DE10158003B4 - Method for generating keys for data encryption and method for data encryption - Google Patents

Abstract

Method for generating number sequences for use as keys in data encryption and data decryption, in which recursion formulas of the type y i + 1 = y i (a - y i ), with i = 0, 1, 2, ... to be used,
characterized in that
a number m of such recursion formulas y i + 1, j = y i, j (a j - y i, j ), where i = 0, 1, 2, ...; j = 0, 1, 2, ..., m - 1 with respective different parameters a _j and / or initial values y _{0, j} , and the values y _{i, j are used} for a fixed value of i and over all j for generating the key.

Description

The The invention relates to a method for generating numerical sequences for use as a key in the data encryption and data decryption according to the preamble of claim 1 and the use of the key for data encryption and data decryption.

Usually become these keys generated with the help of a random number generator so they as possible are safe against cryptanalysis. The quality of a random sequence generator is determined by the equal distribution, the absence of correlations and nonperiodicity determined the generated number sequences.

From the EP 994 598 An encryption system is known in which data to be encrypted or decrypted is both encrypted and decrypted by means of dynamically generated keys.

Of the Invention is based on the object, both an aforementioned method for generating keys as well as to provide a method of data encryption in which the keys as possible good characteristics regarding Equal distribution, nonperiodicity and lack of correlations of Number sequences have. Furthermore, the method for data encryption preferably be safe against cryptanalysis.

These Task is solved by the features of the claims 1 and 10. Advantageous and preferred embodiments of the invention are the subject of the dependent claims and will be closer in the following explained. The content of the claims is by express Reference made to the content of the description.

In the method according to the invention, a parameter a and an initial number y _{0 are} iteratively applied to a recursion formula. This is the logistic equation transformed according to y _j = ax _i y i + 1 = y i (a - y i ) with i = 0, 1, 2 ...

The sequence of y _i shows chaotic behavior for 3.7 <a <4. On the other hand, it quickly goes against -∞ for a> 4. While a key constructed from the y _i can be of any length, a code defining the quantities a and y _{0 is} constant and of short length. In order to improve the statistical properties of the keys thus generated, without significantly reducing the speed of the method, a number m of recursion formulas of the above type, but with different sizes a and y ₀ , are coupled.

The set of resulting equations can be described as follows: y i + 1, j = y i, j (a j - y i, j ), where i = 0, 1, 2, ...; j = 0, 1, 2, ..., m - 1

The set of y _{i, j} for a fixed value of i can be construed as components of a vector of dimension m, this vector being the starting point for the calculation of a key S _i .

For coupling, the values y _{i, j of} the various components of the same iteration stage i are preferably added together. This sum or fraction K thereof is added for each component to the respective value y _{i, j} on the right side of the recursion formula.

Since for the new values y ' _{i, j} thus obtained in the case y' _{i, j} > a _j, the iterations would quickly approach -∞, capping by application of the modulo operation is preferred y '' i, j = y ' i, j mod a j carried out. The modulo operation can be realized either by the function "fmod" for real numbers present in C or C ++, or, if y ' _{i, j is} not much larger than a _j , saving time by repeatedly subtracting a _j an excellent distribution of the values without periodicity or gaps in the distribution achieved This also allows the advantageous use of parameters a _j > 4.

The values y " _{i, j obtained in this way} are used instead of the values y _{i, j} for a next iteration step i + 1.

Particularly preferably, several, in particular eight, recursion formulas are coupled. Each component y _{i, j} is in the implementation of the method with a 32-bit microprocessor a variable of the type "double" (in C programs) consisting of 8 bytes of which, however, in particular only the 4 least significant bytes of the mantissa recycled construction of the key S _i. This results in an extension of the key S _i of 32 bytes of such a group of 8 coupled logistic equations at each iteration. Advantageously, a plurality of such 8-membered groups may be used. When using processors of larger register width, eg 64-bit microprocessors, corresponding higher accuracies for floating-point numbers can be used, and thus more than 4 bytes of the mantissa can be utilized

The enciphering or deciphering itself can be done with several different basic methods. On the one hand, the method of XOR addition is advantageously used. XOR is the exclusive OR, equivalent to a bitwise add-on without carry, which can be done on 32-bit computers on all 32-bit concurrently in one step. The same applies, for example, to 64-bit computers. This method is a symmetric "stream" method, in which ciphering and deciphering are performed with the same operator A, that is, the ciphering of the plaintext k by means of the key S _i to the ciphertext c according to c = Ak = S i XOR k and deciphering according to k = A -1 c = S i XOR c.

