CN104935425B - A kind of cryptographic calculations method based on nonlinear theory - Google Patents
A kind of cryptographic calculations method based on nonlinear theory Download PDFInfo
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Abstract
This patent application discloses a kind of cryptographic calculations methods of high safety.Including two chaos systems F1 and F2, the ciphertext of chaos state is obtained by equation (1) in plain text；Equation (2) starts to calculate using the ciphertext that equation (1) obtains as original state；The calculated result of equation (2) again returns in equation (1) and realizes interative computation as original state, unless ciphertext intensity reaches security requirements；Decryption method is the inverse operation of encryption method.A kind of cryptographic system of this programme as high safety provides another beneficial selection for all kinds of users for needing information safety protection.
Description
Technical field
The present invention relates to a kind of cryptographic systems of information security, it is ensured that the safe transmission and preservation of digital signal.
Background technique
Currently, it is based on nonlinear science, wherein the cryptography research for being based particularly on chaos is widely paid close attention to, reason
By from chaos system, in unknown original state or control parameter, the unpredictability of chaotic dynamics behavior has been sent out
The cloth associated cryptographic system of some classics, to the plaintext (plaintext) of input, these systems are generally with being based on look-up table
The chaos iteration number or chaos state value of (look_up table) carry out certain with other values and mix to generate ciphertext
(ciphertext)。
Baptista proposes a kind of cryptographic system Cryptography based on search mechanisms in Physics Letters A
With chaos. and a series of modified versions based on the design later, plaintext unit length is the 0 to 255 of a byte
Integer, output are the integers of a word, are represented on chaotic orbit since a starting chaos state, chaos system continues to change
Generation, until its chaos state drops into number of iterations required for specified region, as a result, ciphertext scale is one times more compared in plain text,
In theory it includes facilitate attack information be just much higher than in plain text,
Pareek proposes a kind of referred to as Cryptography using multiple one-dimensional
The cryptographic system of chaotic maps, within the system, the integer after ciphertext is rounded by plaintext with chaos state are added and obtain, this
Facilitate attacker and isolate quasi- chaotic orbit relevant to chaos system from ciphertext, becomes the key for attacking entire cryptographic system
Spoon.
The encryption of cryptographic system based on chaos is exactly the unpredictability by chaotic orbit, and such Encryption Algorithm is non-
It is often similar to traditional stream cipher, in 4 kinds of attack means (attack with known plaintext, known plain text attack, the selection plaintext of cryptographic system
Attack, chosen ciphertext attacks) in, it generally requires for three kinds of attacks, stream cipher system after resistance using Cipher Feedback, reaches in plain text
Difference, the key stream generated also has different purposes, but well known chaos cipher system this respect has serious shortcoming, causes
Many systems are attacked.As above two chaos cipher system all has this respect.
The dynamic behavior of chaos system on computers Digital Realization when, since the precision that continuous domain turns numeric field is asked
Topic, there is the crash issue of chaotic orbit, this cryptographic system for being also based on chaos needs to ask by what technological means solved
Topic, but this is also that current announced Chaotic Encryption System is easy the problem of ignoring.
Currently known to be, these designs are generally lower than AES the or DES algorithm being commonly used in efficiency, therefore,
The result of design of existed system is drawn, while jumping out the classical thinking in chaos cipher design, is designed safe and efficient non-thread
Property cryptographic system is that one of ordinary skill in the art are dedicated to solving the problems, such as.
Any discussion of the whole instruction to background technique, not representing the background technique must be fields technology people
The prior art that member is known；Not representing in the whole instruction to any discussion of the prior art thinks the prior art one
It surely is widely known or certain common knowledge for constituting this field.
Summary of the invention
The invention is intended to provide a kind of cryptographic calculations method of high safety.
Cryptographic calculations method of one of this programme based on nonlinear theory, including two chaos system F1And F2, they
Form are as follows:
Encryption method the following steps are included:
A) ciphertext of chaos state is obtained by equation (1) in plain text；
B) equation (2) starts to calculate using the ciphertext that equation (1) obtains as original state；
C) calculated result of equation (2) again returns in equation (1) and realizes interative computation as original state, unless ciphertext
Intensity reaches security requirements；
Decryption method is the inverse operation of encryption method.
Chaos system F1And F2Respectively equation (1) and equation (2), the security requirements can refer to that the number of iteration reaches
To a certain amount of.
