CN110311775A - S box construction method based on DNA operator and chaos system - Google Patents

S box construction method based on DNA operator and chaos system Download PDF

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Publication number
CN110311775A
CN110311775A CN201910718395.1A CN201910718395A CN110311775A CN 110311775 A CN110311775 A CN 110311775A CN 201910718395 A CN201910718395 A CN 201910718395A CN 110311775 A CN110311775 A CN 110311775A
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dna
matrix
box
chaos system
group
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CN110311775B (en
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彭军
彭唯嘉
金尚柱
庞韶宁
张绍春
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Chongqing University of Science and Technology
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Chongqing University of Science and Technology
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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
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • 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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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Measuring Or Testing Involving Enzymes Or Micro-Organisms (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The present invention provides a kind of S box construction method based on DNA operator and chaos system, comprising the following steps: S1: one chaos system of building and DNA switching box in advance, and 8 bits are generated with it；S2: constructing one 16 × 16 S box matrix, and each element in matrix is 8 bits, and is successively filled using step S1 generation and mutual unduplicated 8 bit；S3: carrying out disturbance transformation and DNA operation to S box matrix, obtains final S box output.Its effect is: the present invention is combined by DNA operator and chaos system, while being disturbed again, so that the random performance of S box is stronger, antidecoding capability is higher, effectively promotes the security performance of encryption system.

Description

S box construction method based on DNA operator and chaos system
Technical field
The present invention relates to data encryption technologys, and in particular to a kind of S box building side based on DNA operator and chaos system Method.
Background technique
In cryptography, S box (Substitution-box) is the basic knot for executing displacement in symmetric key algorithm and calculating Structure.S box is used in block cipher, is unique nonlinear organization, and the quality of the index of S box directly determines that password is calculated The quality of method.
Traditional S box building method complexity is cumbersome, is not easy to software and hardware realization, not high, arithmetic speed that there is safeties Slowly, it is difficult to the defects of applying in practice.
Summary of the invention
Based on drawbacks described above, the present invention proposes a kind of S box construction method based on DNA operator and chaos system.This method Chaos system is combined with DNA operator and realizes the building of S box, promotes S box quality, it is ensured that its security performance.
To achieve the goals above, specific technical solution of the present invention is as follows:
A kind of S box construction method based on DNA operator and chaos system, key be the following steps are included:
S1: one chaos system of building and DNA switching box in advance, and 8 bits are generated with it；
S2: constructing one 16 × 16 S box matrix, and each element in matrix is 8 bits, and successively sharp Unduplicated 8 bit filling generated with step S1 and mutual；
S3: carrying out disturbance transformation and DNA operation to S box matrix, obtains final S box output.
The present invention is combined by DNA operator and chaos system, while being disturbed again, so that the random performance of S box is stronger, Antidecoding capability is higher, effectively promotes the security performance of encryption system.
Optionally, the chaos system that step S1 is constructed in advance are as follows:
Wherein: k1、k2、k3For system parameter, x, y, ω, u, υ is the state variable of system, by setting k1、k2、k3Take Value is so that system is in chaos state.The chaos system of other forms can certainly be set, as long as ensuring that system is in chaos State.
Optionally, in step sl, first with the chaos system constructed in advance generate in the following way two 8 two into Number C processed1And C2, wherein xN+sp~xN+5spIndicate chaos system variable x in the case where N+sp~N+5sp corresponds to the number of iterations Value；yN+sp~yN+5spIndicate the value of chaos system variable y in the case where N+sp~N+5sp corresponds to the number of iterations；S1And S2 Belong to intermediate variable；
S1=xN+sp*xN+2sp*xN+3sp*xN+4sp*xN+5sp；
S2=yN+sp*yN+2sp*yN+3sp*yN+4sp*yN+5sp；
C1=floor (mod (abs (S1*1513),256))；
C2=floor (mod (abs (S2*1711),256))；
Then by two 8 bit C1And C2After the DNA switching box carries out 4 round transformations, two 8 are obtained Binary number C1 *And C2 *；
Finally according to C=XOR (C1 *,C2 *) obtain 8 final bit C.
When generating random number using chaos system, the data by extracting multiple the number of iterations are multiplied the present invention, It recycles a coefficient to amplify, improves the random performance of basic data.
