CN110532763A - A kind of cipher constructions method and system based on high-order orthomorphic permutation - Google Patents
A kind of cipher constructions method and system based on high-order orthomorphic permutation Download PDFInfo
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- CN110532763A CN110532763A CN201910828016.4A CN201910828016A CN110532763A CN 110532763 A CN110532763 A CN 110532763A CN 201910828016 A CN201910828016 A CN 201910828016A CN 110532763 A CN110532763 A CN 110532763A
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/30—Authentication, i.e. establishing the identity or authorisation of security principals
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Abstract
The invention belongs to technical field of cryptology, and disclose a kind of cipher constructions method and system based on high-order orthomorphic permutation: encryption side, decryption side uniformly arrange identical random digit generation method；Both sides are based on same procedure and generate random number string；Encryption side is to 8 random division of integer, and then random configuration low order orthomorphic permutation, low order orthomorphic permutation is spliced into high-order orthomorphic permutation, and be based on high-order orthomorphic permutation replacement data, finally concatenation forms encryption data and is sent to decryption side；Decryption side same method construct high-order orthomorphic permutation and inverse permutation, and it is based on inverse permutation replacement data, obtain ciphertext data；Orthomorphic permutation building method proposed by the present invention is directed to same order, it can be more than the number that existing method constructs, and time complexity is minimum, and then a kind of high-order orthomorphic permutation for using dynamic mapping is devised as the cryptographic methods of component based on this method, this method increase the difficulty that cryptographic attack personnel decode, and then increase safety.
Description
Technical field
The invention belongs to technical field of cryptology more particularly to a kind of cipher constructions method based on high-order orthomorphic permutation and
System.
Background technique
Currently, the prior art commonly used in the trade is such that
Orthomorphic permutation has important application in cryptography, for the first time combines orthomorphic permutation and block cipher
People is doctor L.Mittenthal of Teledyne Electronic Arts Inc., the U.S. (TET), he demonstrates GF (2) in nineteen ninety-fivenOn
Orthomorphic permutation have a kind of very excellent Cryptographic Properties-complete equipilibrium (GF (2)nIndicate binary Galois Field n tie up to
Quantity space, similar below), and successfully used orthomorphic permutation based on so-called " dynamic replacement equipment " DSD
In the block cipher design of (Dynamic Substitution Devices), in addition orthomorphic permutation is also proved to have defeated
When entering difference and being not zero, output difference is not equal to the advantageous property of input difference, and non-linear orthomorphic permutation has good bit
Independence and avalanche characteristic etc..
Then, orthomorphic permutation is applied in the Lai-Massey structure of block cipher.In addition Chinese WLAN
The round function of commercial cipher algorithm SMS4 is also based on BDLL orthomorphic permutation Generator Design.And orthomorphic permutation also by with
Come design it is important in DSE arithmetic obscure component-S box, there have been the S of orthomorphic permutation construction in stream cipher Loiss
Box.Orthomorphic permutation equally can also be used to design multi-output Bent function and cryptography Boolean function of good performance, Hash letter
Orthomorphic permutation, which is also played the part of, in several design and analysis important role, and linear orthomorphic permutation can be also used for classical cryptography architecture
The round key of Even-Mansour constructs, and orthomorphic permutation even can be also used for the design of quasi-group.Therefore, orthomorphic permutation has weight
The cryptographic applications value wanted.
The existing cryptographic algorithm constructed based on orthomorphic permutation, used orthomorphic permutation are usually fixed.But
If using the password part of dynamic change in cryptographic algorithm, the difficulty that cryptographic attack personnel break a code will increase, in turn
Increase the safety of cryptographic algorithm.But according to the orthomorphic permutation of dynamic change, then the batch construction of orthomorphic permutation is related to
The problem of.The construction of orthomorphic permutation is always one of focus of attention.Typical cryptography component, such as S box, are typically adopted
With GF (2)nThe excellent displacement of Cryptographic Properties on (n >=8), but due to GF (2)nOrthomorphic permutation on (n > 4) can not pass through letter
Single search generates, therefore according to orthomorphic permutation as cryptography component, then needs to construct GF (2)nHeight on (n >=8)
Rank orthomorphic permutation, present construction cryptography high-order orthomorphic permutation are generally based on the operation of low order orthomorphic permutation to obtain,
Art methods are in the construction and reality for constructing cryptographic algorithm and high-order orthomorphic permutation based on orthomorphic permutation
It is had the following deficiencies in:
(1) orthomorphic permutation employed in cryptographic algorithm is generally fixed and invariable, and which adds by cryptographic attack
Personnel analyze the risk decoded.
(2) method that high-order orthomorphic permutation is constructed by low order orthomorphic permutation is generally more complex, and some algorithm
Time complexity is also excessively high, causes to realize that difficulty is big, cost of implementation is high.Many methods are more complicated, for non-mathematics and password
Indigestion for technical professional is learned, which increases the difficulty that algorithm is realized, and the time of some algorithm is multiple
Miscellaneous degree is also higher, causes cost of implementation higher, to reduce the utilization rate of these methods.
(3) number of the high-order orthomorphic permutation constructed is not also enough, if cause need to generate a large amount of orthomorphic permutations and from
In select or construct the excellent orthomorphic permutation of cryptography (a kind of more typical application mode, for example, using dynamic change just
Shape displacement is used as password part, this just needs to construct a large amount of orthomorphic permutation), need to be separately operable different building methods, into
And it results in inefficient.Although the method time that existing part constructs high-order orthomorphic permutation by low order orthomorphic permutation is complicated
Spend not high, and can generate a certain number of high-order orthomorphic permutations, but compared to for the number of correspondence order orthomorphic permutation still
It is less than normal, if therefore generate a large amount of orthomorphic permutations, need to be separately operable different building methods, improve cost, lead to efficiency not
It is high.