Cleartext information P is made of the Plaintext block of m-bit a series of, thus has N=2mA different Plaintext block value.
The two chaos systems (i.e. equation) are all piecewise linear maps (i.e. PLCM), this selection is since PLCM has
Than other chaos systems, such as Logistic maps good chaotic dynamics behavior, their difference is the control for having different
Parameter b1And b2, the two parameters are also plus F1Original state x0, i.e. triple (b1,b2,x0) constitute the close of cryptographic system
Key Key, as (b1,b2,x0) three values when belonging to section (0,1), the iteration of equation (1,2) is in Chaotic Dynamic Characteristics.
The preliminary chaos encryption of equation (1) enables another chaos equation after calculating, and is starting shape with current chaos state
State starts iterative process.What it is such as current chaos agenda enabling is equation (1), and equation (1) is out of service when meeting the requirements, equation
(2) using the current chaos state of equation (1) as original state, start iteration.In this way, being entirely used for the chaos rail of enciphering/deciphering
Road by equation (1) and equation (2) chaotic orbit staggered.Even if this alternating isolates attacker entirely for password
Chaotic orbit, the track for therefrom isolating equation (1) or (2) again is also a difficult math question.
A kind of cryptographic system of this programme as high safety provides another for all kinds of users for needing information safety protection
Beneficial selection.
Further, including transmitting terminal ST and receiving end ST, each ST is by 2mA unit composition, corresponding 2mA different plaintext
Value, in transmitting terminal ST, a table unit is made of two components, and component entry is position of the unit in table, and component data gives
The value of unit out；In receiving end ST, a table unit is made of three components, and the first two component is identical as transmitting terminal, third
Component index indicates the position of another unit, and the value of this unit is equal to the position of this unit；
In the input port that transmitting terminal ST, entry are units, input is provided for Plaintext block, data is output port, it gives
The ciphertext of plaintext out；And ciphertext is inputted in receiving terminal ST, the entry as input port, output port index, which is provided, to be corresponded to
The plaintext of ciphertext；
Before enciphering/deciphering plaintext/ciphertext block, since corresponding unit, by exchanging the value of multipair ST unit, two ST are
Dynamic will be synchronized to update.
Transmitting terminal ST and receiving end ST respectively refers to two conversion tables for recording data, build the two of communication channel in respectively
Side.
Be conducive to improve decryption speed in communication both ends this inconsistent structure and working method, it is not required to receiving terminal
It takes time to find the plaintext of ciphertext received again, it is only simply using ciphertext as the entry of ST unit, by that unit
Index component values as in plain text export.In order to enhance the safety of encryption system, the value of two ST each units is not fixed
, and operation change can be updated with the ST dependent on plaintext during entire enciphering/deciphering, for correct enciphering/deciphering, channel
The update of both ends ST must keep synchronous.
The function of look-up table is realized with conversion table, plaintext corresponding with ciphertext directly can be obtained in receiving end in system,
Without the search procedure of look-up table, the efficiency of cryptographic system is improved.
Further, m value is 8.To match existing normatron working method.
Further, it defines noise and determines chaos state the number of iterations with following formula:
For the value of noise dependent in plain text, noise will never leak any useful information about plaintext, act as and add
Close noise.Noise is introduced, the quasi- chaotic orbit for generating chaos system realizes the requirement of Cipher Feedback dependent in plain text, improves
Cryptographic system safety.
Further, during enciphering/deciphering, equation (1,2) shape can be used alternatingly in system according to the result of following equations (9)
At chaotic orbit:
f(xi) > β or nop > 100. (9).
Variable nop saves the chaos system encrypted plaintext block number of parameter current, β be an equation (1) and (2) into
The alternate frequency factor of row, value is smaller, alternately more frequent.
For bright ciphertext than keeping 1:1, ciphertext is the value of conversion table, mathematically, is not present with the chaotic orbit of chaos system
Any correlation, prevent attacker from by observe ciphertext obtain chaos system for encryption chaotic orbit.
This alternating can largely overcome digital chaotic system dynamics to degenerate, with the chaos of previous chaos equation
Original state of the state as the chaos equation that will start is equivalent to the primary disturbance to that will start chaos equation operation, this is
It is the effective effective means for preventing chaos system dynamic behavior from degenerating of generally acknowledged one kind.By disturbance, chaos is overcome
The chaotic orbit crash issue that system is generated in the Digital Realization of computer.
