JP2002521740A - An encryption algorithm analysis method using chaos analysis - Google Patents

Abstract

(57) Abstract: A method for analyzing linearity or nonlinearity of an encryption algorithm using a fractal structure analysis technique is provided. In the method, when the encryption key value is continuously generated, a rescale range is analyzed to determine a Hurst exponent, a Lyapunov exponent is measured, and a correlation dimension is determined based on a time series reconstructed in a phase space. Is measured and an attractor is constructed based on the correlation dimension, and then the stability of the encryption algorithm is determined.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

TECHNICAL FIELD OF THE INVENTION

The present invention relates to an encryption algorithm analysis method, and more particularly to an encryption algorithm using chaos analysis that can analyze nonlinearity of an encryption algorithm using a fractal structure analysis technique when a public key or a secret key is disclosed to others. Related to analysis method.

[0002]

[Prior art]

With the rapid development of science and technology and the information environment, most tasks are performed by computers connected through an ultra-high-speed information communication network. It is necessary to prevent eavesdropping, illegal leakage, falsification, destruction, etc. of key information scattered on various sites or information transmitted / received through the network through the network.

An information protection method includes a primary method of restricting physical access to information to be protected and a secondary method of encrypting the information when the primary method fails. Can be roughly divided into

[0004] Encryption is to change a plaintext into an indistinguishable ciphertext. Decryption is to convert the received ciphertext into the original plaintext using various keys used in the encryption. Reliable conversion of plaintext to ciphertext requires confidentiality that only authorized persons can access information in the computer system, integrity that only authorized persons can modify the information, and authority. Only those who receive the information need to be able to use the information.

[0005] Encryption techniques can be classified into ordinary key systems and public key systems depending on the presence or absence of a public key. In a typical key system, the same key is used for encryption and decryption. A representative example is the Data Encryption Standard (DES) published by the US Department of Commerce in 1977. In public key systems, different keys are used for encryption and decryption. The public key system has the advantage that the key transmission is unnecessary even though the processing speed is slow. Examples include the RAS encryption method, the Merkle-Hellmam encryption method, and the finite
(limited-body-phase) encryption method. However, such a conventional encryption system has a disadvantage that the security of the encryption algorithm cannot be verified due to a mathematical analysis problem, and data security is lacking.

[0006]

[Problems to be solved by the invention]

Therefore, a main object of the present invention is to use a fractal structure analysis technique that verifies whether or not a public key or a secret key for a ciphertext can be predicted when another key is replaced with another key in a state where the public key or the secret key is publicly disclosed. An object of the present invention is to provide reliability in developing an encryption algorithm for encrypting transmitted / received data by analyzing the linearity or nonlinearity of the encryption algorithm.

[0007]

[Means for Solving the Problems]

To achieve the above object, according to a preferred embodiment of the present invention, there is provided a method of analyzing an encryption algorithm using chaos analysis, wherein when a continuous generation of an encryption key value is performed, a rescaling range is reduced. Analyzing to obtain the Hurst exponent, measuring the Lyapunov exponent, measuring the correlation dimension based on the time series reconstructed in the phase space, and after configuring the attractor based on the correlation dimension Determining the stability of the encryption algorithm.

[0008]

Embodiments and Examples of the Invention

Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the drawings. FIG. 1 shows a computer 100 with an encryption key generator 110 connected to an analyzer 120. The encryption key generator 110 generates an encryption key using an encryption algorithm and encrypts the text. The analyzer 120 determines the stability of the encryption algorithm. Display 130 connected to computer 100
Displays the output from the computer on it.

If the public or private key generated by the encryption key generator 110 is made public to an unauthorized user, a new public or private key must be generated. The encryption key generator 110 generates a new key using an encryption algorithm and replaces the old key. To determine the integrity of the new key, analyzer 120 analyzes the re-scale range (R / S) of the new key to determine the likelihood of predicting the new key. The display 130 displays the output from the analyzer 120 and displays the stability of the encryption algorithm to indicate the possibility that a new key can be predicted by others.

If the encryption algorithm does not have a random walk property, ie, has linearity, the key generated by the encryption algorithm is predictable. Thus, the random walk property can be used to determine cracking potential.

There are two types of techniques for identifying random walk characteristics, using typical statistical methods and chaotic analysis methods that can prove the nonlinearity of the system. In the present invention, the encryption algorithm is verified using chaos analysis. If the system has chaotic properties, the system is deterministic and can account for and predict the nonlinearity of the system.