Optionally, the initial value of the chaos system is x0=1, y0=1.2, ω0=1.2, u0=1.2, υ0=1.2, be Unite parameter k1=1, k2=4, k3=1.2, spacing parameter sp=5.
Optionally, the DNA switching box that step S1 is constructed in advance includes two input data (H(1) 1L(1) 1)(H(1) 2L(1) 2) and Two output data (H(2) 1L(2) 1)(H(2) 2L(2) 2), in which:
H(1) 1Indicate high 4 digit of first input data；
L(1) 1Indicate low 4 digit of first input data；
H(1) 2Indicate high 4 digit of second input data；
L(1) 2Indicate low 4 digit of second input data；
H(2) 1Indicate high 4 digit of first output data；
L(2) 1Indicate low 4 digit of first output data；
H(2) 2Indicate high 4 digit of second output data；
L(2) 2Indicate low 4 digit of second output data；
The transformation relation of above-mentioned data are as follows:
L(2) 1=f_DNA (H(1) 1,W1), W1=mod ((L(1) 1)^3,6)+1；
L(2) 2=f_DNA (L(1) 1,W2), W2=mod ((H(1) 1)^3,6)+1；
H(2) 1=f_DNA (H(1) 2,W3), W3=mod ((L(1) 2)^3,6)+1；
H(2) 2=f_DNA (L(1) 2,W4), W4=mod ((H(1) 2)^3,6)+1；
Symbol f_DNA (X, W) indicates that logarithm X executes W group DNA operation rule, which group operation rule is the value of W indicate using It is then converted, asks 6 mould to add 1 to determine again after seeking 3 powers according to selected objects again, and each group operation rule specifically:
Group number Transformation rule
First group (AT)(TC)(CG)(GA)
Second group (AT)(TG)(GC)(CA)
Third group (AC)(CT)(TG)(GA)
4th group (AC)(CG)(GT)(TA)
5th group (AG)(GT)(TC)(CA)
6th group (AG)(GC)(CT)(TA)
Wherein: A, T, C, G respectively indicate string of binary characters 01,10,00,11；After operation, previous character will in bracket It is transformed to the latter character in bracket.
Optionally, if the S box matrix before step S3 disturbance is M, the specific steps of step S3 include:
S31: by matrix M generator matrix M*, first summing to each column in matrix M, ifEnable dj=mod (tj, 16), then jth row in matrix M is placed into the d in M*jRow, if djJth row in matrix M is then placed by row non-empty Mod (t in matrix M*j+ 1,16) row, the behavior until finding a certain sky stop；
S32: by matrix M* generator matrix M**, first to each element m in matrix M*i,j, utilize any one group of DNA operator Evolution processing is carried out to it, if mi,jBy DNA operator operation after numerical value beAnd its odd bits and even bit is enabled to constitute Numerical value be denoted as i respectively*And j*, then by mi,jWithIt exchanges；
S33: using final matrix M** as the S box matrix after disturbance.
Beneficial effects of the present invention:
(1) this method generates the random number haveing excellent performance using chaos system, the effect of DNA switching box is excessively taken turns, into one Step promotes quality of random numbers；
(2) this method simulates the DNA operator in biological evolution, carries out evolutionary computation to data, more gets close to nature, into The randomness of one step increase data；
(3) disturbance and DNA operation are carried out to intermediate matrix data, further promotes the quality of S box；
(4) chaos system initial value slightly minor variations can produce entirely different S box, while bringing convenience, again It can guarantee and the S box of high degree of safety is provided.
Detailed description of the invention
It, below will be to specific in order to illustrate more clearly of the specific embodiment of the invention or technical solution in the prior art Embodiment or attached drawing needed to be used in the description of the prior art are briefly described.
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is the structural schematic diagram of used DNA switching box of the invention.
Specific embodiment
It is described in detail below in conjunction with embodiment of the attached drawing to technical solution of the present invention.Following embodiment is only used for Clearly illustrate technical solution of the present invention, therefore be only used as example, and cannot be used as a limitation and limit protection model of the invention It encloses.
It should be noted that unless otherwise indicated, technical term or scientific term used in this application should be this hair The ordinary meaning that bright one of ordinary skill in the art are understood.