Further, noise is first defined0=0, ST conversion table communicate both ends and use equation (1) iteration multiple, make ST each unit
Value be in random initial distribution.
Enciphering/deciphering plain/cipher text is wanted, the value of ST each unit there should be a random initial distribution, and they are leading to
News channel both ends will agree, and be first piece of plaintext of enciphering/deciphering, first define noise0=0, communication both ends use equation (1)
Iteration 100 times, to prevent the conjecture to control parameter b, and obtain the chaos state x of first Plaintext block of encryption1。
Detailed description of the invention
Fig. 1 be the embodiment of the present invention in as m=8 in the dissymmetrical structure schematic diagram of communication channel both ends conversion table ST.
Fig. 2 is encrypting plaintext unit p in the embodiment of the present inventioniThe more new technological process and encrypting plaintext unit p of preceding transmitting terminal STi
The update flow diagram of preceding receiving end ST.
Fig. 3 is in the embodiment of the present invention with Z1=253and Z2The n collected after=41 encryption 265KB filesiWith viDistribution
Schematic diagram.
Fig. 4 is in the embodiment of the present invention with Z1=253, Z2=41, Z3Bright, ciphertext point after=80. encryption 265KB files
Cloth schematic diagram.
Fig. 5 is in the embodiment of the present invention with Z1=253, Z2=41, Z3The ciphertext being collected into after=73 encryption 265KB files
First-order difference distribution schematic diagram.
Specific embodiment
Below by specific embodiment, the present invention is described in further detail:
2.2 main technical schemes
In our invention design, there are two chaos systems, their forms are as follows:
The two chaos systems are all piecewise linear maps (PLCM), this selection is that have due to PLCM than other chaos
System such as Logistic maps good chaotic dynamics behavior, their difference is the control parameter b for having different1And b2,
The two parameters are also plus F1Original state x0, i.e. triple (b1,b2,x0) constitute cryptographic system key Key, as (b1,
b2,x0) three values when belonging to section (0,1), the iteration of equation (1,2) is in Chaotic Dynamic Characteristics.
Cleartext information P is made of the Plaintext block of m-bit a series of, thus has N=2mA different Plaintext block value.
2.2.1 the structure and function of conversion table
As shown in Figure 1, as m=8 in the dissymmetrical structure of communication channel both ends conversion table ST, conversion table has than searching
The higher performance of table, the both ends communicated are known as transmitting terminal and receiving end.
Two conversion tables (to simplify description, it is referred to as ST later for we) build the both sides of communication channel in respectively, and structure is such as
Fig. 1: each ST is by 2mA unit composition, corresponding 2mThe ST structure of a different plaintext value, both ends is not identical: in transmitting terminal, one
Table unit is made of two components, and component entry is position of the unit in table, and component data provides the value of unit；It is receiving
End, a table unit are made of three components, and the first two component is identical as transmitting terminal, and third component index indicates another list
The position of member, the value of this unit are equal to the position of this unit.To simplify description, u is usedt、urRespectively indicate transmitting terminal and receiving terminal
Table unit, but when discuss transmitting terminal and receiving terminal are all suitable for when, indicated with u, further, u (i) .data refers to i-th of unit
Value, u (i) .index refers to the index value of i-th of unit, u (i) .entry=i.The value of three components belongs to identical integer
Domain φ, for m-bit Plaintext block, φ={ 0,1 ..., 2m- 1 }, exist correspondingly, on same domain φ between three components
Strong nonlinearity relationship, to m=8, φ={ 0,1 ..., 255 }, if Fig. 1 is later unless otherwise noted discussed with m=8
Problem.
In transmitting terminal, ut(i) .entry is the input port of unit, provides input, u for Plaintext blockt(i) .data is output
Port, the ciphertext that it provides plaintext i is ut(i).data；And the u in receiving terminal, as input portr(i) .entry input is close
Literary i, output port ur(i) .index provides the plaintext corresponding to ciphertext i.In communication both ends this inconsistent structure and work
Mode is conducive to improve decryption speed, it makes receiving terminal be not required to the plaintext for taking time to find the ciphertext received again, its only letter
Single ground is exported using ciphertext as the entry of ST unit using the index component values of that unit as plaintext.Such as: in Fig. 1,
Transmitting terminal receives in plain text " 253 ", and the 253rd unit of transmitting terminal ST will provide corresponding i.e. u in plain textt(253)=" 3 ", when
Ciphertext " 3 " is transferred to receiving end, so that it may directly obtain from the index component of the 3rd unit of receiving end ST corresponding bright
Literary ur(3) " 253 " .=.In order to enhance the safety of encryption system, the value of two ST each units is not fixed, and can be
Operation change is updated with the ST dependent on plaintext during entire enciphering/deciphering.
