CN100459487C - Chaotic cipher production method under limited precision - Google Patents
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Abstract
The invention discloses a generating method for chaotic cipher in limited precise. The steps are: (1) initialization: generates in random or sets the initial value x1[i] (i=0; l=1, 2... n,) of the chaotic system, and sets with K kinds of variable carrying rules, k is equal or less than n; (2) the chaotic system output x j[i] (j=1, 2... n) correspondent to the carrying rule can be acquired with the K kinds of variable carrying rules according to the input xl [i]; (3) the outputs of different carrying rule x j [i] are converted into value with the same carrying rule x' j [i]; (4) the x' j[i] is coded according to the set coding rule and acquires x'' j[i]; (5) the n chaotic coding series x'' j [i] are arranged into M xi= M xi (I, j)=x'' j[i], xi=1, 2, ...; (6) xl [i+1]=x j[i] according to the set rule; (7) I=i+1, returns to the step (2), till the task is completed. The invention can reduce the correlation of series, increases the linear complexity, thus the chaotic series may has excellent performance.
Description
Technical field
The invention belongs to the password generating technique in the information security, particularly be the chaos cipher production method under a kind of limited precision, it utilizes electronic computer technology, information coding technique and chaos system to adopt the computing technique of multiple system to produce the chaotic encipher series with advantageous property under the condition of limited precision.
Background technology
Along with improving constantly of COMPUTER CALCULATION speed, and distributed treatment technology is growing, and more original cryptographic algorithm are cracked.At present, the domestic cryptographic algorithm that adopts mostly is the low-intensity cryptographic algorithm that abroad will eliminate.The unsafe factor that is brought has become a major issue of current obstruction economic development and threat national security thus.
Recent years, chaos begins to be applied to the coded communication field, and chaos is the external complicated performance that produces owing to intrinsic stochasticity in the deterministic system, is a kind of nonrandom motion that seems to be at random.Because chaotic signal has ergodic, broadband property, noise like, the sensitiveness to initial condition, the auto-correlation of decay fast and faint characteristics such as cross correlation, thereby for realizing that secure communication provides abundant mechanism and method.
But the generation of digital chaotic sequence all is to realize on the device of computer or other limited precision.Therefore, any chaos sequence maker all can be summed up as finite automata to be described, the digital chaotic sequence that is generated under this condition will certainly show performance degradation problems such as short period, strong correlation and little linear complexity, is difficult to design the digital chaotic sequence that satisfies the cryptography requirement.
People such as Li-Hui Zhou propose to adopt raising input resolution that its dual resolution design method far above output resolution ratio is solved in discrete chaotic system because the problems referred to above that the finiteness of precision is brought in document " A New Idea of Using One-Dimensional PWLMap in Digital Secure Communications-Dual-Resolution Approach ".Obviously this method cost is very large.
Summary of the invention
The objective of the invention is to overcome above-mentioned weak point, a kind of digital chaos cryptographic system is provided, this system has solved above-mentioned performance degradation problem effectively under the prerequisite that does not increase computational accuracy.
Chaos cipher production method under a kind of limited precision provided by the invention the steps include:
(1) initialization: produce or set chaos system initial value x at random
l[i], i=0; L=1,2 ..., n, n are the number of chaos system, and set the different system of k kind, and k≤n;
(2) according to the x that imports
l[i], a kind of in the different systems of the k kind of adopt setting respectively obtains the chaos system output x of a corresponding system
l' [i];
(3) with the output x of different systems
l' [i] converts the same system numerical value x of setting uniformly to
l" [i];
(4) to x
l" [i] encodes and obtains x
l" ' [i];
(5) with n chaotically coding sequence x
l" ' [i] carry out exporting as password behind the scramble;
(6) judge whether the password number that is produced reaches required number,, finish if reach; Otherwise, determine x according to the ordering rule of setting
l[i+1]=x
l' [i] makes i=i+1, jumps back to step (2).
The present invention utilizes the low-dimensional chaos dynamical system of different systems to carry out iterative computation, under the situation that does not increase precision, increase the cycle of digital chaotic sequence, reduce the correlation of digital chaotic sequence, increase the linear complexity of digital chaotic sequence, thereby make chaos sequence have good properties.Owing to adopt different systems, also different to the carry rules in the same chaotic maps process, and it is also different to cause doing the value of rounding off that rounds off when handling, the difference of bringing thus makes the chaotic orbit of same chaotic maps under different systems also inequality, so just can increase the cycle of digital chaotic sequence; Owing to, increased linear complexity exporting behind k the chaos sequence value scramble; Adopt k different system, its carry rules and the big or small degree that rounds off are all inequality, thereby have reduced the cross-correlation degree of chaos sequence.