However, in order to obtain a reliable encryption algorithm, in addition to the non-linearity factor, even when the old key is exposed to another person, another person predicts a new key that has replaced the old key. Something that cannot be done. If the private or public key is exposed to others, the text encrypted using an encryption algorithm is mapped in a continuous time-series pattern to determine the predictability of alternative keys by others, and then The characteristics are analyzed by chaos analysis.

As shown in FIG. 1, when a public key, a private key, or a specific encryption algorithm used for encrypting text is disclosed to another person and the old key is replaced with a new key, The re-scaling range (R / S) of the key to maintain the security of the randomly selected encryption algorithm is analyzed to determine the predictability of the key by others.

The re-scale range (R / S) for the corresponding key is defined as follows.

(Equation 1) From the equation (1), the average value of the re-scale range becomes “0” representing the local deviation. By taking the logarithm on both sides of the above equation (1), the following is obtained.

(Equation 2) In the equation (2), since R / S increases rapidly with an increase in the square root of R / S,
It is determined through the following process. First, the length M of the time series is converted to a logarithmic ratio having a length N = M-1 as follows.

(Equation 3) From the above equation (3), a sub-period “A” having a length n and satisfying A · n = N is obtained.

Next, _a label l _a (a = 1, 2,..., N) is given to each sub-period. _{N k, a (k = 1,2} , ..., n) for each element of the label _{l a} After defining the value of, and calculates an average value for the length n and label _{l a} using the following formula .

(Equation 4) Here, _{e a} is the average value of _{N i} including _{l a} has a length n.

Further, the cumulative change from the average value for each label _{l a (accumulated} d
The time series X _{k, a} indicating “epartments” are defined as follows.

(Equation 5) Here, k = 1, 2,..., N.

[0017] Therefore, from equation (4), the re-scale range R _la other keys X _k between follows subperiod l _a, can be determined from the difference between the maximum value and the minimum value of _a.

(Equation 6) Further, the standard deviation _{S la} for each label _{l a} is defined as follows.

(Equation 7)

The re-scale range defined by the above equation (6) is normalized by the ratio of the standard deviation S _la as defined by the equation (7). is identical to _R la _{/ S la} for label _{l a.} The continuous value “A” of the length n is calculated by the equation (3)
) Is defined as follows:

(Equation 8) Here, since (M-1) / n is an integer and the length n increases to the next value, n = (M-
By repeating the above process until 1) / 2, n can be used at the start and end points of the time series. Therefore, log (R / S
Least squares regression is performed by using a) as the dependent variable, where the Hurst exponent "H" is obtained as the slope of the obtained value.

After the Hurst exponent “H” is obtained in the re-scale range R / S through the above-described process, the Lyapunov exponent is measured in step 102. The Lyapunov exponent (L) in the i dimension (p _i (t)) is measured as follows.

(Equation 9) In order to measure the Lyapunov exponent, it is necessary to know the input data, embedding dimension, time delay, number of repetitions, maximum / minimum distance, and average orbital period. From the relational expression m * t (delay) = Q (period),
The average orbital period is obtained from the analysis of the rescaled range, and the maximum / minimum distance is obtained from the embedding dimension.

If the input data, embedding dimension, time delay, number of repetitions, maximum / minimum distance, and average trajectory period are determined, the distance (DI) between two points separated by at least the average trajectory period−
After measuring L ₁ (X ₀ ), an interval (DF) for measuring the Lyapunov exponent
) -L _i (X ₀ ) is determined. Then, the Lyapunov exponent is initialized as follows.

(Equation 10) In the above, the measurement distance of the Lyapunov exponent is DF > Dist_Max
In the case of DF < Dist_min, a new point “DN” is selected. In this case, the time interval of the new point must be at least one cycle. The new point must be between the minimum / maximum distance, and DN and DF in phase space
The angle between must be minimal. If a new point is selected, DI is DN
And the step of initializing the Lyapunov exponent is repeated.

When the measurement of the Lyapunov exponent is completed through the above-described process, the correlation dimension is measured in step 103. Even if the correlation dimension is measured as any one of the time series coefficients, there is a limit with a value between 1 and 2. However, when reconstructing the time series in the phase space, since all the independent variables can be observed, by increasing the radius of the fractal structure using the following equation, the correlation dimension (m ) Is measured.

[Equation 11] _{Here, R- | x i -x j |} > a If 0 Z (x) = 1, otherwise, N is an observation constant, R represents the distance, Cm correlation integrals The function m.