In i-th of plaintext/ciphertext block p of enciphering/decipheringi/ciBefore, from pthi-1A unit starts, by exchanging multipair ST unit
Value, two ST will be synchronized dynamic and update, this means that after a Plaintext block is encrypted, in and then it next
Before a Plaintext block is encrypted, corresponding to its ciphertext originally will be changed.With siThe position for indicating starting table unit, from this
Unit starts, and the value of multipair unit will be exchanged；viExpression will execute the interval of two units of exchange；niIndicate current whole
A exchange process unit logarithm to be swapped,
If xiIt is current chaos state, 0.a1a2…aj... it is its binary representation, equation (3) provides ai,
And
Three are defined by interception xiObtained by its binary representation be respectively as follows: xl=a1…a15, xm=a16…a30,xh=
b31…a45Variable, obtain two kernel kernal mappings such as:
In this way, viAnd niValue just determined by following two formula:
vi=g (xi)modZ1 Z1∈{0,1,2,3……255} (6)
ni=g (xi)modZ2 Z2∈{0,1,2,3……,255} (7)
It is as follows that this entire exchange process is described in detail in we:
Firstly, allowing si=pi-1, start unit positional value is obtained, is executedWith by siUnit with
Si+viThe value of unit is exchanged；Then, from si+viUnit+1 starts to continue to exchange ni-1To table unit, it is,
……
Wherein N=2m, finally, initial pthi-1Value u in unitt(pi-1) .data, that is, correspond to plaintext pi-1Ciphertext,
It is switched to (s+n againi×vi+ni- 1) in mod N unit, this step is the final step in corresponding diagram 2 (a), as a result,
With regard to pthi-1For table unit, its actual exchange is spaced vi' provided by equation (8):
v'i=nivi+ni-1mod N. (8)
The final step of this process can increase calculating exchange interval viDifficulty, otherwise, viIt is possible that being v in secret valuei+
pi-1Plaintext when be compromised；After this ST update, plaintext vi+pi-1Before processed, vi+pi-1Unit ut(vi+pi-1) do not have
There is the probability Γ=(1-2n being comprised in any renewal processi/N)τ(the updated number of passes that τ was executed during representing)
Be it is existing, if niMathematic expectaion be equal to 41/2, ST include 256 units, this possibility calculate are as follows:
From calculating above as can be seen that when the renewal process of period is less than 13 times, table unit ut(vi+pi-1) have 10%
Possibility be not exchanged, only when number is greater than 32 times, not exchanged probability, also could v just less than 1/256i
Ensure not to be hypothesized.
The process (a) of left is the more new technological process of transmitting terminal ST before encrypting plaintext unit pi in Fig. 2；Process (b) is encryption
The more new technological process of the preceding receiving end ST of plaintext unit pi；
The ST renewal process of receiving end is similar to transmitting terminal, and the difference of the two is that the former is more and takes some steps
Index component is handled, to guarantee to be decrypted correctly after updating every time, detailed update step provides by Fig. 2 (b).
For correct enciphering/deciphering, the update of channel both ends ST must keep synchronous, i.e., before the i-th block message of enciphering/deciphering
Afterwards, ut(j) .data=ur(j) .data (j={ 0,1 ... 255 }) must be satisfied.The more new capital the ST on both sides and variable
noiseiIt is closely related:
noisei=ut(pi-1+ni/2×vi+ni/2-1).data. (4)
In this way, noiseiValue depend on plaintext pi-1, then, pi-1Only determine noiseiThe position of taken table unit value,
noiseiAny useful information about plaintext will never be leaked, secret noise is acted as.
Equation (5) diffusion is good, it makes to encrypt piViAnd niIt is related to noise all before, thus and piIt
Preceding entire Plaintext block sequence is related, it is, entire ciphering process is closely related with plaintext, as long as two plaintexts are intermediate one
A block is different, then the later two encryption of plaintext processes of this block will be entirely different, this is exactly wanting substantially for stream cipher design
It asks.