Solve the difficulty of above-mentioned technical problem:
It solves the above problems, it is meant that need to design a kind of high-order orthomorphic permutation for using dynamic mapping for the close of component
Code method, so be intended to design it is a kind of realize simple, time complexity is low and can be based on low order orthomorphic permutation again
Method to construct a large amount of high-order orthomorphic permutations, can just solve the above problems in this way.
Solve the meaning of above-mentioned technical problem:
If being capable of providing a kind of GF (2)nThe simple structure method of cryptography high-order orthomorphic permutation on (n > 4), and should
Method is directed to same order, can go out more orthomorphic permutations than existing method construct, while again complicated with the minimum time
If degree, it will be able to improve the efficiency of construction high-order orthomorphic permutation, to reduce costs, and then can be designed based on this method
A kind of high-order orthomorphic permutation using dynamic mapping for the cryptographic methods of component, this method will increase cryptographic attack personnel decode it is close
The difficulty of code, and then increase the safety of cryptographic methods.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of cipher constructions methods based on high-order orthomorphic permutation
And system.
The invention is realized in this way a kind of cipher constructions method of high-order orthomorphic permutation, specifically includes:
Step 1, encryption side and decryption side both sides uniformly arrange identical random number seed, random digit generation method, integer
The following the example of of random number bit position needed for random division, the random configuration institute of the random division method of integer, low order orthomorphic permutation
Need random number bit position follow the example of and the random configuration method of low order orthomorphic permutation.
Step 2, encryption side and decryption side are based on identical random number seed and random digit generation method is generated with bit
Position is the random number string of unit, and the random number bit position in the random number string is executed in random number seed and random digit generation method
Continual generation in the process.
Step 3, encryption side carries out random division to integer 8, and is based on division result random configuration low order orthomorphic permutation.
Low order orthomorphic permutation is spliced into high-order orthomorphic permutation by encryption side, and is set based on high-order orthomorphic permutation to data
It changes and operates and repeatedly construct high-order orthomorphic permutation, all data are serially connected after having operated and are sent to decryption side.
Step 4 after decryption side has received data, equally executes random division to integer 8, and random based on division result
Construct low order orthomorphic permutation.
Low order orthomorphic permutation is spliced into high-order orthomorphic permutation by decryption side, and then obtains the inverse permutation of high-order orthomorphic permutation,
And replacement operator is carried out to data based on inverse permutation, and it is intermediate optionally to need repeatedly construction high-order orthomorphic permutation, it has operated
Afterwards all data be serially connected as decryption after data.
Further, in step 3, encryption side is based on identical random number seed and random digit generation method is generated with bit
Position is that the method for the random number string of unit includes:
Step I, encryption side are followed the example of according to random number bit position needed for the integer random division appointed by arriving in the past
Sequence afterwards takes a certain number of random number bit positions from random number string, and is based on these bits as random number to integer
8, which carry out following random integers, divides, and obtains
8=n1+n2+…+ns(s≥2,2≤ni≤4,1≤i≤s)。
Step II, encryption side take according to random number bit position needed for the random configuration of low order orthomorphic permutation appointed
Method is taken a certain number of random number bit positions by vertical sequence from random number string, and based on these bits be used as with
The machine number low order orthomorphic permutation following using the random configuration method random configuration of low order orthomorphic permutation:
On an orthomorphic permutation: P(1)(x(1)), P(1)(x(1)) with one includeThe array of a element is deposited
Storage, each element includes n1A binary bit,
OnA orthomorphic permutation:Wherein
Each orthomorphic permutation uses oneThe array of a element stores, each element includes n2A binary bit,
Wherein
OnA orthomorphic permutation:
Wherein each orthomorphic permutation uses one and includesThe array of a element
It stores, each element includes n3A binary bit, wherein
……。
OnA orthomorphic permutation: Wherein each conformality is set
It changes and includes with oneThe array of a element stores, each element includes nsA binary bit, wherein
Step III, encryption side construct as followsOn a high-order orthomorphic permutation P
(x):
P (x) with comprisingThe array of a element is stored, each element includes n1+n2+…+nsA two into
Bit processed；
Wherein,
Wherein, x is a 8 (8=n1+n2+…+ns) position binary variable, value range is
Step IV, encryption side judge that data also to be encrypted whether more than 16 bytes, take continuous 16 bytes if being more than
Data, then to each byte data mi(1≤i≤16) carry out replacement operator using orthomorphic permutation P (x) and obtain displacement result P
(mi) (1≤i≤16), and by result in order in a manner of binary bit string together, i.e. P (m1)P(m2)P(m3)P
(m4)P(m5)P(m6)P(m7)P(m8)P(m9)P(m10)P(m11)P(m12)P(m13)P(m14)P(m15)P(m16), then by this 16
The serial data of byte is adding behind good close data (if any) before.Then it is transferred to step 1；
If encryption side's data also to be encrypted are no more than 16 bytes, orthomorphic permutation P (x) is utilized to each byte data
Carry out replacement operator replaced as a result, and by result in order in a manner of binary bit string together, then by this
A little serial datas are adding behind good close data (if any) before.Then encryption side is just by all data encrypted
It is sent to decryption side, the encryption side of algorithm, which works, to complete.
Further, in step 4, decryption side is based on identical random number seed and random digit generation method is generated with bit
Position is that the method for the random number string of unit includes:
Step A: decryption side receives the data that good encryption side sends over.
