analysis is carried out to the data of mistake, r will appear special definite value in obtained wrong data, and the definite value is
The cryptographic Hash e, i.e. r=e of plaintext needed for SM2 signature.The formula that SM2 calculates r is r=x1+e, shows attack so that this adds
Method is bypassed, and the value for storing this register of r does not change after addition has been calculated, and is still the value of last storage
e.It repeats to test, obtains the discovery of mass data post analysis, this addition of temp1=k+r can be equally skipped, and be occurred same
Error model.
Error injection attack is carried out to the addition for having k to participate in, it is possible to when calculating s, so that the value of k+r becomes " special
Value ", i.e., the result of addition may and be not preserved or without carry out add operation (addition is skipped), should store
The value of the register of sum is still the value of last storage, and k is not engaged in the process for calculating s.If what the register was deposited originally
Value be algorithm parameter or in plain text etc. known to numerical value, and and nonrandom unknowable number, to SM2 in the prior art signature in
For the implementation of s, temp1 is exactly a known number, due to s=(1+dA)-1* temp1-r, temp1 it is known that r it is known that s
It is known that private key dA can be found out, there are security risks.
For attacker, in this case it is not apparent that the numerical value of median does not know the storage situation of register yet.But it attacks
The person of hitting possesses data r and s, and knows the process for calculating s, such as the realization stream of s in the SM2 signature in the prior art with protection
Journey, s=(1+dA)-1* temp1-r (indicates r+k's as a result, i.e. "and" with temp1 here, wherein temp1=r+k, for indicate should
The variable of addition results, value, that is, r+k value of temp1；For prime formula s=(1+dA)-1* (k-r*dA), temp1 also can be used
Indicate the subtraction result of k-r*dA, i.e. " poor ", temp1 is the variable for indicating addition results or subtraction result).Attack
Person carries out multiple error injection attack for the above new error model, that is, is directed to the addition results or subtraction result temp1
It is attacked, obtains the value of multiple groups s and r, following attacker can guess the value of temp1, it is assumed that the value of temp1 is
Elliptic curve parameter a, b, p, xG, yG are perhaps worth known to montgomery multiplication parameter or plaintext r etc..Attacker is to institute
Possible situation carries out traversal calculating, if designer is when designing program, the last time for storing the register of temp1 is put
Value be exactly one of them in conjecture value, then attacker, which guesses, calculates dA, if there is two identical dA values, then this
A dA value is exactly correct private key.
In SM2 signature algorithm, why the algorithm security risk of the above analysis exists, and why attacker can attack
Success is because random number k is as a unpredictable number, is for protecting private key, because not knowing in the algorithm of script
The value of road random number k, to be unable to get private key relevant information.But the addition and subtraction by participating in random number k is calculated and is carried out
Attack, so that during calculating s, the not participation of random number k, even if can also be attacked then do not know the value of k,
Obtain key.That is, prime formula s=(1+dA) in the prior art-1* (k-r*dA) and deformed formula s=(1+
dA)-1* the signed magnitude arithmetic(al) that (r+k)-r has random number k to participate in can not protect on proposed by the present invention formula deformation
State attack option.
Embodiment 3
The embodiment of the present invention 3 provides a kind of attack verifying device for SM2 signature algorithm, including attack module, is used for
Error injection attack is carried out in the addition position of SM2 signature algorithm.
As a preferred embodiment, the attack module, comprising:
Measuring unit obtains the energy mark of SM2 signature, i.e. power consumption waveform for measuring；
Analytical unit finds position of the additive process for calculating temp1 on the power consumption waveform for analyzing by SPA
It sets, records the position corresponding time point as trigger time；
Unit is interfered, for carrying out laser injection in trigger time, interferes additive process；And it is repeated in trigger time
Laser injection is carried out, the data of mistake are obtained.
Embodiment 4
The embodiment of the present invention 4 provides the means of defence for being directed to SM2 signature algorithm, for avoiding 1-3 of embodiment of the present invention institute
It was found that security risk, the means of defence comprising steps of to random number k participate in addition and subtraction process protect.
The key for solving prior art SM2 signature algorithm security breaches is the process for the addition and subtraction to participate in random number k
It is protected, and existing technological means does not all carry out protection verification to k during participating in random number k and calculating s.
