CN107070632A - Impossible differential and zero correlation path automatic search method based on SAT - Google Patents
Impossible differential and zero correlation path automatic search method based on SAT Download PDFInfo
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- CN107070632A CN107070632A CN201710155958.1A CN201710155958A CN107070632A CN 107070632 A CN107070632 A CN 107070632A CN 201710155958 A CN201710155958 A CN 201710155958A CN 107070632 A CN107070632 A CN 107070632A
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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
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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
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
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Abstract
The invention belongs to cryptanalysis method and technology field, and in particular to a kind of impossible differential and zero correlation path automatic search method based on SAT, comprise the following steps：Constraint formula is converted using ARX types password；Using Boolean satisfiability restricted problem, constraint formula is carried out to meet checking；Constraint formula is verified using SAT checkings, with traditional impossible differential（Zero correlation）Path automatic search algorithm, the property of non-linear component can not be taken into full account, thus it can not show that complete, accurate result is compared, the features such as impossible differential of the present invention based on SAT and zero correlation path automatic search method have accurate, efficiency, under conditions of using parallel, generally obtained a result in the time quickly.In today of computing resource still costliness, with good application value.Due to algorithm efficiently, make it possible the longer impossible differential for taking turns number of searching and zero correlation path, to accelerate the progress of impossible differential and zero correlation analysis.
Description
Technical field
The invention belongs to cryptanalysis method and technology field, and in particular to a kind of impossible differential based on SAT and
Zero correlation path automatic search method.
Background technology
For block cipher, it is impossible to which it is all critically important analysis means that difference and zero correlation, which are analyzed, and extensively should
In the cryptanalysis for using various structures.Impossible differential analysis is proposed by Biham and Knudsen earliest, for analyzing DEAL
It is a kind of effective cryptanalysis method with Skipjack.The difference of a maximum probability is found with difference analysis
Path is different, it is impossible to which difference analysis purpose is the differential path that one probability of searching is zero, and the candidate for carrying out debug is close
Key.It is at present not possible to which differential attack has been widely applied in the attack of the block cipher of various structures, in AES, MISTY1 etc.
There is extraordinary attack effect on password.Generally, realize that impossible differential attack mainly includes two steps, be to construct not respectively
Possible difference circuit sectionalizer and recovery key.Zero correlation linear analysis method by Bogdanov and Rijmem in 2012 propose, with
The linear relationship for the high deviation that linear analysis is utilized is opposite, the linear approximation that zero correlation linear analysis is mainly zero using deviation
Relation distinguishes cryptographic algorithm and random function, and then obtains some or all of key information.The of zero correlation linear analysis
One step is zero correlation linear approximation relation of the construction on cryptographic algorithm.Second step is close using obtained circuit sectionalizer progress
Key recovers.
Occur in that the automation search in many impossible differentials for being directed to block cipher and zero correlation path is calculated in recent years
Method, such as μ-method, UID-method.μ methods therein provide impossible in a kind of general scheme searching algorithm
Password differential path, the S boxes with algorithm are unrelated, and the diffusion layer of only algorithm is relevant.But these algorithms there is also some shortcomings and
Deficiency, due to not taking into full account the property of non-linear component (such as S boxes), tends not to the difference travel of accurate description cryptographic algorithm
Property.
The content of the invention
The present invention is directed to the deficiency of existing impossible differential and zero correlation path automatic search method, non-linear by studying
The property that assembly mould adds, and then obtain the constraint formula for portraying ARX types password wheels function difference and linear propagation characteristic, then base
In Boolean satisfiability restricted problem, a kind of impossible differential and zero correlation path automatic search method based on SAT are proposed.
The technical scheme is that：A kind of impossible differential and zero correlation path automatic search method based on SAT, bag
Include following steps：
Constraint formula is converted using ARX types password；
Using Boolean satisfiability restricted problem, constraint formula is carried out to meet checking；
Constraint formula is verified using SAT checkings.
The described impossible differential and zero correlation path automatic search method based on SAT, the utilization ARX types password turns
Changing constraint formula mainly includes：Using linear, the non-linear component property in ARX type passwords, difference is constructed by round function
Boolean constrains formula, and then constructs the difference travel constraint formula of whole n wheels password, and n is natural number.