Step B, decryption side are followed the example of according to random number bit position needed for the integer random division appointed by arriving in the past
Sequence afterwards takes a certain number of random number bit positions from random number string, and is based on these bits as random number to integer
8, which carry out following random integers, divides, and obtains
8=n1+n2+…+ns(s≥2,2≤ni≤4,1≤i≤s)。
Step C, decryption side take according to random number bit position needed for the random configuration of low order orthomorphic permutation appointed
Method is taken a certain number of random number bit positions by vertical sequence from random number string, and based on these bits be used as with
The machine number low order orthomorphic permutation following using the random configuration method random configuration of low order orthomorphic permutation:
On an orthomorphic permutation: P(1)(x(1)), P(1)(x(1)) with one includeThe array of a element is deposited
Storage, each element includes n1A binary bit,
OnA orthomorphic permutation:Wherein
Each orthomorphic permutation uses oneThe array of a element stores, each element includes n2A binary bit,
Wherein
OnA orthomorphic permutation:
Wherein each orthomorphic permutation uses one and includesThe array of a element
It stores, each element includes n3A binary bit, wherein
……。
OnA orthomorphic permutation: Wherein each conformality is set
It changes and includes with oneThe array of a element stores, each element includes nsA binary bit, wherein
Step D, encryption side construct as followsOn a high-order orthomorphic permutation P
(x):
P (x) with comprisingThe array of a element is stored, each element includes n1+n2+…+nsA two into
Bit processed；
Wherein,
Wherein, x is a 8 (8=n1+n2+…+ns) position binary variable, value range is
Finally, decryption side constructs the inverse permutation of P (x) as follows
Whether step E, decryption side judgement also need the data of decryption more than 16 bytes, take continuous 16 byte numbers if being more than
According to then to each byte data ci(1≤i≤16) utilize displacement P-1(x) it carries out replacement operator and obtains displacement result P-1(ci)
(1≤i≤16), and by result in order in a manner of binary bit string together, i.e. P-1(c1)P-1(c2)P-1(c3)P-1
(c4)P-1(c5)P-1(c6)P-1(c7)P-1(c8)P-1(c9)P-1(c10)P-1(c11)P-1(c12)P-1(c13)P-1(c14)P-1(c15)P-1
(c16), then by the serial data of this 16 bytes before behind the data of Xie Haomi (if any).Then it is transferred to
Step A；
If decryption side also needs the data of decryption to be no more than 16 bytes, displacement P is utilized to each byte data-1(x) into
Line replacement operate replaced as a result, and by result in order in a manner of binary bit string together, then by these
Serial data before behind the data of Xie Haomi (if any).The decryption side of algorithm, which works, to be completed, obtained number
According to regard to being the data after decrypting
Wherein, in decryption side step B, by the random number seed of use, random digit generation method, integer random division institute
The random number bit position needed is followed the example of, and the random division method of integer is identical as in the corresponding step in encryption side, so finally
The integer partitioning mode of integer 8 is also identical as the division methods in the corresponding step in encryption side, so 8=n here1+n2+…+ns
(s≥2,2≤ni≤ 4,1≤i≤s) the duplicate parameter of step corresponding with encryption side is also used to indicate.
In decryption side step C, due to random number seed, random digit generation method, the low order (GF (2) of usen(2≤n≤
4)) random number bit position needed for the random configuration of orthomorphic permutation follow the example of and the random configuration method of low order orthomorphic permutation is equal
It is identical as in the corresponding step in encryption side, so finally constructing obtained low order orthomorphic permutation also in step corresponding with encryption side
Low order orthomorphic permutation is identical, so these low order orthomorphic permutations also use the duplicate parameter of step corresponding with encryption side
It indicates.
In decryption side step D, high-order conformality of the high-order orthomorphic permutation constructed also in step corresponding with encryption side is set
Commutation is same, so this high-order orthomorphic permutation also uses the duplicate parameter of step corresponding with encryption side to indicate.
Another object of the present invention is to provide a kind of cipher constructions systems based on high-order orthomorphic permutation.
Another object of the present invention is to provide a kind of cipher constructions methods described in realize based on high-order orthomorphic permutation
Information data processing terminal.
Another object of the present invention is to provide a kind of computer readable storage mediums, including instruction, when it is in computer
When upper operation, so that computer executes the cipher constructions method based on high-order orthomorphic permutation.
In conclusion advantages of the present invention and good effect are as follows:
This method devises a kind of orthomorphic permutation for using dynamic mapping for the cryptographic methods of component, because in cryptographic algorithm
In use dynamic change orthomorphic permutation as password part, therefore increase the difficulty that cryptographic attack personnel break a code,
And then increase the safety of cryptographic algorithm.
It realizes simply, and is directed to same order, more orthomorphic permutations can be gone out than existing method construct, and have most
Low time complexity, which improves the efficiency of construction cryptography high-order orthomorphic permutation, to reduce costs, Jin Erwei
Encryption Algorithm provides more convenient effective method as cryptography component using high-order orthomorphic permutation.
The present invention solves construction present in the existing method for constructing high-order orthomorphic permutation by low order orthomorphic permutation
Method is generally more complex, and the time complexity of some algorithm is also excessively high, causes to realize that difficulty is big, cost of implementation is high to ask
Topic.Because many methods are more complicated in the prior art, it is difficult to manage for non-mathematics and cryptography technical professional
Solution, which increases the difficulty that algorithm is realized, and the time complexity of some algorithm is also higher, cause cost of implementation compared with
Height, to reduce the utilization rate of these methods.
This invention also solves the number of the cryptography high-order orthomorphic permutation constructed in the prior art is not also enough, lead
If cause need to generate a large amount of orthomorphic permutations and therefrom select or construct a kind of (the more typical application of the excellent orthomorphic permutation of cryptography
Mode, for example use the orthomorphic permutation of dynamic change as password part, this just needs to construct a large amount of orthomorphic permutation), it needs
It is separately operable different building methods, and then results in inefficient problem.Although existing part passes through low order orthomorphic permutation
It is not high come the method time complexity that constructs cryptography high-order orthomorphic permutation, and a certain number of high-order orthomorphic permutations can be generated,
But it is still less than normal compared to for the number of corresponding order orthomorphic permutation, if therefore a large amount of orthomorphic permutations need to be generated and therefrom selected
Or the orthomorphic permutation that construction cryptography is excellent, it needs to be separately operable different building methods, improves cost, lead to efficiency not
It is high.
