KR100453258B1 - Generating method of balanced numerical progression using chaos function equation - Google Patents

Abstract

The present invention improves the method of generating an initial condition compared to the existing sequence generation algorithm, and in order to ensure the balance and randomness of the sequence in generating a sequence required for encryption using a chaotic function, a constant interval during the sequence generation. By evaluating the balance and adjusting the threshold value, the confidentiality of the encryption is improved.

Description

Generating method of balanced numerical progression using chaos function equation

The present invention relates to a method for generating a sequence required for document encryption, and more particularly, in generating a sequence for data encryption using chaotic theory, by using a chaotic function such as a logistic equation to generate an initial condition applied to the document. In addition, the present invention relates to a hydrothermal generation method using a chaotic function that satisfies the secretion for data encryption and improves its reliability by adjusting the threshold according to the balance analysis during hydrothermal generation.

Recently, research on 'chaos cryptosystem' using Chaos Theory has been increasing.

Chaos theory refers to the irregular and complex trajectories found in the deterministic dynamics, which are unpredictable because they show very different patterns over time even with very small initial conditions. This characteristic that is sensitive to the initial conditions is also called the butterfly effect (Butterfly effect).

Encryption using the chaos can be said to effectively generate random numbers using the dependence, excellent autocorrelation, and aperiodic characteristics sensitive to the initial conditions of the chaos.

Generally, technologies related to data encryption have a long history and many methods are known from the classical methods to the modern DES, RSA, etc., but these conventional methods are not inherently secure and decipherable but It only has computational security that it is difficult to decipher because of the large amount of computation required.

Accordingly, as the development of various algorithms for decryption and computer technology have been developed, there is a problem in that the ciphertext by the existing encryption system can be easily decrypted.

In order to solve the above problems, Bianco et al. Introduced a chaotic theory-based encryption system, generating chaotic signals from chaotic signal generators using logistic equations, and converting them into binary values of '0' and '1'. After quantization, we propose a stream cipher system that XORs the original text.

The algorithm of Bianco et al. Receives a maximum and minimum range for quantizing a key and a chaotic signal to be used for encryption from the outside, and quantizes a signal generated from a logistic equation to '0' or '1'. At this time, the key sequence is generated by quantizing the chaotic signal using a middle value between the maximum value and the minimum value as a threshold value.

The present inventors have developed a method and apparatus for encrypting and decrypting information using a chaotic signal improved from the above method (Patent Application No. 2000-58017). The above technique encrypts a cipher key sequence generated using a chaotic signal obtained by using a chaotic function (logical difference equation, etc.) by XOR operation in bit units and plain text, and decrypts it in the same manner. Chaos signals are used to make self-decryption impossible.

However, although the problem of period and correlation has been solved by using a chaotic characteristic by the existing chaotic sequence generation algorithm as described above, in this method, the balance and random characteristics may be disproportionately represented. That is, there is a problem that the algorithm and the stability of the sequence for generating the sequence used for encryption cannot be confirmed.

An object of the present invention is to improve the existing chaos sequence generation method in encrypting data, and to provide a new chaos sequence generation method that guarantees balance and random characteristics without aperiodic and no correlation.

1 is a flow chart showing a hydrothermal generation process according to an embodiment of the present invention.

2 is a comparative distribution diagram illustrating a change of '0' and '1' according to a change of a threshold value.

The present invention improves the method for generating an initial condition compared to the existing sequence generation algorithm, and in order to ensure the balance and random characteristics of the sequence in generating the sequence, during the sequence generation, the balance is evaluated at regular intervals to evaluate the criticality. The above problem is solved by allowing the value to be adjusted.

Specifically, the present invention is a method of generating a sequence of encrypting data using a chaotic signal,

(A) generating an initial population X, an increase rate α, among initial conditions necessary for generating a chaos signal using a chaos function from an arbitrary secret key;

(B) generating a chaotic signal by adding the initial population X and the increase rate α generated in step (a) to the chaotic function;

(C) converting the chaos signal selectively obtained in step (b) into a binary signal of '0' or '1' using a threshold to obtain a sequence of binary values;

(D) performing a random characteristic balance analysis of the partial sequence consisting of the binary values obtained in step (c); and if the random characteristic does not satisfy a predetermined range, adjusting the threshold value through balance analysis to adjust the threshold value. And (c) repeating the following steps.