Z should be given1Biggish value is selected, Z is given2Smaller value；Z1The larger list that can guarantee renewal process and make each position
The chance that member is selected to tends to be equal, even if niIt is smaller；Z2The upper limit of decision table elements exchange logarithm, in order to improve system effectiveness,
It should be as small as possible on the basis of guaranteeing safety.And the two should be prime number.
In the present invention, it is proposed that Z1=253, Z2=41.
2.2.2 encrypting and decrypting designs
During enciphering/deciphering, equation (1,2) can be used alternatingly according to the result of equation (9) and form chaotic orbit for system.
f(xi) > β or nop > 100. (9)
Or refers to logic or operation, and when equation (9) value is true (true), encryption system stops the iteration of current chaos equation,
Another chaos equation is enabled, and starts iterative process using current chaos state as initial state.Such as, current chaos agenda enables
Be equation (1), when equation (9) very, equation (1) is out of service, equation (2) using the current chaos state of equation (1) as
Original state starts iteration.In this way, entirely for the chaotic orbit of enciphering/deciphering by the chaotic orbit of equation (1) and equation (2)
Staggered.Even if this alternating makes attacker isolate the entire chaotic orbit for being used for cryptography, equation is therefrom isolated again
(1) or the track of (2) is also a difficult math question.
Variable nop saves the chaos system encrypted plaintext block number of parameter current, β ∈ [0,2m-1] it is an equation
(1) and (2) carry out alternate frequency factor, and value is smaller, alternately more frequent.
This alternating can largely overcome digital chaotic system dynamics to degenerate, with the chaos of previous chaos equation
Original state of the state as the chaos equation that will start is equivalent to the primary disturbance to that will start chaos equation operation, this is
It is the effective effective means for preventing chaos system dynamic behavior from degenerating of generally acknowledged one kind.
Enciphering/deciphering plain/cipher text is wanted, the value of ST each unit there should be a random initial distribution, and they are leading to
News channel both ends will agree, and be first piece of plaintext of enciphering/deciphering, first define noise0=0, communication both ends use equation (1)
Iteration 100 times, to prevent the conjecture to control parameter b, and obtain the chaos state x of first Plaintext block of encryption1。
It a, is i-th piece of plaintext p of encryptioni, following operation sequentially executed:
N is calculated according to equation (4)-(7)iAnd viIf s=pi-1(if i=1, if s=0)
ST is updated according to process shown in Fig. 2 (a), and calculates noisei。
Directly from ut(pi) .data taking-up piCiphertext ci。
Do following preparation for next piece of plaintext of encryption: accounting equation (9) is to judge whether to replace currently used chaos
Equation, if result be it is true, replacement is set up, if it is vacation, be changed without chaos agenda, no matter equation (9) result why, all to work as
Preceding chaos state xiStart iterative chaotic system kiIt is secondary, obtain encrypting plaintext pi+1Chaos state xi+1, wherein kiBy following equation
(10) it provides:
From Fig. 3,With the distribution balanced in domain, in this way, the mathematic expectaion of k is 43/2, paper
“Selection of chaotic states in cryptosystem based on chaos with differential
Analysis " (EI:20124515635632) passes through theory analysis and it is demonstrated experimentally that the chaos system that piecewise linear maps are formed
Need the distribution per at least 10 obtained chaos states of iteration that there is good differential characteristic, therefore, in the present invention, selection
The mathematic expectaion of k is 43/2.
It b, is i-th piece of ciphertext c of decryptioni, following operation sequentially executed:
N is calculated according to equation (4)-(7)iAnd viIf s=pi-1(if i=1, if s=0)
Receiving end ST is updated according to process shown in Fig. 2 (b), and calculates noisei。
Directly from ur(ci) .index taking-up ciPlaintext pi。
Do following preparation for next piece of ciphertext of decryption: accounting equation (9) is to judge whether to replace currently used chaos side
Journey, if result be it is true, replacement is set up, if it is vacation, be changed without chaos agenda, no matter equation (9) result why, all with current
Chaos state xiStart iterative chaotic system kiIt is secondary, obtain decryption ciphertext ci+1Chaos state xi+1。
2.4 implementing
To implement cryptographic system of the present invention, each parameter is as follows in first definition scheme:
One, m=8, Z1=253, Z2=41.