A kind of GF (2) is proposed in the present inventionnThe simple structure method of cryptography orthomorphic permutation on (n > 4), and the party
Method is directed to same order, more orthomorphic permutations can be gone out than existing method construct, and have minimum time complexity, in this way
The efficiency of construction cryptography high-order orthomorphic permutation is just improved, to reduce costs, and then one kind is devised based on this method
Use the high-order orthomorphic permutation of dynamic mapping for the cryptographic methods of component, this method will increase what cryptographic attack personnel broke a code
Difficulty, and then increase the safety of cryptographic methods.
Detailed description of the invention
Fig. 1 is the cipher constructions method flow diagram provided in an embodiment of the present invention based on high-order orthomorphic permutation.
Fig. 2 is the cipher constructions method frame figure provided in an embodiment of the present invention based on high-order orthomorphic permutation.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Art methods are in the construction and reality for constructing cryptographic algorithm and high-order orthomorphic permutation based on orthomorphic permutation
It is had the following deficiencies in:
(1) orthomorphic permutation employed in cryptographic algorithm is generally fixed and invariable, and which adds by cryptographic attack
Personnel analyze the risk decoded.
(2) method that high-order orthomorphic permutation is constructed by low order orthomorphic permutation is generally more complex, and some algorithm
Time complexity is also excessively high, causes to realize that difficulty is big, cost of implementation is high.Many methods are more complicated, for non-mathematics and password
Indigestion for technical professional is learned, which increases the difficulty that algorithm is realized, and the time of some algorithm is multiple
Miscellaneous degree is also higher, causes cost of implementation higher, to reduce the utilization rate of these methods.
(3) number of the high-order orthomorphic permutation constructed is not also enough, if cause need to generate a large amount of orthomorphic permutations and from
In select or construct the excellent orthomorphic permutation of cryptography (a kind of more typical application mode, for example, using dynamic change just
Shape displacement is used as password part, this just needs to construct a large amount of orthomorphic permutation), need to be separately operable different building methods, into
And it results in inefficient.Although the method time that existing part constructs high-order orthomorphic permutation by low order orthomorphic permutation is complicated
Spend not high, and can generate a certain number of high-order orthomorphic permutations, but compared to for the number of correspondence order orthomorphic permutation still
It is less than normal, if therefore generate a large amount of orthomorphic permutations, need to be separately operable different building methods, improve cost, lead to efficiency not
It is high.
In view of the problems of the existing technology, the present invention provides a kind of cipher constructions methods based on high-order orthomorphic permutation
And system, the present invention is explained in detail with reference to the accompanying drawing.
As shown in Figure 1, the present invention implements the cipher constructions method (GF (2) based on high-order orthomorphic permutation providedn(n>4)
The building method of upper high-order orthomorphic permutation) include:
S101, encryption side and decryption side both sides uniformly arrange identical random number seed, random digit generation method, integer with
It follows the example of, needed for the random division method of integer, the random configuration of low order orthomorphic permutation random number bit position needed for machine division
Random number bit position follow the example of and the random configuration method of low order orthomorphic permutation.
S102, encryption side and decryption side are based on identical random number seed and random digit generation method is generated with bit
For the random number string of unit, the random number bit position in the random number string was executed in random number seed and random digit generation method
Continual generation in journey.
S103, encryption side carries out random division to integer 8, and is based on division result random configuration low order orthomorphic permutation.
Low order orthomorphic permutation is spliced into high-order orthomorphic permutation by S104, encryption side, and based on high-order orthomorphic permutation to data
It carries out replacement operator and repeatedly constructs high-order orthomorphic permutation, all data are serially connected after having operated and are sent to decryption side.
S105 after decryption side has received data, equally executes random division to integer 8, and based on division result with mechanism
Make low order orthomorphic permutation.
Low order orthomorphic permutation is spliced into high-order orthomorphic permutation by S106, decryption side, and then obtains the inverse of high-order orthomorphic permutation
Displacement, and replacement operator is carried out to data based on inverse permutation, it is intermediate optionally to need repeatedly construction high-order orthomorphic permutation, behaviour
After finishing all data be serially connected as decryption after data.
Fig. 2 is the cipher constructions method frame figure provided in an embodiment of the present invention based on high-order orthomorphic permutation.
Of the invention is further described combined with specific embodiments below.
Embodiment 1:
The present invention implement provide the cipher constructions method based on high-order orthomorphic permutation include:
Step 1, encryption side and decryption side both sides uniformly arrange identical random number seed, random digit generation method, integer
Random number bit position needed for random division is followed the example of, the random division method of integer, low order (GF (2)n(2≤n≤4)) conformality
Random number bit position needed for displaced random configuration follow the example of and the random configuration method of low order orthomorphic permutation.