As shown in Figure 1 and Figure 2, the present embodiment discloses a kind of S box construction method based on DNA operator and chaos system, including Following steps:
S1: one chaos system of building and DNA switching box in advance, and 8 bits are generated with it；
The chaos system constructed in advance in the present embodiment are as follows:
The initial value of chaos system is x0=1, y0=1.2, ω0=1.2, u0=1.2, υ0=1.2, system parameter k1=1, k2=4, k3=1.2, spacing parameter sp=5.
The DNA switching box constructed in advance includes two input data (H(1) 1L(1) 1)(H(1) 2L(1) 2) and two output datas (H(2) 1L(2) 1)(H(2) 2L(2) 2), in which:
H(1) 1Indicate high 4 digit of first input data；
L(1) 1Indicate low 4 digit of first input data；
H(1) 2Indicate high 4 digit of second input data；
L(1) 2Indicate low 4 digit of second input data；
H(2) 1Indicate high 4 digit of first output data；
L(2) 1Indicate low 4 digit of first output data；
H(2) 2Indicate high 4 digit of second output data；
L(2) 2Indicate low 4 digit of second output data；
The transformation relation of above-mentioned data are as follows:
L(2) 1=f_DNA (H(1) 1,W1), W1=mod ((L(1) 1)^3,6)+1；
L(2) 2=f_DNA (L(1) 1,W2), W2=mod ((H(1) 1)^3,6)+1；
H(2) 1=f_DNA (H(1) 2,W3), W3=mod ((L(1) 2)^3,6)+1；
H(2) 2=f_DNA (L(1) 2,W4), W4=mod ((H(1) 2)^3,6)+1；
Symbol f_DNA (X, W) indicates that logarithm X executes W group DNA operation rule, which group operation rule is the value of W indicate using It is then converted, asks 6 mould to add 1 to determine again after seeking 3 powers according to selected objects again, and each group operation rule specifically:
Group number Transformation rule
First group (AT)(TC)(CG)(GA)
Second group (AT)(TG)(GC)(CA)
Third group (AC)(CT)(TG)(GA)
4th group (AC)(CG)(GT)(TA)
5th group (AG)(GT)(TC)(CA)
6th group (AG)(GC)(CT)(TA)
Wherein: A, T, C, G respectively indicate string of binary characters 01,10,00,11；After operation, previous character will in bracket It is transformed to the latter character in bracket.
Two 8 bit C are generated in the following way first with the chaos system constructed in advance1And C2, wherein xN+sp ~xN+5spIndicate the value of chaos system variable x in the case where N+sp~N+5sp corresponds to the number of iterations；yN+sp~yN+5spIt indicates The value of chaos system variable y in the case where N+sp~N+5sp corresponds to the number of iterations；S1And S2Belong to intermediate variable；
S1=xN+sp*xN+2sp*xN+3sp*xN+4sp*xN+5sp；
S2=yN+sp*yN+2sp*yN+3sp*yN+4sp*yN+5sp；
C1=floor (mod (abs (S1*1513),256))；
C2=floor (mod (abs (S2*1711),256))；
Then by two 8 bit C1And C2After the DNA switching box carries out 4 round transformations, two 8 are obtained Binary number C1 *And C2 *；
Finally according to C=XOR (C1 *,C2 *) obtain 8 final bit C.
In the present embodiment, intermediate variable S1And S2It is to be multiplied by the resulting variable of chaos system successive ignition and obtained, has Stronger randomness calculates two 8 bit C1And C2When, two amplification coefficients 1513 and 1711 are introduced, putting here Big coefficient is generally the odd number of 4~5 digits, then does DNA transformation to it again, preferably uses 4 round transformations in this example, take turns number mistake Few, randomness is not strong, and wheel number is excessive, and increases operation time, and when specifically calculating, abs () function representation asks absolute value, mod () function representation modulus, floor () function representation are rounded downwards, and exclusive or is sought in XOR () expression, by caused by the above process 8 bit C, have sufficiently used the performance of chaos system and DNA operator.
S2: constructing one 16 × 16 S box matrix, and each element in matrix is 8 bits, and successively sharp Unduplicated 8 bit filling generated with step S1 and mutual；If encountered when filling the data of generation with it is existing Data duplication, then operating procedure S1 is regenerated.Certainly, present inventive concept can also be applied based on the demand of S box here In the S box building process of other dimension sizes.
S3: carrying out disturbance transformation and DNA operation to S box matrix, obtains final S box output.