Two, key triple (b1,b2,x0)=(0.333,0.777,0.111111111111)
This algorithm is realized on III 866M Hz PC, 196MB memory of old machine Pentium, VC6.0,
In order to assess performance of the invention, and compared with Baptista type algorithm makees one, a series of experiments result is listed in
In table 1；Baptista (1) in table 1 represents Baptista Prototype Algorithm, and Baptista (2) is that K.W.Wong is proposed
Close plaintext is than the smallest algorithm in Baptista type modification algorithm.Four files are taken up an official post from internet in the mind to be carried.
The performance that 1 three kinds of chaos encryption algorithms of table encrypt four files compares
Cell upstream format: encryption times (sec)/decryption time (sec)
Cell downstream format；Ciphertext size
From above-mentioned table 1 as it can be seen that the present invention is than other two kinds of classical system much more efficients.
Equation (4,5) comes balanced distribution, such as Fig. 3 with continuous exclusive or, and which show with Z1=253and Z2=41 encryption
The ni and vi collected after 265KB file is distributed, as long as related data is not enough, analyst can not find ginseng from its result
With the useful information of each variable of operation, in the present invention, xl、xm、xh、noisei-1Except occurring one in the equation (4) secondly, its phase
Closing information cannot be again from piIt is obtained in the ciphering process of later Plaintext block, and presses the property of chaos, the phase between chaotic signal
Guan Du ensure that x with the increase exponential damping of number of iterations for the Average Iteration number of encrypting plaintext block in the present inventioni+1Substantially
It is upper not include xiInformation, therefore, continuous exclusive or improves the safety of system.
This balanced distribution of Fig. 3 can resist attack based on probability, and this be distributed also makes the distribution of ciphertext have same one
The distribution of cause, such as Fig. 4, which show with Z1=253, Z2=41, Z3Bright, ciphertext distribution after=80. encryption 265KB files, it is bright
Although the promulgation of text is extremely uneven, ciphertext equally insusceptibly has consistent distribution.
Fig. 5 gives with Z1=253, Z2=41, Z3The first-order difference for the ciphertext being collected into after=73 encryption 265KB files
Distribution, this linear decrease illustrate that there is no correlations between ciphertext, can greatly resist Inference Attack, this illustrates in equation (10)
Setting is appropriate for modular arithmetic with 43.
What has been described above is only an embodiment of the present invention, and the common sense such as well known specific structure and characteristic are not made herein in scheme
Excessive description, technical field that the present invention belongs to is all before one skilled in the art know the applying date or priority date
Ordinary technical knowledge can know the prior art all in the field, and have using routine experiment hand before the date
The ability of section, one skilled in the art can improve and be implemented in conjunction with self-ability under the enlightenment that the application provides
This programme, some typical known features or known method should not become one skilled in the art and implement the application
Obstacle.It should be pointed out that for those skilled in the art, without departing from the structure of the invention, can also make
Several modifications and improvements out, these also should be considered as protection scope of the present invention, these all will not influence the effect that the present invention is implemented
Fruit and patent practicability.The scope of protection required by this application should be based on the content of the claims, the tool in specification
The records such as body embodiment can be used for explaining the content of claim.
Claims (2)
1. a kind of cryptographic calculations method based on nonlinear theory, it is characterised in that:
The method includes encryption methods and decryption method；
Encryption method the following steps are included:
A) ciphertext of chaos state is obtained by equation (1) in plain text；
B) equation (2) starts to calculate using the ciphertext that equation (1) obtains as original state；
C) calculated result of equation (2) again returns in equation (1) and realizes interative computation as original state, unless ciphertext intensity
Reach security requirements；
Decryption method is the inverse operation of encryption method；
Wherein the expression formula of equation (1) and equation (2) is as follows:
In formula:
b1And b2For control parameter；Different control parameter b1And b2, original state x of the two parameters plus equation (1)0, three
Tuple (b1,b2,x0) key Key is constituted, as (b1,b2,x0) three values when belonging to section (0,1), the iteration of equation (1,2)
In Chaotic Dynamic Characteristics；
In encryption, chaos state xiChaos state x is obtained after encryptioni+1；In decryption, chaos state xiChaos is obtained after decryption
State xi+1；
The method uses asymmetric conversion table in transmitting terminal and receiving end；