In this example, random number seed can use the included CryptGenRandom function of windows to generate, with
The binary number that the several sub- seed of machine are one 32.Random digit generation method can using in C language rand () function and
Srand () function, wherein srand () function needs one 32 initialization seed parameters, using 32 two just generated into
Number processed is as seed parameter.Random number bit position needed for integer random division follow the example of and the random division method of integer,
Due to pertaining only to the division to integer 8 in our invention, and meet
8=n1+n2+…+ns(s≥2,2≤ni≤ 4,1≤i≤s),
Therefore following method can be used: takes three random number bit positions, if it is 000, then n1=n2=n3=n4=
2；If it is 001, then n1=2, n2=n3=3；If it is 010, then n2=2, n1=n3=3；If it is 011, then n3=2, n1=
n2=3；If it is 100, then n1=n2=2, n3=4；If it is 101, then n1=n3=2, n2=4；If it is 110, then n2=n3
=2, n1=4；If it is 111, then n1=n2=4.As for low order (GF (2)n(2≤n≤4)) orthomorphic permutation random configuration institute
Need random number bit position follow the example of and the random configuration method of low order orthomorphic permutation, can in bibliography [1] 3.3 it is low
The quick enumeration building method of rank orthomorphic permutation.Method in document is not related to random configuration, here can be as follows
Randomizing factor is added.Arrangement is constructed by random number bit.For example, wanting random configuration GF (2)2On a low order just
Shape replaces (GF (2)3, GF (2)4The case where and so on), then one from 00 is constructed first, 01,10,11 random alignment.Tool
Body method is: two taken from random number bit position, then judge whether the number of this two binary system compositions has recorded, if
Unwritten words are just recorded, and are just skipped if having recorded, and then proceed to take two from random number bit position, weight
Multiple judgement, until 00,01,10,11, this four numbers are all recorded.One 00,01,10,11 random row is thus obtained
Column.After random alignment generates, this is then arranged into the line home position array beginning being assigned in document [1] 3.3 again
And row number array, starting line number removes flagfirst, pre, next, link array since 0, then is correspondingly arranged and judges
The mark bit array and judge the mark bit array whether line number row number exclusive or value uses whether row number uses, are then just transported
Row enumeration searches for orthomorphic permutation, is recorded if finding one as a result, and terminating search.Thus random configuration one
A GF (2)2On orthomorphic permutation.
Step 2, encryption side and decryption side are based on identical random number seed and random digit generation method is generated with bit
Position is the random number string of unit, and the random number bit position in the random number string can be continual in entire method implementation procedure
It generates.
In this example, continuous based on rand () function using 32 bits appointed as random number seed
Generation random number bit position.
The cipher constructions method based on high-order orthomorphic permutation is described from encryption side and two angles of decryption side separately below.
Encryption side:
Step I, encryption side are followed the example of according to random number bit position needed for the integer random division appointed by arriving in the past
Sequence afterwards takes a certain number of random number bit positions from random number string, and is based on these bits as random number to integer
8, which carry out following random integers, divides, and obtains
8=n1+n2+…+ns(s≥2,2≤ni≤4,1≤i≤s)。
In this example, integer 8 is divided according to the method in one embodiment of common step, it is assumed that the feelings of division
Condition is n=8, s=3, n1=2, n2=3, n=3.
Step II, encryption side take according to random number bit position needed for the random configuration of low order orthomorphic permutation appointed
Method is taken a certain number of random number bit positions by vertical sequence from random number string, and based on these bits be used as with
The machine number low order orthomorphic permutation following using the random configuration method random configuration of low order orthomorphic permutation:
On an orthomorphic permutation: P(1)(x(1)), P(1)(x(1)) with one includeThe array of a element is deposited
Storage, each element includes n1A binary bit,
OnA orthomorphic permutation:Wherein
Each orthomorphic permutation uses oneThe array of a element stores, each element includes n2A binary bit,
Wherein
OnA orthomorphic permutation:
Wherein each orthomorphic permutation uses one and includesThe array of a element
It stores, each element includes n3A binary bit, wherein
……。
OnA orthomorphic permutation: Wherein each orthomorphic permutation is used
One includesThe array of a element stores, each element includes nsA binary bit, wherein
In this example, carry out random configuration orthomorphic permutation according to the method in one embodiment of common step, specifically obtain:
GF(2)2On an orthomorphic permutation: P(1)(x(1)): 03 01 00 02 (it is hexadecimal representation herein, it is corresponding
Two binary bits can be written as 11 01 00 10, similar below), this indicates P(1)[0]=3, P(1)[1]=1, P(1)
[2]=0, P(1)[3]=2, similar below.
GF(2)3On 22A orthomorphic permutation: P(2)(1)(x(2)), P(2)(2)(x(2)), P(2)(3)(x(2)),
Each element of each orthomorphic permutation is made of 3 binary bits.
GF(2)3On 25A orthomorphic permutation:
Each element of each orthomorphic permutation is made of 3 binary bits.
Step III, encryption side construct as followsOn a high-order orthomorphic permutation P
(x):
P (x) with comprisingThe array of a element is stored, each element includes n1+n2+…+nsA two into
Bit processed；
Wherein,
Wherein, x is a 8 (8=n1+n2+…+ns) position binary variable, value range is
In this example,
Wherein, ((i1-1)23+i2-1)23≤ x < ((i1-1)23+i2)23,1≤i1≤4,1≤i2≤8。
Work as i1=1, i2When=1,0≤x < 8, at this time P (x)=(P(1)(x(1)),P(2)(1)(x(2)),P(3)(1)(1)(x(3))),
And it is known
P(1)(x(1)): 03 01 00 02, P(2)(1)(x(2)): 00 02 04 06 03 01 07 05, P(3)(1)(1)(x(3)):
05 06 03 00 02 01 04 07, it constructs in accordance with the following steps:
Each 8 x can split into one two x(1), one three x(2), one three x(3)。
So as x=0, x(1)=0, x(2)=0, x(3)=0；P [0]=(P(1)[0],P(2)(1)[0],P(3)(1)(1)[0])
=(03,00,05).
Specific implementation can be by array element P(1)[0] and P(2)(1)[0]、P(3)(1)(1)[0] it shifts in order, it is then sharp
With or operation splicing obtain P [0], i.e. P [0]=(P(1)[0] < < (2+3)) | (P(2)(1)[0] < < 3) | P(3)(1)(1)[0]=
C5 (hexadecimal), other elements, such as P [i] (1≤i < 8), the method for generation is similar.
