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Pseudo-random number generation method based on chaotic function combination selection

A chaotic function and pseudo-random number technology, applied in the field of cryptography, can solve the problems of complex calculation process and fast software chaotic degradation, and achieve the effects of high selection accuracy, high degree of disturbance and high degree of confusion

Pending Publication Date: 2019-04-05
XIDIAN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, the chaotic system as a pseudo-random number algorithm still has many problems, such as the calculation process is too complicated or the chaotic degradation of the software is fast, etc.

Method used

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  • Pseudo-random number generation method based on chaotic function combination selection
  • Pseudo-random number generation method based on chaotic function combination selection
  • Pseudo-random number generation method based on chaotic function combination selection

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Embodiment 1

[0031] refer to Figure 1-Figure 4 , in order to solve the existing technical problems of complicated calculation process and fast chaotic degradation when using chaotic system as pseudo-random number algorithm, the present invention provides a pseudo-random number generation method based on chaotic function combination selection, including the following steps :

[0032] A pseudo-random number generation method based on chaotic function combination selection, comprising the following steps:

[0033] Step 1: Put n chaotic functions f 1 , f 2 , f 3 ,... f i ... f n Initialize, generate n initial function value sequence r 1 , r 2 , r 3 ,...r i ...r n , where n≥3;

[0034] Specifically, the n initial values ​​a 1 , a 2 , a 3 ,...a i ...a n Corresponding input to n chaotic functions f 1 , f 2 , f 3 ,... f i ... f n Among them, due to the characteristics of the chaotic system, the chaotic function f 1 , f 2 , f 3 , f i ... f n Output n corresponding initial...

Embodiment 2

[0070] In this embodiment, a kind of specific implementation model of the present invention is provided:

[0071] In addition, the set of chaotic functions {f i} = f 1 , f 2 , f 3 ,... f i ... f n , taking n=3 as an example: f 1 , f 2 is a classic logistic function (the expression is: x n +1=μx n (1-x n )), and let the control parameter of the chaotic system μ=4, when μ=4, the ergodic performance of the logistic function is the best; and f 3 It is a new function composed of infinite chaotic folded chaotic function and Logistic function. According to the characteristics of chaotic function, this new function still has chaotic nature. The new function f 3 The expression of is as follows:

[0072] x n +1=mod(e / x n +λx n (1-x n ), s)

[0073] Then in three chaotic functions f 1 , f 2 , f 3 Enter {a 1 , a 2 , a 3} = {0.5232, 0.77491, 0.06528}, and f 3 When e=10, λ=4, and s=1, the initial pseudo-random number sequences b1, b2, and b3 are all 10,000 bits, and ...

Embodiment 3

[0075] In this embodiment, when n=4, the grading method is given:

[0076] The grading principle is to ensure that the first level has at least two random number sequences:

[0077] There are three grading methods:

[0078] I: When M=2:

[0079] 1) Take b1, b2, b3 as the first level, and b4 as the second level;

[0080] In this grading method, select the calculation method as follows:

[0081] Choose 3 times at the first level: use b4 to select b12, b13, b23;

[0082] The second stage selects once: use b4 to select b12, b13, b23 and b4, thereby outputting the final pseudo-random number sequence bf;

[0083] 2) With b1, b2 as the first level, b3, b4 as the second level, the selection calculation method in this classification method is: first level selection once: use b3 to select b1, b2, and generate b12;

[0084] The second stage selects once: use b4 to select b3, b12 to generate the final pseudo-random number sequence bf;

[0085] II: When M=3:

[0086] II: When M=3: ...

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Abstract

The invention relates to a pseudo-random number generation method based on chaotic function combination selection, comprising the following steps: S1, initializing n chaotic functions f1, f2, f3-fi, fn to generate n initial function value sequences r1, r2, r3-ri-rn, where n is greater than or equal to 3; S2, simplifying each of the n initial function value sequences r1, r2, r3-ri-rn into an initial pseudo-random number sequence b1, b2, b3,-bn which only contains 0 or 1 through calculation; S3, dividing the n initial pseudo-random number sequences b1, b2, b3-bn into M levels cj; And S4, carrying out item-by-item selection on the pseudo-random number sequences with the same level or low level through the high-level pseudo-random number sequences so as to generate an ultimate pseudo-random number sequence bf. According to the pseudorandom number generation method, the new pseudorandom number sequence is generated through mutual item-by-item selection among the chaotic functions, and compared with the pseudorandom number sequence generated through column-by-column selection in the prior art, the combined selection method is higher in precision.

Description

technical field [0001] The invention belongs to the technical field of cryptography, and in particular relates to a method for generating pseudo-random numbers based on combination selection of chaotic functions. Background technique [0002] Pseudo-random numbers are a sequence of random numbers from [0, 1] uniform distribution calculated by a certain algorithm, and play a huge role in cryptography, communication engineering, information security and other fields. Currently commonly used pseudo-random number generation algorithms are linear congruence method and shift register method, which are widely used in various aspects. However, from the point of view of mathematical analysis, these two pseudo-random number generation algorithms have flaws that cannot be ignored. [0003] Matteis-Pagnutti has theoretically proved that all linear and nonlinear congruential sequences have long-period correlations. In addition, the well-known defect of linear congruential sequence is i...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F7/58H04L9/00
CPCG06F7/582H04L9/001
Inventor 尤伟何策成王健凯文浩斌
Owner XIDIAN UNIV
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