In the present embodiment, if the S box matrix before step S3 disturbance is M, then execute according to the following steps:
S31: by matrix M generator matrix M*, first summing to each column in matrix M, ifEnable dj=mod (tj, 16), then jth row in matrix M is placed into the d in M*jRow, if djJth row in matrix M is then placed by row non-empty Mod (t in matrix M*j+ 1,16) row, the behavior until finding a certain sky stop；
S32: by matrix M* generator matrix M**, first to each element m in matrix M*i,j, utilize any one group of DNA operator Evolution processing is carried out to it, if mi,jBy DNA operator operation after numerical value beAnd its odd bits and even bit is enabled to constitute Numerical value be denoted as i respectively*And j*, then by mi,jWithIt exchanges；
S33: using final matrix M** as the S box matrix after disturbance.
The S box that obtained one group of size is 16 × 16 through this embodiment is (data are expressed with 16 systems) as shown in table 1, The S box is tested, the results showed that there are excellent Cryptographic Properties, such as strict avalanche effect, preferable nonlinearity, most Big Difference formula probability is 0.0391, and correlation matrix average value is 0.5051 etc..
By above description it is appreciated that a kind of S box building side based on DNA operator and chaos system provided by the invention Method, the S box built can be efficiently applied in information encryption system, and system has good stochastic behaviour, anti-decoding energy Power is strong, and degree of safety is high.
The S box that the size that 1 algorithm of table generates is 16 × 16
70 C5 7B 35 57 BB FF FD EC 4A DB D7 81 34 14 E3
64 AB 18 F4 4C CE 29 36 3B 43 9F B8 D8 98 C4 25
92 5D 8D 2F 4B AE AD 19 6D DE A7 F1 30 78 11 79
B6 CD 0B AA 0E 40 38 16 A0 DC 63 B7 50 EF 0F 28
93 06 26 F9 9C 42 6B 9B 7C F7 37 A1 49 7A C9 97
3F 9E 5E F2 D9 E1 89 B5 DA EA 4F 33 D4 C8 DF 04
BF 53 CB 17 09 00 E7 1F 5B A2 9A A8 5C 13 61 56
E2 D2 03 E5 55 05 86 3E CA F5 45 44 32 90 94 23
2D 95 EB 6C B1 3A 99 EE 2C 65 CC 7D D6 96 9D 69
8A F3 73 C6 FA D1 2B 76 A6 B0 C3 27 D3 7E 88 15
87 F6 3D 8F 7F 83 3C 85 0D 1C FE 02 58 1A 47 68
D0 BC 1E 07 D5 1B 67 66 62 75 10 E8 FC B3 B4 DD
52 A4 01 39 6A 84 FB 21 2A 80 AF 48 4D 0C 59 1D
08 E0 51 BE 8C 91 E4 0A B9 E6 CF 60 C0 71 6E 22
F8 8B 5F F0 C2 B2 ED 4E 8E 74 E9 46 C1 82 C7 BD
12 A9 6F 31 24 5A A5 A3 54 41 20 77 72 AC BA 2E
Finally it should also be noted that, the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations； Although present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its It is still possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features It is equivalently replaced；And these are modified or replaceed, various embodiments of the present invention skill that it does not separate the essence of the corresponding technical solution The range of art scheme should all cover within the scope of the claims and the description of the invention.

Claims (6)

1. a kind of S box construction method based on DNA operator and chaos system, it is characterised in that the following steps are included:
S1: one chaos system of building and DNA switching box in advance, and 8 bits are generated with it；
S2: constructing one 16 × 16 S box matrix, and each element in matrix is 8 bits, and successively utilizes step Unduplicated 8 bit filling that rapid S1 is generated and mutual；
S3: carrying out disturbance transformation and DNA operation to S box matrix, obtains final S box output.
2. the S box construction method according to claim 1 based on DNA operator and chaos system, it is characterised in that: step S1 The chaos system constructed in advance are as follows:
Wherein: k1、k2、k3For system parameter, x, y, ω, u, υ is the state variable of system, by setting k1、k2、k3Value make The system of obtaining is in chaos state.