Embodiment 5
The embodiment of the present invention 5 provides a preferred embodiment of the means of defence for SM2 signature algorithm.
In the preferred embodiment, repetition is taken to import the safeguard procedures calculated: after s has been calculated, the weight from memory
It is new to import random number k and private key dA, second of the calculating of s is carried out, calculated result verification will be compared twice, and prevent dA and k
It goes wrong.
Specifically, which includes:
If message to be signed is M, in order to obtain the digital signature (r, s) of message M, the user A as signer should be real
Existing following calculation step:
(1): setting M=ZA//M；
(2): calculating e=Hv (M)；
(3): generating random number k ∈ [1, n-1] with randomizer；
(4): calculating elliptic curve point (x1, y1)=[k] G；
(5): calculating r=(e+x1) mod n, return step (3) if r=0 or r+k=n；
(6): calculating s=(1+dA)-1(k+r)-r mod n returns to (3) if s=0；
(7): importing k and dA from memory again, be denoted as k ' and dA ', s '=(1+dA ')-is calculated again1·(k’+r)-r
modn
(8): compare whether s is equal to s ':
If s=s ', sign successfully, output<r, s>；
If s ≠ s ', signature failure returns to mistake.
Wherein, M is message to be signed, ZAFor the Hash Value of user A, e is the cryptographic Hash of M, and Hv (M) is hash function, G
For the basic point of elliptic curve, [k] G is to calculate more times of points of elliptic curve, and (x1, y1) is the coordinate of calculated elliptic curve point, r
It is one of signature result, s is another signature result, and dA is private key, and mod, that is, MOD function, n refer to the rank of elliptic curve basic point G.
It should be noted that using this kind of protectiving scheme generation during calculating s can be chosen after r has been calculated
Median carries out second and calculates, it is not necessary to have to be verified after s has been calculated, those skilled in the art can be according to the actual situation
It is protected.
If there is above-mentioned error model during calculating r+k, calculated then importing random number k again, just
It can find that calculated result twice is different, thus calculated two s differences, then can not be by verification, attacker must not
To valid data.As it can be seen that corresponding risk can be effectively reduced using the present embodiment safeguard procedures, the peace of SM2 signature algorithm is promoted
Quan Xing.
Embodiment 6
The embodiment of the present invention 6 provides another embodiment of the means of defence for SM2 signature algorithm.
When to algorithm performance requirement is not very high, the present invention proposes that a kind of relatively safer safeguard procedures are to sign
Sign test verification is directly carried out after complete, to guarantee that private key is not leaked.
Specifically, check part carries out the safeguard procedures of SM2 sign test:
SM2 signature is carried out according to the process of script, obtains signature result r ", s "；Here the process of script is either mark
Quasi- specification original process, be also possible to for reply DPA risk to calculate s (in the present embodiment for s ") formula equivalent variations after
Process.
T=(r "+s ") mod n is calculated to verify and do not pass through if t=0；
Calculate elliptic curve point (x1', y1')=[s "] G+ [t] PA；The formula calculates more times of points of two elliptic curves, then
The point for carrying out an elliptic curve again adds, some point in obtained result or elliptic curve, (x1', y1') it is exactly this point
Coordinate value；
Calculate R=(e '+x1') modn, whether checking R=r " is true, is verified if setting up；Otherwise it verifies obstructed
It crosses.
Wherein, (x1', y1') be calculated elliptic curve point coordinate, [s "] G and [t] PAIt is more times of elliptic curve
The calculating of point, wherein a G point of [s "] G, that is, s " is added, [t] PAThat is t PAPoint is added, and G is the basic point on elliptic curve, PAFor public affairs
Key, mod, that is, MOD function, n refer to the rank of elliptic curve basic point G.
Protection effect: if there is above-mentioned error model during calculating r+k, then obtained s " is exactly mistake
, and then x1' value mistake, so the value of R is not equal to the r " of signature result, verification can not just pass through, attacker
It just cannot get valid data.
Embodiment 7
The embodiment of the present invention 7 provides the further embodiment of the means of defence for SM2 signature algorithm.