Work as i1=1, i2When=2,8≤x < 16, at this time P (x)=(P(1)(x(1)),P(2)(1)(x(2)),P(3)(1)(2)(x(3))),
Copy the value of above-mentioned method equally 8 elements of available P [i] (8≤i < 16).
Successively similar, the value of available all P [i] (0≤i < 256) then obtains a GF (2)8On high-order just
Shape is replaced into (hexadecimal)
Step IV, encryption side judge that data also to be encrypted whether more than 16 bytes, take continuous 16 bytes if being more than
Data, then to each byte data mi(1≤i≤16) carry out replacement operator using orthomorphic permutation P (x) and obtain displacement result P
(mi) (1≤i≤16), and by result in order in a manner of binary bit string together, i.e. P (m1)P(m2)P(m3)P
(m4)P(m5)P(m6)P(m7)P(m8)P(m9)P(m10)P(m11)P(m12)P(m13)P(m14)P(m15)P(m16), then by this 16
The serial data of byte is adding behind good close data (if any) before.Then it is transferred to step I；
If encryption side's data also to be encrypted are no more than 16 bytes, orthomorphic permutation P (x) is utilized to each byte data
Carry out replacement operator replaced as a result, and by result in order in a manner of binary bit string together, then by this
A little serial datas are adding behind good close data (if any) before.Then encryption side is just by all data encrypted
It is sent to decryption side, the encryption side of algorithm, which works, to complete.
In this example, it will be assumed that the data of Yao Jiami have 8 bytes, are 37 76 1B C9 A0 0E 53 of DB, then
P(m1)P(m2)P(m3)P(m4)P(m5)P(m6)P(m7)P(m850 F6 of)=8F FB, 90 3C D0 44, encryption data has generated
Finish.
Decryption side:
Step A: decryption side receives the data that good encryption side sends over.
In this example, decryption side receives the data that good encryption side sends over, i.e. 50 F6 of 8F FB, 90 3C D0
44。
Step B, decryption side are followed the example of according to random number bit position needed for the integer random division appointed by arriving in the past
Sequence afterwards takes a certain number of random number bit positions from random number string, and is based on these bits as random number to integer
8, which carry out following random integers, divides, and obtains
8=n1+n2+…+ns(s≥2,2≤ni≤4,1≤i≤s)。
In this example, integer 8 is divided according to the method in one embodiment of common step, it is assumed that the feelings of division
Condition is n=8, s=3, n1=2, n2=3, n=3, it is consistent with encryption side.
Step C, decryption side take according to random number bit position needed for the random configuration of low order orthomorphic permutation appointed
Method is taken a certain number of random number bit positions by vertical sequence from random number string, and based on these bits be used as with
The machine number low order orthomorphic permutation following using the random configuration method random configuration of low order orthomorphic permutation:
On an orthomorphic permutation: P(1)(x(1)), P(1)(x(1)) with one includeThe array of a element is deposited
Storage, each element includes n1A binary bit,
OnA orthomorphic permutation:Wherein
Each orthomorphic permutation uses oneThe array of a element stores, each element includes n2A binary bit,
Wherein
OnA orthomorphic permutation:
Wherein each orthomorphic permutation uses one and includesThe array of a element
It stores, each element includes n3A binary bit, wherein
……。
OnA orthomorphic permutation: Wherein each conformality is set
It changes and includes with oneThe array of a element stores, each element includes nsA binary bit, wherein
In this example, carry out random configuration orthomorphic permutation according to the method in one embodiment of common step, specifically obtain:
GF(2)2On an orthomorphic permutation: P(1)(x(1)): 03 01 00 02.
GF(2)3On 22A orthomorphic permutation: P(2)(1)(x(2)), P(2)(2)(x(2)), P(2)(3)(x(2)),
Each element of each orthomorphic permutation is made of 3 binary bits.
GF(2)3On 25A orthomorphic permutation:
Each element of each orthomorphic permutation is made of 3 binary bits.The low order orthomorphic permutation constructed with
Encryption side constructs consistent.
Step D, encryption side construct as followsOn a high-order orthomorphic permutation P
(x):
P (x) with comprisingThe array of a element is stored, each element includes n1+n2+…+nsA two into
Bit processed；
Wherein,
Wherein, x is a 8 (8=n1+n2+…+ns) position binary variable, value range is
In this example,
Wherein, ((i1-1)23+i2-1)23≤ x < ((i1-1)23+i2)23,1≤i1≤4,1≤i2≤8。
Work as i1=1, i2When=1,0≤x < 8, at this time P (x)=(P(1)(x(1)),P(2)(1)(x(2)),P(3)(1)(1)(x(3))),
And it is known
P(1)(x(1)): 03 01 00 02, P(2)(1)(x(2)): 00 02 04 06 03 01 07 05, P(3)(1)(1)(x(3)):
05 06 03 00 02 01 04 07, it constructs in accordance with the following steps:
Each 8 x can split into one two x(1), one three x(2), one three x(3)。
So as x=0, x(1)=0, x(2)=0, x(3)=0,
P [0]=(P(1)[0],P(2)(1)[0],P(3)(1)(1)[0])=(03,00,05), specific implementation can be by array members
Plain P(1)[0] and P(2)(1)[0]、P(3)(1)(1)[0] shift in order, then using or operation splicing obtain P [0], i.e. P [0]=
(P(1)[0] < < (2+3)) | (P(2)(1)[0] < < 3) | P(3)(1)(1)[0]=C5 (hexadecimal), other elements, such as P [i] (1
≤ i < 8), the method for generation is similar.
Work as i1=1, i2When=2,8≤x < 16, at this time P (x)=(P(1)(x(1)),P(2)(1)(x(2)),P(3)(1)(2)(x(3))),
Copy the value of above-mentioned method equally 8 elements of available P [i] (8≤i < 16).