Description of drawings
Fig. 1 is a flow chart of the present invention.
Embodiment
In the technical solution used in the present invention, no matter be step (2) chaos system, or step (3) in the same system set, and the coding rule of setting in the step (4), all only need add, decipher both sides and arrange in advance, adopt in a like fashion to handle and get final product, be not limited to a kind of specific mode.The given implementation method of step (5) has two kinds of connotations in fact: both can be to n the chaotically coding sequence rank rear x that sorts
j" [i] exports after resequencing; Can directly export by former sequence again.Similarly, the given implementation method of step (6) in fact also has two kinds of connotations: both can be to the output x of n chaos system
jCorresponding its next input x of conduct of difference after [i] sequence is resequenced
l[i+1], this moment, l not necessarily equated with j; Again can be by former output x
j[i] sequence directly feeds back to chaos system as its Next input x
l[i+1], this moment, l equated with j.
The present invention is further detailed explanation in the mode enumerated below.
Example one
Chaotic maps in this method is to use simple one dimension logistic iteration
Calculating
The time, because the input value of next iteration remains 64, but x
i 2It is 128, so must be with x
i 2The method that truncates is adopted in the processing of rounding off in this method.(to the explanation of rounding method).
But, in order to improve Cipher Strength and iteration cycle, the present invention uses " shuffling algorithm " that the output valve of 8 chaotic maps is carried out scramble behind the decimal number that calculates 8 different system correspondences, from but the value of 8 chaos sequences according to a revocable order output.
At this, introduce shuffling algorithm earlier:
Standard playing card has experienced the differentiation and the development in century more than one since 1872 originate from the U.S., obtain in the world already popularizing very widely.It not only is popular in the various folk entertainment activities (comprise gambling and divine), and has appeared at global formal athletic competition project---among the bridge.For the justice that guarantees these recreations and match and credible, just must make through the putting in order of every playing cards after shuffling to have good " randomness ".Inspired by this, the present invention proposes " shuffling " algorithm that above-mentioned code book is on-the-fly modified.
1. D during the top board is inserted
Cb(q)
With q is parameter, when p 〉=0, and with sequence 0,1 ... the 1st and q code word exchange in 7.Finish algorithm D
Cb(p.q) sequence as a result after is:
q，…，q-1，0，q+1，，…，7
2. cut board algorithm T
Cb(q)
With q be the border with sequence 0,1 ..., q-1, q, q+1 ..., 7 front and back intersect.Finish algorithm T
Cb(p) sequence as a result after is:
q+1，…，7，0，1，…，q-1，q
The rule that pseudorandom number generator adopts also is an one dimension logistic iteration:
Binary system is adopted in calculating in the iterative process.
In this algorithm according to pseudorandom m
iDetermine the shuffling algorithm that this code book conversion is adopted.Work as m
iUse the top board to insert middle algorithm (q=[8*m in the time of≤0
i] ,-1＜m
i＜1), otherwise use that q=1's cut the board algorithm.
Must be pointed out: in order to narrate conveniently, initiation sequence is set at the sequence of arranging by natural order at this with being without loss of generality, promptly 0,1 ..., 7.Obviously, all can do same processing to different initiation sequences.
Its algorithmic procedure is as follows:
(1) produces the initial value m that exports control law at random
0With chaos system initial value x
l[0], (l=1,2 ... 8), selected 8 systems 6,7,9,11,12,13,14 and 15;
(2)x
j[i]＝x
l[i]，(j＝1，2，…8)；
(3) by x
j[i] is according to chaotic maps
Adopt different systems to calculate respectively and produce chaotic maps output x
j[i+1] (j=1,2 ... 8);
(4) with the x of different systems
j[i+1] converts decimal system x ' to
j[i+1] (j=1,2 ... 8);
(5) with x '
j[i+1] is according to [256*acos (x
j' [i+1])] ([] expression rounds downwards) coding obtains x
j" [i+1];
(6) by m[i] according to chaotic maps
Adopt binary computations to produce chaotic maps output m[i+1 respectively], and according to m[i+1] the corresponding shuffling algorithm of positive and negative selection with x
j" [i+1] upsets order back output M
ξ≡ M
ξ(i, j)=x
j" [i+1] (j=1,2 ..., n; ξ=1,2 ...);
(7) make x
l[i+1]=x
j[i+1], l=j, (l, j=1,2 ... 8), i=i+1 jumps back to step (2), up to task termination;
Adopting the digital chaotic sequence Cycle Length of binary computations is 29,685,894.The cycle of other systems sees the following form:
| The system number | Cycle Length | The system number | Cycle Length |
| 6 systems | 92,219,771 | 12 systems | 161,223,070 |
| 7 systems | 89,744,731 | 13 systems | 71,878,812 |
| 9 systems | 24,744,402 | 14 systems | 284,595,078 |
| 11 systems | 23,354,844 | 15 systems | 544,406,163 |
From top data as can be seen: calculate if only carry out chaotic maps based on the binary system computer or the fpga chip, its cycle is except bigger than novenary and 11 systems, much smaller than the cycle of other systems.