In this embodiment, the safeguard procedures for being directed to register: the case where being not covered with for the value of register are proposed,
The register for storing addition and subtraction result can be subjected to " special storage ", it can store random number before calculating addition and subtraction.
Specifically, random number can be stored before the computation in the register of storage temp1, there is random digital-to-analogue in chip
Block moves random number in register after generating random number.After can so calculating process being prevented to be skipped, register be obtained
Value.
Embodiment 8
The embodiment of the present invention 8 provides a kind of protective device for SM2 signature algorithm, which includes protection mould
Block, the addition and subtraction process for participating in random number k are protected.
As a preferred embodiment, which includes repeating import unit, sign test verification unit and register protection
Unit.
Import unit is repeated, for importing random number k and private key again from memory after signature result s has been calculated
DA carries out second of the calculating of signature result s, calculated result will compare verification twice.
Sign test verification unit is leaked private key dA not for directly carrying out sign test verification after having signed.
Register protective unit the case where being not covered with for the value for register, makes to store addition and subtraction result
Register stores random number before calculating addition and subtraction.
To sum up, the present invention analyzes the safety that SM2 signature is realized, if there are the risk of Key Exposure and provides protection and arranges
It applies, first proposed a kind of attack method, the SM2 after taking safeguard procedures in the prior art is demonstrated by the attack method and is calculated
Method still has loophole；Next proposes the safeguard procedures for the loophole, improves SM2 signature by corresponding safeguard procedures
The safety of algorithm guarantees people's property safety.
In addition, typically, device described in the disclosure, equipment etc. can be various electric terminal equipments, such as mobile phone, individual
Digital assistants (PDA), tablet computer (PAD), smart television etc. are also possible to large-scale terminal device, such as server, therefore this
Disclosed protection scope should not limit as certain certain types of device, equipment.Client described in the disclosure can be with electricity
The combining form of sub- hardware, computer software or both is applied in any one of the above electric terminal equipment.
In addition, being also implemented as the computer program executed by CPU, the computer program according to disclosed method
It may be stored in a computer readable storage medium.When the computer program is executed by CPU, executes and limited in disclosed method
Fixed above-mentioned function.
In addition, above method step and system unit also can use controller and for storing so that controller is real
The computer readable storage medium of the computer program of existing above-mentioned steps or Elementary Function is realized.
In addition, it should be appreciated that computer readable storage medium (for example, memory) as described herein can be it is volatile
Property memory or nonvolatile memory, or may include both volatile memory and nonvolatile memory.As example
And not restrictive, nonvolatile memory may include read-only memory (ROM), programming ROM (PROM), electrically programmable to son
ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory.Volatile memory may include arbitrary access
Memory (RAM), the RAM can serve as external cache.As an example and not restrictive, RAM can be with more
Kind form obtains, such as synchronous random access memory (DRAM), dynamic ram (DRAM), synchronous dram (SDRAM), double data rate SDRAM
(DDR SDRAM), enhancing SDRAM (ESDRAM), synchronization link DRAM (SLDRAM) and directly RambusRAM (DRRAM).Institute
The storage equipment of disclosed aspect is intended to the memory of including but not limited to these and other suitable type.
Those skilled in the art will also understand is that, various illustrative logical blocks, mould in conjunction with described in disclosure herein
Block, circuit and algorithm steps may be implemented as the combination of electronic hardware, computer software or both.It is hard in order to clearly demonstrate
This interchangeability of part and software, with regard to various exemplary components, square, module, circuit and step function to its into
General description is gone.This function is implemented as software and is also implemented as hardware depending on concrete application and application
To the design constraint of whole system.Those skilled in the art can realize described in various ways for every kind of concrete application
Function, but this realization decision should not be interpreted as causing a departure from the scope of the present disclosure.
Various illustrative logical blocks, module and circuit, which can use, in conjunction with described in disclosure herein is designed to
The following component of function described here is executed to realize or execute: general processor, digital signal processor (DSP), dedicated collection
At circuit (ASIC), field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, divide
Any combination of vertical hardware component or these components.General processor can be microprocessor, but alternatively, processing
Device can be any conventional processors, controller, microcontroller or state machine.Processor also may be implemented as calculating equipment
Combination, for example, the combination of DSP and microprocessor, multi-microprocessor, one or more microprocessors combination DSP core or any
Other this configurations.