Successively similar, the value of available all P [i] (0≤i < 256) then obtains a GF (2)8On high-order just
Shape is replaced into (hexadecimal)
It is constructed with encryption side consistent.
Finally, decryption side constructs the inverse permutation of P (x) as follows
It arrives
Whether step E, decryption side judgement also need the data of decryption more than 16 bytes, take continuous 16 byte numbers if being more than
According to then to each byte data ci(1≤i≤16) utilize displacement P-1(x) it carries out replacement operator and obtains displacement result P-1(ci)
(1≤i≤16), and by result in order in a manner of binary bit string together, i.e. P-1(c1)P-1(c2)P-1(c3)P-1
(c4)P-1(c5)P-1(c6)P-1(c7)P-1(c8)P-1(c9)P-1(c10)P-1(c11)P-1(c12)P-1(c13)P-1(c14)P-1(c15)P-1
(c16), then by the serial data of this 16 bytes before behind the data of Xie Haomi (if any).Then it is transferred to
Step A.
If decryption side also needs the data of decryption to be no more than 16 bytes, displacement P is utilized to each byte data-1(x) into
Line replacement operate replaced as a result, and by result in order in a manner of binary bit string together, then by these
Serial data before behind the data of Xie Haomi (if any).The decryption side of algorithm, which works, to be completed, obtained number
According to regard to being the data after decrypting.
Due to needing data to be decrypted there was only 8 bytes, decryption side uses P to each byte of this 8 bytes-1
(x) it replaces, and together by result string, obtains 37 76 1B C9 A0 0E 53 of DB, decryption finishes.
Below with reference to the good effect of acquirement, the invention will be further described.
According to the method based on low order orthomorphic permutation construction high-order orthomorphic permutation in the present invention, for given n,
It can construct altogether
A GF (2)nOn orthomorphic permutation, whereinIt indicatesThe number of upper orthomorphic permutation.
In the present invention, method of the invention and several high-order conformalities that typically constructed by low order orthomorphic permutation are set
The method changed is compared analysis, without loss of generality, here with n=n1+n2+n3(ni>=2,1≤i≤3) partitioning scheme be
Example, whereinIt indicatesThe number of upper linear orthomorphic permutation, while known | O2(F2) |=8, |
O2(F3) |=384, | LO2(F2) |=2, | LO3(F2) |=48:
It can be seen that the high-order orthomorphic permutation building method in of the invention possesses minimum time complexity
Simultaneously known this patent the number of getable orthomorphic permutation be also most, or even under same order (in table as above),
This method the number orthomorphic permutation more getable than preceding four kinds of methods of getable orthomorphic permutation summation it is more, thus
A large amount of orthomorphic permutations (such as cipher constructions side of the orthomorphic permutation based on dynamic mapping used in the present invention can needed to construct
Method encrypts mass data) when give full play to advantage.
Bibliography
[1] the property research of Tong Yan orthomorphic permutation and the construction Wuhan [D] that develops: Wuhan University, 2008.
[2] construction [J] the communication security of Feng Dengguo, Liu Zhenhua about orthomorphic permutation, 1996 (02): 61-64.
[3] construction [J] the Shaanxi Normal University journal (natural science of Li Zhihui, Li Ruihu, Li Xueliang orthomorphic permutation
Version), 2002 (04): 18-22.
[4] several results [J] the applied science journal of Zhu Huaan, Xie Duanqiang about orthomorphic permutation in cipher system,
2004(02):132-135。
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (10)
1. a kind of cipher constructions method based on high-order orthomorphic permutation, which is characterized in that described based on the close of high-order orthomorphic permutation
Code constructing method specifically includes the following steps:
It is random that step 1, encryption side and decryption side both sides uniformly arrange identical random number seed, random digit generation method, integer
Divide following the example of, needed for the random division method of integer, the random configuration of low order orthomorphic permutation for required random number bit position
Random number bit position follow the example of and the random configuration method of low order orthomorphic permutation；
Step 2, encryption side and decryption side are based on identical random number seed and random digit generation method generates with bit and is
The random number string of unit, the random number bit position in the random number string is in random number seed and random digit generation method implementation procedure
In continual generation；
Step 3, encryption side carries out random division to integer 8, and is based on division result random configuration low order orthomorphic permutation；
Low order orthomorphic permutation is spliced into high-order orthomorphic permutation by encryption side, and carries out displacement behaviour to data based on high-order orthomorphic permutation
Make and repeatedly construct high-order orthomorphic permutation, all data are serially connected after having operated and are sent to decryption side；
Step 4 after decryption side has received data, equally executes random division to integer 8, and be based on division result random configuration
Low order orthomorphic permutation；
Low order orthomorphic permutation is spliced into high-order orthomorphic permutation by decryption side, and then obtains the inverse permutation of high-order orthomorphic permutation, and base
Replacement operator is carried out to data in inverse permutation, it is intermediate optionally to need repeatedly construction high-order orthomorphic permutation, institute after having operated
Have data be serially connected as decryption after data.