In a specific embodiment of the present invention, in step (d), a threshold value change algorithm for adjusting the threshold value through random characteristic and balance analysis is used.

The chaotic function in the present invention is not particularly limited, and a chaotic function such as a general logic difference equation, a low lens equation, a Roesler equation, and a logistic equation may be applied.

1 is a flow chart showing an embodiment of the hydrothermal generation process of the present invention using a logistic equation as a chaotic function, with reference to the accompanying Figure 1 will be described in detail the method of generating a hydrothermal according to the present invention.

First, in step (a), an initial population X and an increase rate α are generated (S30) among initial conditions necessary for generating a chaos signal from a random secret key S10 K using a logistic equation S20 that is a chaotic function. .

Since the initial condition generated in step (a) is used as the initial condition of the logistic equation (S40) to be performed in step (b), the generated initial condition must satisfy the range of the initial condition of the logistic equation.

Therefore, the initial population X 'is generated within the range 0 <X' <1, and the increase rate α is generated within the range 3.6 <α <4.

To this end, in the present invention, for example, using Robert May's logistic equation, the initial condition generation algorithm is implemented as follows.

(The symbols used in Equation 1 represent K: secret key, p: logistic equation stabilization variable, value_X: number of individuals, value_α: growth rate, asctoval (): secret key K conversion function, and conv (): a value conversion function, respectively. )

[Equation 1]

function init ()

begin

get_key K;

p: = asctoval (K);

loop

X _{n + 1} : = αX _n (1-X _n );

until p;

X: = αX _n (1-X _n );

α: = conv (αX (1-X));

end

In the method of the present invention, the initial value (= X₁) and the increase rate (= α) are obtained by inserting the secret key K as described above. At this time, the value obtained by converting the secret key K inputted from the initial condition generation algorithm into the ASCII value is obtained. It is used as a repetition coefficient for stabilization of logistic equations. By doing so, the chaotic characteristics of the logistic equation can be maximized, and the logistic equation can be changed largely according to the difference of the secret key, so that the relationship between the generated X₁, α and the secret key cannot be found. Therefore, the initial condition to be used as the input of the chaotic function to be used for generating the key sequence is generated by the logistic equation, which is one of the chaotic functions.

When the process of step (a) is completed as described above, in the next step (b), the initial condition X 'and α generated using the secret key in the initial condition generation process are put into the logistic function (S40). To generate (S50).

For this purpose, for example, the following algorithm is applied using X = αX (1-X) modeled by Robert May of the logistic function.

[Formula 2]

function Cf (value_X, value_α)

begin

X (n) = value_X

α = value_α

loop X (n + 1) = αX (n) (1-X (n)), p

loop X (n + 1) = αX (n) (1-X (n))

sub St (X (n + 1))

end

The next step (c) includes converting the chaotic signal selectively obtained by the secret key into a binary signal S60 of '0' or '1' using the threshold value S100.

In the method of the present invention, an algorithm for quantizing a chaotic signal into '0' and '1' using a threshold value is shown in Equation 3 below.

[Equation 3]

function St ()

begin

loop

X _{n + 1} = αX _n (1-X _n )

if X _n > threshold then

{keystream: = 1; counter1 ++; }

else {keystream: = 0; counter0 ++; }

if 0 = (n mod p) then Reset (counter0, counter1);

output: = keystream XOR data;

until end of message;

end

However, if there are too many '0's or' 1's in the generated key sequence, the ciphertext can be easily decrypted by this property. Therefore, it is important that a function that generates a good binary sequence not only has the same number of '1's and' 0's, but also has the same probability of '00', '01', '10', and '11'. In the same way, '0 ... 00', '0 ..... 01', '...', '1 .... 10' and '1 ..... 11' It is preferable to be generated as.