The described impossible differential and zero correlation path automatic search method based on SAT, the round function is divided into wheel letter
Add without key mould in number and there is key mould to add in round function.
The described impossible differential and zero correlation path automatic search method based on SAT, the utilization Boolean satisfiability
Restricted problem, can meet checking to the progress of constraint formula includes：The input of given difference, output set, can by every a pair under set
The input and output difference of energy, brings constraint formula into, using Boolean satisfiability restricted problem, and constraint formula is carried out to meet checking.
The described impossible differential and zero correlation path automatic search method based on SAT, the utilization SAT checkings are to about
Beam formula is verified as：Constraint formula is verified with SAT respectively, all ungratified differential pairs (mask to) are exported, it is each
Individual differential pair (mask to) is an impossible differential zero correlation path.
The beneficial effects of the invention are as follows：A kind of impossible differential and zero correlation path automatic search method based on SAT, with
Traditional impossible differential (zero correlation) path automatic search algorithm, it is impossible to take into full account the property of non-linear component, thus not
It can show that complete, accurate result is compared, impossible differential and zero correlation path automatic search method tool of the present invention based on SAT
Ask path efficiency very high, under conditions of using parallel, generally obtained a result in the time quickly.Due to algorithm efficiently, make to seek
Look for it is longer wheel number impossible differential and zero correlation path be possibly realized, accelerate impossible differential and zero correlation analysis enter
Exhibition.The algorithm also can determine whether whether specific differential pair (mask to) constitutes an impossible differential in addition to for searching for automatically
(zero correlation) path, facilitates the design and analysis of ARX type passwords.
Brief description of the drawings
Fig. 1 is automatic search routine schematic diagram of the invention.
Embodiment
Embodiment 1, with reference to Fig. 1, a kind of impossible differential and zero correlation path automatic search method based on SAT, it is special
Levy and be, comprise the following steps：
Constraint formula is converted using ARX types password, is mainly included：Utilize linear, the non-linear component in ARX type passwords
Matter, constructs boolean constraint formula of the difference by round function, and then constructs the difference travel constraint formula of whole n wheels password, and n is
Natural number.Round function, which is divided into round function, to be added without key mould and has key mould to add in round function.
Using Boolean satisfiability restricted problem, constraint formula is carried out to meet checking, including：It is the inputting of given difference, defeated
Go out set, by every a pair of possible input and output difference under set, bring constraint formula into, it is right using Boolean satisfiability restricted problem
Constraint formula carries out that checking can be met.
Constraint formula is verified using SAT checkings, including：Constraint formula is verified with SAT respectively, output is all not
The differential pair of satisfaction, each differential pair is an impossible differential zero correlation path.
Embodiment 2, with reference to Fig. 1, impossible differential and zero correlation path automatic search method based on SAT,
Step one, Changeover constraint formula is as follows in principle of the conversion constraint formula step used in us：Difference is provided first (to cover
Code) pass through the propagation constraint formula that non-linear component mould adds, then with being combined by the constraint formula of linear modules, provide whole
The difference (mask) of round function propagates constraint formula.
For in step one, we build constraint formula by following theorem.
On situation about adding in round function without key mould：
Theorem 1. we use xdp+(α, β → γ) is represented adds 2 by mouldnDifference travel probability, wherein α, β for input it is poor
Point, γ is output difference, and (α, β → γ) is an effective bang path, and and if only if：
Wherein
Theorem 2. (v, w → u) is to add 2 by mouldnMask transmission, wherein u be output masking, v, w is input mask.z
It is a n-dimensional vector for meeting following formula,
Then,
Know from above formula, we can obtain an effective mask propagation path, and if only if meets,
zn-1=0
Wherein 0≤i≤n-1,0≤j≤n-3.
On the situation for thering is key mould to add in round function：
Theorem 3. (α, β → γ) is one and adds 2 by mouldnEffective difference bang path, and if only if α, beta, gamma is most
Low order non-zero bit position is identical.
Theorem 4. (v, w → u) is one and adds 2 by mouldnEffective mask bang path, and if only if v, w, u highest
Significance bit non-zero bit positions are identical.