2. as described in claim 1 based on the cipher constructions method of high-order orthomorphic permutation, which is characterized in that step 3 is specifically wrapped
It includes:
Step I, encryption side are followed the example of according to random number bit position needed for the integer random division appointed by vertical
Sequence takes a certain number of random number bit positions from random number string, and based on these bits as random number to integer 8 into
The following random integers of row divide, and obtain
8=n1+n2+…+ns(s≥2,2≤ni≤4,1≤i≤s)；
Step II, encryption side according to random number bit position needed for the random configuration of low order orthomorphic permutation appointed follow the example of by
Vertical sequence takes a certain number of random number bit positions from random number string, and based on these bits as random number
Utilize the random configuration method random configuration low order orthomorphic permutation of low order orthomorphic permutation；
Step III, encryption side construct as followsOn a high-order orthomorphic permutation P (x):
P (x) with comprisingThe array of a element is stored, each element includes n1+n2+…+nsA binary system ratio
Special position；
Wherein,
Wherein, x is a 8 (8=n1+n2+…+ns) position binary variable, value range is
Step IV, encryption side judge that data also to be encrypted whether more than 16 bytes, take continuous 16 byte datas if being more than,
Then to each byte data mi(1≤i≤16) carry out replacement operator using orthomorphic permutation P (x) and obtain displacement result P (mi)(1
≤ i≤16), and by result in order in a manner of binary bit string together, i.e. P (m1)P(m2)P(m3)P(m4)P(m5)
P(m6)P(m7)P(m8)P(m9)P(m10)P(m11)P(m12)P(m13)P(m14)P(m15)P(m16), then by the number of this 16 bytes
Adding behind good close data according to string；Then it is transferred to step I.
3. as claimed in claim 2 based on the cipher constructions method of high-order orthomorphic permutation, which is characterized in that step II is specifically wrapped
It includes:
On an orthomorphic permutation: P(1)(x(1)), P(1)(x(1)) with one includeThe array of a element stores, often
One element includes n1A binary bit,
OnA orthomorphic permutation:It is wherein each
Orthomorphic permutation uses oneThe array of a element stores, each element includes n2A binary bit, wherein
OnA orthomorphic permutation: Wherein each orthomorphic permutation uses one and includesThe array of a element
It stores, each element includes n3A binary bit, wherein
……；
OnA orthomorphic permutation: Wherein each conformality is set
It changes and includes with oneThe array of a element stores, each element includes nsA binary bit, wherein。
4. as claimed in claim 2 based on the cipher constructions method of high-order orthomorphic permutation, which is characterized in that
In step IV, if encryption side's data also to be encrypted are no more than 16 bytes, each byte data is set using conformality
Change P (x) carry out replacement operator replaced as a result, and by result in order in a manner of binary bit string together, so
These serial datas are being added before behind good close data afterwards；Then all data encrypted are just sent to by encryption side
Decryption side.
5. as described in claim 1 based on the cipher constructions method of high-order orthomorphic permutation, which is characterized in that step 4 is specifically wrapped
It includes:
Step A: decryption side receives the data that good encryption side sends over；
Step B, decryption side are followed the example of according to random number bit position needed for the integer random division appointed by vertical
Sequence takes a certain number of random number bit positions from random number string, and based on these bits as random number to integer 8 into
The following random integers of row divide, and obtain
8=n1+n2+…+ns(s≥2,2≤ni≤4,1≤i≤s)；
Step C, decryption side according to random number bit position needed for the random configuration of low order orthomorphic permutation appointed follow the example of by
Vertical sequence takes a certain number of random number bit positions from random number string, and based on these bits as random number
Utilize the random configuration method random configuration low order orthomorphic permutation of low order orthomorphic permutation；
Step D, encryption side construct as followsOn a high-order orthomorphic permutation P (x):
P (x) with comprisingThe array of a element is stored, each element includes n1+n2+…+nsA binary system ratio
Special position；
Wherein,
Wherein, x is a 8 (8=n1+n2+…+ns) position binary variable, value range is
Decryption side constructs the inverse permutation of P (x) as follows
Whether step E, decryption side judgement also need the data of decryption more than 16 bytes, take continuous 16 byte datas if being more than,
Then to each byte data ci(1≤i≤16) utilize displacement P-1(x) it carries out replacement operator and obtains displacement result P-1(ci)(1≤
I≤16), and by result in order in a manner of binary bit string together, i.e. P-1(c1)P-1(c2)P-1(c3)P-1(c4)
P-1(c5)P-1(c6)P-1(c7)P-1(c8)P-1(c9)P-1(c10)P-1(c11)P-1(c12)P-1(c13)P-1(c14)P-1(c15)P-1
(c16), then by the serial data of this 16 bytes behind the data of Xie Haomi；Then it is transferred to step A.
6. as claimed in claim 5 based on the cipher constructions method of high-order orthomorphic permutation, which is characterized in that step C is based on this
A little bits are utilized as random number in the low order orthomorphic permutation of random configuration method random configuration of low order orthomorphic permutation, specifically
Include:
On an orthomorphic permutation: P(1)(x(1)), P(1)(x(1)) with one includeThe array of a element stores, often
One element includes n1A binary bit,
OnA orthomorphic permutation:It is wherein each
Orthomorphic permutation uses oneThe array of a element stores, each element includes n2A binary bit, wherein
OnA orthomorphic permutation: Wherein each orthomorphic permutation uses one and includesThe array of a element
It stores, each element includes n3A binary bit, wherein
……；
OnA orthomorphic permutation: Wherein each conformality is set
It changes and includes with oneThe array of a element stores, each element includes nsA binary bit, wherein
7. as claimed in claim 5 based on the cipher constructions method of high-order orthomorphic permutation, which is characterized in that in step E, if solution
Close side also needs the data of decryption to be no more than 16 bytes, then utilizes displacement P to each byte data-1(x) replacement operator is carried out to obtain
To displacement as a result, and by result in order in a manner of binary bit string together, then by these serial datas before
Behind the data of Xie Haomi；After the completion of decryption side work, obtained data are the data after decryption.
8. it is a kind of implement claim 1~7 any one described in the cipher constructions method based on high-order orthomorphic permutation based on height
The cipher constructions system of rank orthomorphic permutation.
9. a kind of Information Number for realizing the cipher constructions method described in claim 1~7 any one based on high-order orthomorphic permutation
According to processing terminal.
10. a kind of computer readable storage medium, including instruction, when run on a computer, so that computer executes such as
Based on the cipher constructions method of high-order orthomorphic permutation described in claim 1-7 any one.
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