Each transmitting terminal conversion table or receiving end conversion table are by 2mA unit composition, corresponding 2mA different plaintext value, wherein m table
The digit of text is shown, m value is 8；In the conversion table of transmitting terminal, a table unit is made of two components, the transmitting terminal first component
Entry is position of the unit in table, and transmitting terminal second component data provides the value of unit；Conversion table in receiving end, one
Table unit is made of three components, and the first two component is identical as transmitting terminal, and third member index indicates the position of another unit,
The value of this unit is equal to the position of this unit；
In the conversion table of transmitting terminal, transmitting terminal first component entry is the input port of unit, provides input for Plaintext block, hair
Sending end second component data is output port, it provides the ciphertext of plaintext；
In the conversion table of receiving terminal, the receiving terminal first component entry as input port inputs ciphertext, output port receiving terminal
Third member index provides the plaintext corresponding to ciphertext；
Before enciphering/deciphering plaintext/ciphertext block, since corresponding unit, by exchanging the value of multipair conversion table cell, two conversions
Table synchronizes dynamic during entire enciphering/deciphering and updates；
Use ut、urThe table unit of transmitting terminal and receiving terminal is respectively indicated, but when discussion is all suitable for transmitting terminal and receiving terminal, uses u
It indicates, further, u (i) .data refers to the value of i-th of unit, and u (i) .index refers to the index value of i-th of unit, u (i)
.entry=i, the value of three components belongs to identical integer field Ф, for m Plaintext blocks, Ф={ 0,1 ..., 2m- 1 }, three
There is one-to-one, the strong nonlinearity relationship on same domain Ф between component, to m=8, Ф={ 0,1 ..., 255 }；
In transmitting terminal, ut(i) .entry is the input port of unit, provides input, u for Plaintext blockt(i) .data is output end
Mouthful, the ciphertext that it provides plaintext i is ut(i).data；And the u in receiving terminal, as input portr(i) .entry inputs ciphertext
I, output port ur(i) .index provides the plaintext corresponding to ciphertext i；
In i-th of plaintext/ciphertext block p of enciphering/decipheringi/ciBefore, from pthi-1A unit starts, by exchanging multipair conversion table cell
Value, two conversion tables will all be synchronized dynamic update, it means that once a Plaintext block be encrypted after, and then it
Before next Plaintext block is encrypted, corresponding to its ciphertext originally will be changed, with siThe position for indicating starting table unit, from
This unit starts, and the value of multipair unit will be exchanged；viExpression will execute the interval of two units of exchange；niExpression is worked as
The preceding entire exchange process unit logarithm to be swapped,
Wherein, it is iterating through following formula described in the step (c) and determines current chaos state xiThe number of iterations:
If xiIt is current chaos state, 0.a1a2…aj... it is its binary representation, equation (3) provides ai,
And
Three are defined by interception xiObtained by its binary representation be respectively as follows: xl=a1…a15, xm=a16…a30,xh=a31…
a45Variable, obtain two kernel kernal mappings:
viAnd niValue just determined by following two formula:
vi=g (xi)modZ1Z1∈{0,1,2,3……255} (6)
ni=g (xi)modZ2Z2∈{0,1,2,3……,255} (7)
Wherein:
First define noise0=0, conversion table communicates both ends and uses equation (1) iteration multiple, makes the value of conversion table each unit in random
Initial distribution；
For correct enciphering/deciphering, the update of channel both ends conversion table must keep synchronous, i.e., before the i-th block message of enciphering/deciphering
Afterwards, ut(j) .data=ur(j) .data (j={ 0,1 ... ... 255 }) must be satisfied, the conversion table on both sides more new capital and variable
noiseiIt is closely related:
noisei=ut(pi-1+ni/2×vi+ni/2-1).data
In this way, noiseiValue depend on plaintext pi-1, then, pi-1Only determine noiseiThe position of taken table unit value.
2. a kind of cryptographic calculations method based on nonlinear theory according to claim 1, it is characterised in that: adding/solving
During close, equation (1,2) can be used alternatingly according to the result of following equations (9) and form chaotic orbit for system:
f(xi) > β or nop > 100 (9)；
In formula:
Variable nop saves the chaos system encrypted plaintext block number of parameter current, β ∈ [0,2m-1] be an equation (1) and
(2) alternate frequency factor is carried out.
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| EP1326363A1 (en) * | 2001-12-27 | 2003-07-09 | STMicroelectronics S.r.l. | Chaos-based block encryption |
| CN101222318A (en) * | 2008-01-23 | 2008-07-16 | 黑龙江大学 | Chaotic sequence generation method and sequence generator of high speed high-precision chaotic function |
| CN101527823A (en) * | 2009-04-10 | 2009-09-09 | 南京大学 | Network video monitoring system based on FPGA chaotic encryption |
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