Using four theorems above, using linear, the non-linear component property in ARX type passwords, construct difference and (cover
Code) by boolean's constraint formula of round function, and then construct difference (mask) the propagation constraint formula of whole n wheels password.Linear group
Part mainly includes XOR and cyclic shift, and differential path (α, β → γ), its input difference α, β, output difference γ pass through XOR
Afterwards, it then follows relation be：Input difference α is after ring shift left r, and its output difference is met：α<<<r.Cover
Code bang path (v, w → u), its input mask v, w, output masking u are after XOR, and the relation followed should be v=w=u.
Its input mask v is after ring shift left r, and its output masking meets v<<<r.
Step 2：Bring input and output differentiation step into, using Boolean satisfiability restricted problem, constraint formula is carried out to meet
Checking.We concentrate in input and output difference (mask) and choose any to input and output difference (mask), and by constraint formula
Input and output mask value is replaced with this pair of input and output difference (mask) chosen.
Can this method can determine that any to input and output difference (mask), constitute effective difference (zero correlation) road
Footpath.But in view of the block length of ARX type passwords, such as SPECK32, its block length is 32bit, all input and output difference
Situation to (mask to) has 264Kind, it is very unrealistic with current computing capability.So we only consider specifically input it is defeated
Go out differential pair situation, the weight that generally we give tacit consent to input and output difference (mask) is 1.We will each input again
Output difference is to (mask to), the constraint formula brought into previous step.
Step 3：SAT verify, we are verified above-mentioned constraint formula with SAT respectively, judged result whether be
false.We by result for false difference (mask) to preserve.Such difference (mask) is to being one impossible poor
Divide (zero correlation) path.
Claims (5)
1. a kind of impossible differential and zero correlation path automatic search method based on SAT, it is characterised in that including following step
Suddenly：
Constraint formula is converted using ARX types password；
Using Boolean satisfiability restricted problem, constraint formula is carried out to meet checking；
Constraint formula is verified using SAT checkings.
2. impossible differential and zero correlation path automatic search method according to claim 1 based on SAT, its feature exist
In the utilization ARX types password conversion constraint formula mainly includes：Using linear, the non-linear component property in ARX type passwords,
Construct difference and pass through boolean's constraint formula of round function, and then construct the difference travel constraint formula of whole n wheels password, n is certainly
So count.
3. impossible differential and zero correlation path automatic search method according to claim 1 based on SAT, its feature exist
In：The round function, which is divided into round function, to be added without key mould and has key mould to add in round function.
4. impossible differential and zero correlation path automatic search method according to claim 1 based on SAT, its feature exist
In, the utilization Boolean satisfiability restricted problem, can meet checking to the progress of constraint formula includes：Input, the output of given difference
Set, by every a pair of possible input and output difference under set, brings constraint formula into, using Boolean satisfiability restricted problem, to about
Beam formula carries out that checking can be met.
5. impossible differential and zero correlation path automatic search method according to claim 1 based on SAT, its feature exist
In：It is described that constraint formula is verified as using SAT checkings：Constraint formula is verified with SAT respectively, all be unsatisfactory for is exported
Differential pair, each differential pair is an impossible differential path.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112398638A (en) * | 2020-10-19 | 2021-02-23 | 山东大学 | Zero correlation linear code analysis method, system, medium and electronic equipment |
| CN112953703A (en) * | 2021-01-28 | 2021-06-11 | 华东师范大学 | MILP-based Tweakable GOST2 differential route searching method |
-
2017
- 2017-03-15 CN CN201710155958.1A patent/CN107070632A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112398638A (en) * | 2020-10-19 | 2021-02-23 | 山东大学 | Zero correlation linear code analysis method, system, medium and electronic equipment |
| CN112398638B (en) * | 2020-10-19 | 2022-04-26 | 山东大学 | Zero correlation linear code analysis method, system, medium and electronic equipment |
| CN112953703A (en) * | 2021-01-28 | 2021-06-11 | 华东师范大学 | MILP-based Tweakable GOST2 differential route searching method |
| CN112953703B (en) * | 2021-01-28 | 2022-12-06 | 华东师范大学 | MILP-based Tweakable GOST2 differential route searching method |
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