3. the S box construction method according to claim 1 or 2 based on DNA operator and chaos system, it is characterised in that:
Two 8 bit C are generated in the following way first with the chaos system constructed in advance1And C2, wherein xN+sp~ xN+5spIndicate the value of chaos system variable x in the case where N+sp~N+5sp corresponds to the number of iterations；yN+sp~yN+5spIndicate institute State the value of chaos system variable y in the case where N+sp~N+5sp corresponds to the number of iterations；S1And S2Belong to intermediate variable；
S1=xN+sp*xN+2sp*xN+3sp*xN+4sp*xN+5sp；
S2=yN+sp*yN+2sp*yN+3sp*yN+4sp*yN+5sp；
C1=floor (mod (abs (S1*1513),256))；
C2=floor (mod (abs (S2*1711),256))；
Then by two 8 bit C1And C2By the DNA switching box carry out 4 round transformations after, obtain two 8 two into Number C processed1 *And C2 *；
Finally according to C=XOR (C1 *,C2 *) obtain 8 final bit C.
4. the S box construction method according to claim 3 based on DNA operator and chaos system, it is characterised in that: described mixed The initial value of ignorant system is x0=1, y0=1.2, ω0=1.2, u0=1.2, υ0=1.2, system parameter k1=1, k2=4, k3= 1.2, spacing parameter sp=5.
5. the S box construction method according to claim 1 based on DNA operator and chaos system, it is characterised in that: step S1 The DNA switching box constructed in advance includes two input data (H(1) 1 L(1) 1)(H(1) 2 L(1) 2) and two output data (H(2) 1 L(2) 1)(H(2) 2 L(2) 2), in which:
H(1) 1Indicate high 4 digit of first input data；
L(1) 1Indicate low 4 digit of first input data；
H(1) 2Indicate high 4 digit of second input data；
L(1) 2Indicate low 4 digit of second input data；
H(2) 1Indicate high 4 digit of first output data；
L(2) 1Indicate low 4 digit of first output data；
H(2) 2Indicate high 4 digit of second output data；
L(2) 2Indicate low 4 digit of second output data；
The transformation relation of above-mentioned data are as follows:
L(2) 1=f_DNA (H(1) 1,W1), W1=mod ((L(1) 1)^3,6)+1；
L(2) 2=f_DNA (L(1) 1,W2), W2=mod ((H(1) 1)^3,6)+1；
H(2) 1=f_DNA (H(1) 2,W3), W3=mod ((L(1) 2)^3,6)+1；
H(2) 2=f_DNA (L(1) 2,W4), W4=mod ((H(1) 2)^3,6)+1；
Symbol f_DNA (X, W) indicates that logarithm X executes W group DNA operation rule, the value of W indicate to organize using which operation rule into Row transformation, asks 6 mould to add 1 to determine again, and each group operation rule again after seeking 3 powers according to selected objects specifically:
Group number Transformation rule First group (AT) (TC) (CG) (GA) Second group (AT) (TG) (GC) (CA) Third group (AC) (CT) (TG) (GA) 4th group (AC) (CG) (GT) (TA) 5th group (AG) (GT) (TC) (CA) 6th group (AG) (GC) (CT) (TA)
Wherein: A, T, C, G respectively indicate string of binary characters 01,10,00,11；After operation, previous character will be converted in bracket For the latter character in bracket.
6. the S box construction method according to claim 5 based on DNA operator and chaos system, it is characterised in that: set step S box matrix before S3 disturbance is M, and the specific steps of step S3 include:
S31: by matrix M generator matrix M*, first summing to each column in matrix M, ifEnable dj=mod (tj, 16), Jth row in matrix M is then placed into the d in M*jRow, if djJth row in matrix M is then placed into matrix M* by row non-empty Mod (tj+ 1,16) row, the behavior until finding a certain sky stop；
S32: by matrix M* generator matrix M**, first to each element m in matrix M*i,j, using any one group of DNA operator to it Evolution processing is carried out, if mi,jBy DNA operator operation after numerical value beAnd the number for enabling its odd bits and even bit constitute Value is denoted as i respectively*And j*, then by mi,jWithIt exchanges；
S33: using final matrix M** as the S box matrix after disturbance.
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Publication number Priority date Publication date Assignee Title
CN107992948A (en) * 2017-10-30 2018-05-04 东北林业大学 Quantum resume image based on chaos system and DNA dynamic codings
AU2018101324A4 (en) * 2018-09-10 2018-10-11 Jiangxi university of finance and economics Study on unequal protection of image data in social media
CN109803063A (en) * 2018-12-20 2019-05-24 福建师范大学福清分校 A kind of image encryption method based on five dimension ultra-chaos systems

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Title
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