Of the Term "text" is in this Context for any data in binary Shape.

Here, operator A = (S _i XOR) and its inverse A ^{-1 are} identical.

at a particularly quick minimal version of the invention is only uses this XOR addition. In another embodiment The invention additionally applies substitution to the plaintext, at every value of the plaintext that can be represented by a byte a given table is assigned to another byte. Furthermore Advantageously, this substitution may be additional to the position depending on the character be made. In this way it avoids that the well-known relative frequency used by certain letters for cryptanalysis of the key can be.

Of further it is additional or alternatively possible, that a transposition is applied to the plaintext. In the Transposition is performed in a block of e.g. 256 bytes the position of the individual bytes exchanged for a specific table. In this Variant thus takes place a triple encryption, whereby the order from XOR addition on the one hand and position-dependent Substitution + transposition, on the other hand, can be reversed with each with a different result. When deciphering must in the the reverse order of the methods as in the enciphering proceeded become. The mentioned Tables are also using the described random number generator generated.

Substitution and transposition, in contrast to XOR addition, are asymmetric methods in which the operator A and its inverse A ^{-1 are} not identical.

In order to determine the initial values y _{0, j} and the parameter a _{j of} the logistic equations used to generate the above-mentioned tables, a separate code is used in each case.

While the keys S _i are newly generated for encryption by means of the XOR addition at each iteration step i, a key S _s for generating the substitution table and a key S _t for generating the transposition table by inserting the respective initial values y _{0, j} and the parameter a _{j is} generated in the logistic equations.

In the method according to the invention for generating sequences of numbers for use as keys in data encryption and data decryption and the use according to the invention of a key for data encryption and data decryption, the keys are generated on the basis of the initial values y _{0, j} and the parameters a _{j of} the logistic equations.

The the initial values determining codes originate from one in the encryption and the decryption device identically deposited code database, wherein in this various records are deposited. For example, this is a thousand records of 256 bytes. To a record in the code database is indicated by a pointer directed. The pointer is sent from the encryption device to the decryption means indirectly, by indicating the position of the pointer in a pointer list. This pointer list is in the encryption and decryption facility also identically deposited. The code database and the pointer list are generated separately with the described or other random number generators, whereby there are various possibilities for their initialization. Thereby becomes an attack on the encryption system further complicated.

Known are such pointers as so-called transaction numbers TAN. A such TAN may preferably be a six digit decimal number, both of which each three-digit parts each on a data set of 256 bytes demonstrate.

With Help of the thus obtained parameters and initial values catches the decryption station advantageous to those who sent encrypted To decrypt data.

Of the all initial values determining code is in the mentioned embodiment 512 bytes = 4096 bits long, which is a 1233-digit decimal number of mutually different possibilities. He is therefore not easy to guess by systematic testing.

The 512 bytes of the code are distributed among the basic methods used as follows: Each logistic equation contains a parameter a _j and an initial value y _{0, j} , which are real numbers of type "double" with a representation of 8 bytes Constant coarse adjustment is finely adjusted by 6 bytes each from the code, resulting in 12 bytes per logistic equation or 96 bytes per group of 8. For XOR encryption, 4 different 8-er groups are used alternately, resulting in 384 bytes In order for every single bit of the entire code to have an effect on all encrypted bytes and not just a quarter, these values are mixed by linear combination before the parameters and initial values are calculated, since for the calculation of the above-mentioned position-dependent substitution and transposition tables own random number generators from coupled logistic equation are required, which after demselb If Scheme 2 consumed 8 more groups, ie 192 bytes, but the total number is 512, and not 576, only 4 instead of 6 bytes per "double" size are used. This complicated procedure is completely invisible to the user.

In addition, can a personal identification number PIN for identifying for the procedure will be used by authorized users, with the PIN in the encryption and decryption device is stored identically. This PIN is a password.