[0022] Z (x) is referred to as a Heaviside function. The correlation dimension refers to the probability that there are two points within the fractal radius between t and t-1. The correlation dimension is based on log (C _m [R]) versus log ([
R]) can be obtained by measuring the slope of the graph.

Once the correlation dimension has been determined, at step 104 the attractor is reconstructed.
For example, sun An original vector sequence is obtained.

If these points are plotted in a three-dimensional space, a three-dimensional attractor showing the dynamic characteristics of the system is obtained. If the value of n is properly selected in a range equal to or greater than the value of the original dimension of the attractor, the vector sequence will exhibit the same dynamic characteristics as the original motion.

An unfamiliar attractor reconstructed in the manner described above generally has a deformed configuration that does not exactly match the original attractor. However, since the Lyapunov exponent and the fractal dimension do not change with such deformation, the above values can be calculated from the reconstructed attractor.

Therefore, according to the present invention, it is possible to determine whether or not the security of a new key to be replaced is safe from another person while the public key or the secret key is exposed to another person.
It can provide reliability and security for the development of encryption algorithms.

[Brief description of the drawings]

FIG. 1 is a schematic diagram of an apparatus for analyzing an encryption algorithm using chaos analysis.

FIG. 2 is a flowchart illustrating a process of analyzing an encryption algorithm using chaos analysis according to a preferred embodiment of the present invention.

[Explanation of symbols]

 Reference Signs List 100 computer 110 encryption key generator 120 analyzer 130 display

──────────────────────────────────────────────────続 き Continuation of front page (81) Designated country EP (AT, BE, CH, CY, DE, DK, ES, FI, FR, GB, GR, IE, IT, LU, MC, NL, PT, SE ), OA (BF, BJ, CF, CG, CI, CM, GA, GN, GW, ML, MR, NE, SN, TD, TG), AP (GH, GM, KE, LS, MW, SD, SL, SZ, UG, ZW), EA (AM, AZ, BY, KG, KZ, MD, RU, TJ, TM), AE, AL, AM, AT, AU, AZ, BA, BB, BG, BR , BY, CA, CH, CN, CU, CZ, DE, DK, EE, ES, FI, GB, GD, GE, GH, GM, HR, HU, ID, IL, IN, IS , JP, KE, KG, KP, KR, KZ, LC, LK, LR, LS, LT, LU, LV, MD, MG, MK, MN, MW, MX, NO, NZ, PL, PT, RO, RU, SD, SE, SG, SI, SK, SL, TJ, TM, TR, TT, UA, UG, US, UZ, VN, YU, ZA, ZW (72) Inventor Lee Won Ha Incheon, Korea Yongsu Jugong Apartment 102-1508 F-term (reference) 5J104 AA34 JA21 NA02 NA19

Claims (4)

[Claims] 1. A method for analyzing an encryption algorithm using chaos analysis, comprising the steps of: a) determining a Hurst exponent by analyzing a rescale range when an encryption key value is continuously generated; and Lyapunov exponent. Measuring the correlation dimension based on the time series reconstructed in the phase space; and c. Configuring the attractor based on the correlation dimension, and then determining the stability of the encryption algorithm. And d. Determining an encryption algorithm. 2. The method according to claim 1, wherein the step (a) comprises: when M is the length of the time series, converting the rescaling range into a logarithmic ratio value of length N = M-1; A2 step of calculating an average value for a length n and _a label la attached to the sub-period, a3 step of calculating a cumulative change of the time series and a range thereof, and _a standard deviation for each la. The encryption algorithm analysis method according to claim 1, further comprising: after calculation, an a4 step of obtaining a start point and an end point of the time series; and an a5 step of obtaining the Hurst exponent using least squares regression. . Wherein the first b step, a second b1 step of measuring at least one orbital period by measuring the distance _{(Dl) -L 1 (x a} ) between two selected points, the Lyapunov exponent measurement distance _{(DF) -L 1 (x 1} ) after determining the, and the b2 step of initializing the Lyapunov exponent, the measured distance of the Lyapunov exponent DF > a Dist_Max, D
F < If Dist_min, a new point “DN” is selected.
The encryption algorithm of claim 1, further comprising: if the new point is selected, setting DI to DN, and then repeating each of the steps to initialize the Lyapunov exponent. Analysis method. 4. The method according to claim 1, wherein the step (c) comprises: increasing the embedding dimension from m = 2; increasing the radius of the fractal structure (c2); and forming a graph to measure the correlation dimension. The method of claim 1, further comprising: c3.