The step of method in conjunction with described in disclosure herein or algorithm, can be directly contained in hardware, be held by processor
In capable software module or in combination of the two.Software module may reside within RAM memory, flash memory, ROM storage
Device, eprom memory, eeprom memory, register, hard disk, removable disk, CD-ROM or known in the art it is any its
In the storage medium of its form.Illustrative storage medium is coupled to processor, enables a processor to from the storage medium
Information is written to the storage medium in middle reading information.In an alternative, the storage medium can be with processor collection
At together.Pocessor and storage media may reside in ASIC.ASIC may reside in user terminal.It is replaced at one
In scheme, it is resident in the user terminal that pocessor and storage media can be used as discrete assembly.
In one or more exemplary designs, the function can be real in hardware, software, firmware or any combination thereof
It is existing.If realized in software, can be stored in using the function as one or more instruction or code computer-readable
It is transmitted on medium or by computer-readable medium.Computer-readable medium includes computer storage media and communication media,
The communication media includes any medium for helping for computer program to be transmitted to another position from a position.Storage medium
It can be any usable medium that can be accessed by a general purpose or special purpose computer.As an example and not restrictive, the computer
Readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disc memory apparatus, disk storage equipment or other magnetic
Property storage equipment, or can be used for carry or storage form be instruct or data structure required program code and can
Any other medium accessed by general or specialized computer or general or specialized processor.In addition, any connection is ok
It is properly termed as computer-readable medium.For example, if using coaxial cable, optical fiber cable, twisted pair, digital subscriber line
(DSL) or such as wireless technology of infrared ray, radio and microwave to send software from website, server or other remote sources,
Then the wireless technology of above-mentioned coaxial cable, optical fiber cable, twisted pair, DSL or such as infrared elder generation, radio and microwave is included in
The definition of medium.As used herein, disk and CD include compact disk (CD), laser disk, CD, digital versatile disc
(DVD), floppy disk, Blu-ray disc, wherein disk usually magnetically reproduce data, and CD using laser optics reproduce data.On
The combination for stating content should also be as being included in the range of computer-readable medium.
Disclosed exemplary embodiment, but disclosed exemplary embodiment should be infused, it should be noted that without departing substantially from
Under the premise of the scope of the present disclosure that claim limits, it may be many modifications and modify.According to disclosure described herein
Function, step and/or the movement of the claim to a method of embodiment are not required to the execution of any particular order.In addition, although this public affairs
The element opened can be described or be required in the form of individual, it is also contemplated that it is multiple, it is unless explicitly limited odd number.
It should be understood that it is used in the present context, unless the context clearly supports exceptions, singular " one
It is a " it is intended to also include plural form.It is to be further understood that "and/or" used herein refers to including one or one
Any and all possible combinations of a above project listed in association.
Above-mentioned embodiment of the present disclosure serial number is for illustration only, does not represent the advantages or disadvantages of the embodiments.
Those of ordinary skill in the art will appreciate that realizing that all or part of the steps of above-described embodiment can pass through hardware
It completes, relevant hardware can also be instructed to complete by program, the program can store in a kind of computer-readable
In storage medium, storage medium mentioned above can be read-only memory, disk or CD etc..
It should be understood by those ordinary skilled in the art that: the discussion of any of the above embodiment is exemplary only, not
It is intended to imply that the scope of the present disclosure (including claim) is limited to these examples；It is above under the thinking of the embodiment of the present invention
It can also be combined between technical characteristic in embodiment or different embodiments, and exist and implement present invention as described above
Many other variations of the different aspect of example, for simplicity, they are not provided in details.Therefore, all in the embodiment of the present invention
Spirit and principle within, any omission, modification, equivalent replacement, improvement for being made etc. should be included in the embodiment of the present invention
Within protection scope.
Claims (10)
1. being directed to the attack verification method of SM2 signature algorithm, which is characterized in that comprising steps of
Error injection attack is carried out in the addition position of SM2 signature algorithm.