In addition will advantageously a method is created using the key, which is constructed as a so-called master-slave system. To do this advantageously uses encryption methods, where the operator for encryption and its inverse to decryption are no longer identical, as in the position-dependent substitution and transposition, and thus also in the overall transformation formulated using the XOR method the case is. This means that one master is superior to several slaves is and can communicate bidirectionally with each of these slaves. The slaves themselves can not communicate with each other. In this way, the security can be increased.

A additional increase Security can be achieved by encrypting Data is hidden in itself. This is through so-called steganography possible. You can do this for transmission the encrypted Data will be hidden in other data, preferably in data of graphics or sound. Here in the case of pixel graphics or even Sound files a hidden broadcast encrypted Data is done. In the case of pixel graphics are particularly preferred Targa files are used in which the red, green and blue values (RGB) of each pixel, ie each pixel, with 256 brightness levels stored in one byte each to 8 bits without data compression. Although information storage is digital, they are often on the recording side of analog devices with a background noise in the game. The eye can, however, itself in a purely digital technology based application, do not differentiate such a fine gradation. Thus, at least the least significant bit of each byte is redundant and can by a foreign information such as a bit of a Cryptographic file to be replaced. The same applies to the least significant one Bits of each byte of a sound file in wave format, e.g. a call.

Especially the method is preferred with a microprocessor or computer carried out.

Claims (15)

Method for generating number sequences for use as keys in data encryption and data decryption, in which recursion formulas of the type y i + 1 = y i (a - y i ), with i = 0, 1, 2, ... be used, characterized in that a number m of such recursion formulas y i + 1, j = y i, j (a j - y i, j ), where i = 0, 1, 2, ...; j = 0, 1, 2, ..., m - 1 with respective different parameters a _j and / or initial values y _{0, j} , and the values y _{i, j are used} for a fixed value of i and over all j for generating the key. Method according to claim 1, further characterized in that the coupling of the recursion formulas by adding a fraction K of the sum of all values y _{i, j} for a fixed value of i to the respective values y _{i, j}

is carried out. Method according to claim 2, further characterized in that the values y ' _{i, j} for a fixed value of i are the modulo operation y '' i, j = y ' i, j mod a j is applied and the values y '' _{i, j are used} instead of the values y _{i, j} for a next iteration step i + 1. Method according to one of claims 1 to 3, further characterized characterized in that m = 8 recursion formulas are coupled. Method according to one of claims 1 to 4, further characterized in that for all recursion formulas a _j > 4 applies. Method according to one of Claims 1 to 5, further characterized in that a key S _{i of} an iteration stage i is formed by combining all values y _{i, j} for a fixed value of i and for combination of y _{i, j} in a floating-point number representation only the Mantissa or a least significant part of the mantissa of the values y _{i, j} is used. Method according to one of claims 1 to 6, further characterized in that - the initial values y _{0, j} and parameters a _{j are constructed} from a code database identically deposited in the encryption and decryption means, in which different codes are stored the initial values y _{0, j} and parameter a _{j are} referenced in a code database by means of a pointer, - the pointer to a specific code is transmitted from the encryption device indirectly to the decryption device by specifying the position of the pointer in a table. Method according to claim 7, further characterized that the pointer is a six-digit decimal number. The method of claim 7 or 8, further characterized marked that in addition a password for the identification of approved for the process Users, with the password in the encryption key. and the decryption device is stored identically. Use of a key according to one of claims 1 to 9 for data encryption and data decryption. Use according to claim 10, further characterized in that in the encryption a ciphertext c is generated by XOR addition of a plaintext k with the key S _i according to the following relationship: c = S i XOR k and in a decryption the clear text k is generated by XOR addition of the ciphertext c with the key S _i according to the following relationship: k = S i XOR c. Use according to claim 10 or 11, further characterized in that in the encryption and decryption characters are position-dependent exchanged for other characters and a table used for the exchange is generated using a key S _s . Use according to one of claims 10 to 12, further characterized in that, in an encryption and decryption, the position of a character is exchanged for the position of another character and a table used for permutation is generated by means of a key S _t . Use according to any one of claims 10 to 13, further thereto characterized in that the data so encrypted in other data be hidden, especially in data of graphics or sound. Use according to any one of claims 10 to 14, further thereto characterized in that the method of data encryption and data decryption a parent System and one or more subordinate systems, wherein through the use of asymmetric encryption methods only between the parent System and its subordinate systems, not between them subordinate systems can be communicated.