Adopt 8 chaotic maps in this method, all adopt binary computations if these 8 chaotic maps and pseudo random number produce, the cycle of the digital chaotic sequence of so final output is: 29685894 and Ta[i] least common multiple of (code book transformation period).And adopt cycle of digital chaotic sequence of the final output of this method to be: 29685894,92219771,89744731,24744402,23354844,161223070,71878812,284595078,544406163 and Ta[i] least common multiple, this is an astronomical figure, is far longer than the cycle of only adopting binary method.
Example two
Can also adopt the cycle and linear complexity that increase digital chaotic sequence in the following method: the method for employing cyclic shift exchanges the iterative value of different systems, and then carries out iterative computation.Its arthmetic statement is as follows:
(1) produces the initial value m that exports control law at random
0With chaos system initial value x
l[0], (l=1,2 ... 8), selected 8 systems 12,13,14,15,28,29,30 and 31;
(2) x
j[i]=x
l[i], j=l+1, (l=1,2 ... 7), when l=8, j=1;
(3) by x
j[i] is according to chaotic maps
Adopt different systems to calculate respectively and produce chaotic maps output x
j[i+1] (j=1,2 ... 8);
(4) with the x of different systems
j[i+1] converts decimal system x ' to
j[i+1] (j=1,2 ... 8);
(5) with x '
j[i+1] is according to [256*acos (x
j' [i+1])] ([] expression rounds downwards) coding obtains x
j" [i+1];
(6) pseudorandom number generator is according to m[i] and the piecewise linearity chaotic maps:
Produce m[i+1], and according to m[i+1] the corresponding shuffling algorithm of positive and negative selection with x
j" [i+1] upsets order back output M
ξ≡ M
ξ(i, j)=x
j" [i+1] (j=1,2 ..., n; ξ=1,2 ...);
(7) make x
l[i+1]=x
j[i+1], l=j, (l, j=1,2 ... 8), i=i+1 jumps back to step (2), up to task termination;
Explanation to (2) step: the iteration output valve at the i moment 8 systems is respectively x
1[i], x
2[i] ... x
8[i], in the i+1 moment in the example one, 8 different systems are respectively in i+1 chaos iteration input value constantly: x
1[i], x
2[i] ... x
8[i], i.e. x
j[i+1]=x
j[i] (j=1,2 ... 8), in the i+1 moment in example two, the input value of the chaos iteration of 8 different systems no longer is: x
i[1], x
i[2] ... x
iBut x [8],
j[i+1]=x
l[i], j=(l+1) mod 8+1, (j, l=1,2 ... 8).Wherein cyclic shift is a kind of method wherein, can also adopt other exchanged form.
Example three
Because existing microprocessor and hardware arithmetic unit all are based on binary computations, so realize must adopting the FPGA technology to realize the arithmetical operation of M system in the mapping of M system digital chaos in example one, wherein the design of multiplier needs a large amount of hardware resources.And existing based on binary hardware multiplier, quite ripe on method for designing, on algorithm, quite optimize.If can combine based on binary hardware multiplier and the computing of M system, so just can when reducing design difficulty, reduce hardware resource with existing.
So can calculate chaotic maps employing binary computations, the x as a result that will obtain then
K+1Be converted to the M system and count x '
K+1, and then the M system counted x '
K+1Be converted to binary system x "
K+1
Because the carry rules of N system is different with binary system, the precision that rounds off that causes rounding off when handling also is different with binary system, thus under the prerequisite of limited precision x '
K+1≠ x "
K+1, and x
K+1-x "
K+1Be a kind of random perturbation as can be seen.This improvement has increased the cycle of sequence equally under the situation that does not improve digitlization chaotic maps numerical precision.Export successively behind last 8 chaos iteration value scrambles that will produce again, can increase the correlation of the linear complexity and the reduction chaos sequence of chaos sequence.