Therefore, in the present invention, in the following step (d), a random characteristic balance analysis (S80) of the sequence 70 consisting of the binary values (S60) obtained in the step (c) is performed, and the random characteristics satisfy a predetermined range. If not, the threshold is adjusted through a balance analysis (S90), and the above (c) step is repeated.

In this step, the balance analysis is performed using, for example, a chi-square test that is well known in a frequency test, and 0.05, which is a general value, as a significance level for determining a judgment value.

As a result of the verification, if the test statistic is less than 3.841, the random characteristic is determined to be excellent. If the test statistic is greater than 3.841, the threshold for generating the next key sequence is adaptively changed. That is, the adaptive variation of the threshold value is to maintain the previous threshold value in the next step when the test statistics are within 3.841 of the rejection range, and according to the number of '0' and '1' when the test statistics are larger than the rejection range of 3.841. When the number of '0's is large, the threshold is decreased by 0.05. When the number of' 1 'is large, the threshold is increased by 0.05 and applied to the threshold for generating the next partial sequence by p lengths. Here, the change of the threshold value of 0.05 is empirically determined to give a 10-step change based on an average value of 0.5 because the chaos signal ranges from 0 <X <1 in a state in which no related studies have yet been established. to be.

In this step, in the process of changing the chaos signal to a binary value by applying a threshold value, the balance value and the random characteristic of the sequence are increased by increasing or decreasing the threshold value by 0.05 through a balance analysis at regular intervals for the key sequence. will be.

Looking at the process to improve the balance of the sequence through the threshold value through the algorithm shown in [Equation 4] as follows.

[Equation 4]

function Reset (counter0, counter1)

begin

balance: = Counter1: Counter0;

if balance> 0.5 then threshold: = threshold-0.05

else threshold: = threshold + 0.05;

end

2 is a comparative distribution diagram showing an example of a change of '0' and '1' according to a change of a threshold value. Referring to FIG. 2, when the threshold value is changed by 0.05 using the above algorithm, the chaos signal values are changed to '0' and '1', respectively. When the threshold value is 0.70, '0' and ' The ratio of 1 'is 15:15, the ratio when the threshold is 0.75 is 17:13, and the ratio when the threshold is 0.80 is 21: 0. It can be confirmed that it is affecting.

That is, through the above method, the balance change of the sequence is performed at regular intervals during the generation of the sequence in the threshold value change algorithm for improving the balance, and when the number of '0's is high, the threshold value is decreased by 0.05 to' 1 '. If the threshold value is adjusted to generate a lot, and '1' occurs a lot, on the contrary, by increasing the threshold value by 0.05, the '0' is generated a lot so that the balance and randomness of the sequence can be increased.

By XORing the sequence consisting of the binary signal of the chaos signal value obtained through the sequence generation method using the logistic equation according to the present invention with the binary value of the information to be encrypted, the corresponding information (plain text) is changed to cipher text.

If the process after the above step (c) is repeatedly performed until all the information to be encrypted is encrypted, the ciphertext of the information is generated.

As described above, the present invention improves the method of generating an initial condition compared to the existing sequence generation algorithm, and evaluates the balance value at regular intervals during the sequence generation in order to perform the encryption using the chaotic function. By adjusting, the confidentiality of the encryption is improved to ensure the balance and random characteristics of the generated sequence.

Claims (2)

In the method for generating a sequence for data encryption using a chaotic signal, (A) generating an initial population X and an increase rate α of initial conditions necessary for generating a chaos signal using a chaos function from an arbitrary secret key; (I) Generating a chaotic signal by putting the initial conditions X and α generated in the step (a) into a chaotic function; (C) converting the chaos signal selectively obtained in step (b) into a binary signal of '0' or '1' using a threshold to obtain a sequence of binary values; (D) perform a random characteristic balance analysis of the partial sequence consisting of the binary values obtained in the step (c); and if the random characteristic does not satisfy the predetermined range, set the threshold value of the step (c) And repeating the steps (c) and later so that the components constituting the binary sequence are balanced by increasing or decreasing the random characteristics so as to satisfy a predetermined range. The method of claim 1, wherein the step (d) comprises using a threshold value change algorithm for adjusting the threshold value through a random characteristic and balance analysis.