2. the attack verification method according to claim 1 for SM2 signature algorithm, which is characterized in that sign and calculate in SM2
The addition position of method carry out error injection attack comprising steps of
Measurement obtains the energy mark of SM2 signature, i.e. power consumption waveform；
It is analyzed by SPA, finds position of the additive process for calculating temp1 on the power consumption waveform, it is corresponding to record the position
Time point as trigger time；
Laser injection is carried out in the trigger time, interferes the additive process；
Repeat laser injection in the trigger time, obtains the data of mistake.
3. the attack verification method according to claim 2 for SM2 signature algorithm, which is characterized in that obtain mistake
After data, comprising steps of
The data of the mistake are analyzed, r will appear certain value in obtained wrong data, and the definite value is SM2 signature
The cryptographic Hash e of required plaintext, i.e. r=e.
4. device is verified in the attack for SM2 signature algorithm characterized by comprising
Module is attacked, for carrying out error injection attack in the addition position of SM2 signature algorithm.
5. device is verified in attack according to claim 4, which is characterized in that the attack module, comprising:
Measuring unit obtains the energy mark of SM2 signature, i.e. power consumption waveform for measuring；
Analytical unit finds position of the additive process for calculating temp1 on the power consumption waveform, note for analyzing by SPA
The position corresponding time point is recorded as trigger time；
Unit is interfered, for carrying out laser injection in the trigger time, interferes the additive process；And in the triggering
Between point repeat laser injection, obtain mistake data.
6. being directed to the means of defence of SM2 signature algorithm, which is characterized in that comprising steps of
The addition and subtraction process participated in random number k is protected.
7. the means of defence according to claim 4 for SM2 signature algorithm, it is characterised in that:
The addition and subtraction process participated in random number k is protected, comprising steps of after signature result s has been calculated, from memory
Again random number k and private key dA are imported, second of the calculating of signature result s is carried out, calculated result will compare verification twice；
And/or the addition and subtraction process participated in random number k is protected, comprising steps of directly carrying out sign test after having signed
Verification, is leaked private key dA not；
And/or the addition and subtraction process participated in random number k is protected, comprising steps of the value for register is not covered with
The case where, so that the register for storing addition and subtraction result is stored random number before calculating addition and subtraction.
8. the means of defence according to claim 5 for SM2 signature algorithm, which is characterized in that the step is calculating
After complete signature result s, random number k and private key dA are imported again from memory, carry out second of the calculating of signature result s, it will
Calculated result compares verification twice, specifically includes:
(1) M=Z is setA//M；
(2) e=Hv (M) is calculated；
(3) random number k ∈ [1, n-1] is generated with randomizer；
(4) elliptic curve point (x1, y1)=[k] G is calculated；
(5) r=(e+x1) modn is calculated, (3) are returned if r=0 or r+k=n；
(6) s=(1+dA) is calculated-1(k+r)-rmodn returns to (3) if s=0；
(7) k and dA is imported from memory again, is denoted as k ' and dA ', it calculates again
S '=(1+dA ')-1·(k’+r)-r modn
(8) compare whether s is equal to s ':
If s=s ', sign successfully, output<r, s>；
If s ≠ s ', signature failure returns to mistake；
Wherein, M is message to be signed, and (r, s) is the digital signature of message M, ZAFor the Hash Value of user A, e is the Hash of M
Value, Hv (M) are hash function, and G is the basic point of elliptic curve, and [k] G is to calculate more times of points of elliptic curve, and (x1, y1) is to calculate
Elliptic curve point coordinate, r is one of signature result, dA is private key, and mod, that is, MOD function, n are elliptic curve basic point G
Rank.
9. the means of defence according to claim 5 for SM2 signature algorithm, which is characterized in that the step is being signed
Sign test verification is directly carried out after complete, is leaked private key dA not, is specifically included:
SM2 signature is carried out, signature result r ", s " are obtained；
T=(r "+s ") modn is calculated to verify and do not pass through if t=0；
Calculate elliptic curve point (x1', y1')=[s "] G+ [t] PA；
Calculate R=(e '+x1') modn, whether checking R=r " is true, is verified if setting up；Otherwise it verifies and does not pass through；
Wherein, (x1', y1') be calculated elliptic curve point coordinate, G is the basic point on elliptic curve, PAFor public key.
10. being directed to the protective device of SM2 signature algorithm, which is characterized in that including protection module, for what is participated in random number k
Addition and subtraction process is protected.
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