Its arthmetic statement is as follows:
(1) produces the initial value m that exports control law at random
0With chaos system initial value x
l[0], (l=1,2 ... 8), selected 8 systems 60,61,62,63,124,125,126 and 127;
(2)x
j[i]＝x
l[i]，(j＝1，2，…8)；
(3) by x
j[i] is according to the piecewise linearity chaotic maps:
Adopt binary computations to produce chaotic maps output x
j[i+1] (j=1,2 ... 8), again with x
j[i+1] is converted to corresponding system x respectively
j K[j][i+1], (j=1,2 ... 8), k[1], k[2] ... k[8] be followed successively by 8 selected in the step (1) systems, again with x
j K[j][i+1] is converted to corresponding x respectively
j[i+1];
(4) with the x of different systems
j[i+1] converts decimal system x ' to
j[i+1] (j=1,2 ... 8);
(5) with x '
j[i+1] is according to [256*acos (x
j' [i+1])] ([] expression rounds downwards) coding obtains x
j" [i+1];
(6) pseudorandom number generator is according to m[i] and
And according to m[i+1] the corresponding shuffling algorithm of positive and negative selection " [i+1] upsets order back output M with xj
ξ≡ M
ξ(i, j)=x
j" [i+1] (j=1,2 ..., n; ξ=1,2 ...);
(7) make x
l[i+1]=x
j[i+1], l=j, (l, j=1,2 ... 8), i=i+1 jumps back to step (2), up to task termination;
Need further specify following 2 points:
(1) in the process of the specific implementation of this method, selects chaotic maps for use
With the piecewise linearity chaotic maps, also can use said method to other chaotic maps.
(2) all adopted 8 concrete systems in each specific implementation in the method, in fact can adopt for arbitrary carry system.But for the chaos iteration formula, the chaos character of some system is degenerated to some extent, so these systems are not adopted in suggestion.
Example four
Can also adopt the cycle and linear complexity that increase digital chaotic sequence in the following method: the method that employing is shuffled exchanges the iterative value of different systems, and then carries out iterative computation, and its arthmetic statement is as follows:
(1) produces the initial value m that exports control law at random
0With chaos system initial value x
l[0], (l=1,2 ... 8), selected 8 systems 12,13,14,15,28,29,30 and 31;
(2) by x
l[i] is according to the piecewise linearity chaotic maps:
Adopt binary computations to produce chaotic maps output x
j[i] (j=1,2 ... 8)
(3) with the x of different systems
j[i] converts decimal system x ' to
j[i] (j=1,2 ... 8);
(4) with x '
j[i] is according to [256*acos (x
j' [i])] ([] expression rounds downwards) coding obtains x
j" [i];
(5) with x
j" [i] order output;
(6) pseudorandom number generator is according to m[i] and the piecewise linearity chaotic maps:
Produce m[i+1], and according to m[i+1] the corresponding shuffling algorithm of positive and negative selection with x
j[i] upsets the order back to x
l[i+1] assignment: x
l[i+1]=x
j[i], j are the code book address before the shuffling algorithm, and l is the code book address behind the shuffling algorithm;
(7) i=i+1 jumps back to step (2), up to task termination.
Claims (3)
1, the chaos cipher production method under a kind of limited precision the steps include:
(1) initialization: produce or set chaos system initial value x at random
l[i], i=0; L=1,2 ..., n, n are the number of chaos system, and set the different system of k kind, and k≤n;
(2) according to the x that imports
l[i], a kind of in the different systems of the k kind of adopt setting respectively obtains the chaos system output x ' of a corresponding system
l[i];
(3) with the output x ' of different systems
l[i] converts the same system numerical value x of setting uniformly to "
l[i];
(4) to x "
l[i] encodes and obtains x " '
l[i];
(5) with n chaotically coding sequence x " '
l[i] carries out exporting as password behind the scramble;
(6) judge whether the password number that is produced reaches required number,, finish if reach; Otherwise, determine x according to the ordering rule of setting
l[i+1]=x '
l[i] makes i=i+1, jumps back to step (2).
2, method according to claim 1 is characterized in that: step (5) realizes in the following ways: according to x " '
lThe data characteristic of [i], according to shuffling algorithm with n chaotically coding sequence x " '
l[i] upsets back output.
3, method according to claim 1 and 2 is characterized in that: the chaos system in the step (2) is one dimension logistic iteration chaotic mapping system or piecewise linearity chaotic mapping system.
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| CN101394266B (en) * | 2008-10-24 | 2010-12-08 | 华中科技大学 | Method for generating variable parameter chaos signal and chaos secret communication system |
| CN101436928B (en) * | 2008-12-09 | 2011-01-26 | 华中科技大学 | Parameter estimation method for chaos system |
| CN105407085B (en) * | 2015-10-26 | 2018-04-06 | 武汉帕菲利尔信息科技有限公司 | The method and device of user name password is generated according to patient user's information |
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