WO2005046117A1

WO2005046117A1 - Method for encoding electrical data

Info

Publication number: WO2005046117A1
Application number: PCT/DE2004/001865
Authority: WO
Inventors: Luis Rocha
Original assignee: Europa-Universität Viadrina Franfurt (Oder)
Priority date: 2003-10-31
Filing date: 2004-08-20
Publication date: 2005-05-19
Also published as: DE10351022A1; DE10351022B8; DE10351022B4; DE112004002623D2

Abstract

The invention relates to a method for encoding a quantity of electronic data quantity to be sent from an emitter device to a receiver device. Said method can be implemented at a low cost and ensures a temporally efficient encoding of electronic data, meeting the required safety standards. The encoding is based on codes of a variable length, fitting a prefix property.

Description

METHOD FOR ENCRYPTING ELECTRICAL DATA

The invention is in the field of encryption of electronic data, in particular with the aid of coding techniques that use variable length codes (VLC - "Variable Length Code").

State of the art

Elements of electronic data sets are encrypted to prevent unauthorized access to the data. Various cryptographic procedures are known from the prior art, which are usually implemented in connection with electronic data with the aid of so-called crypto chips. The crypto chips are able to perform the operations necessary to encrypt / decrypt the electronic data. For this purpose, they are equipped with the corresponding application software according to the desired process. In addition, different crypto chip modules can be produced with the help of different hardware designs. For example, a device for encrypting or decrypting electronic data is known from document DE 199 63 042 AI.

A known form of coding technology that is used to encrypt electronic data sets is the coding technology of the variable code length, namely the VLC coding technology. VL codes are characterized in that not all code words of one code have the same length, but that the code words of one code have different lengths and that the code of each element to be coded is unique and never to be coded from left to right in the code of another code Element of greater length is included. A code word is formed from a set of coding elements, so that with the aid of the coding elements a code word belonging to a respective element of an alphabet to be coded is created. The set of all code words for all elements of the alphabet to be encoded forms the associated code.

The encryption / decryption of electronic data is important in a wide variety of applications in which electronic data are to be transmitted, for example, via a communication line between a transmitter module and a receiver module. The transmission of the electronic data can, for example, also include the filing or interpretation. relate to electronic data in or from a memory. But also in connection with any telecommunications application, for example in mobile telephones or the like, there is often a need to protect electronic data from unauthorized access. A method for encrypting numerical information and a transmission module are known from document DE 199 58 599 A1.

Coding methods with variable word lengths are known from the prior art, for example the Huffman code, which is a VLC method. One of its essential properties is that elements of an alphabet to be encoded that occur very often have a shorter code length than elements of the alphabet to be encoded that do not occur very often. In addition, such methods have an extraordinary property: the code of a coded element is never contained at the beginning of a code of another coded element of greater length. Therefore, such a code is called: prefix code. The result is that such a code permits unambiguous decoding without having to divide the set of elements to be decoded into blocks of fixed length. The prefix property also means that the code of each element of the alphabet to be encoded is unique and is never contained from left to right in the code of another element of the alphabet of greater length to be encoded. This enables clear decoding and prevents manipulation of the encrypted message.

Known encryption methods, whether with or without a prefix property, often require a great deal of computational effort when encrypting the data in electronic form, which on the one hand leads to the need for considerable computing capacity in order to keep the encryption / decryption within a reasonable time frame. Otherwise there are longer computing processes, which are often not accepted by users.

SUMMARY OF THE INVENTION The object of the invention is to provide an improved method for encrypting an electronic amount of data, in which the encryption / decryption can be carried out while maintaining a sufficient security standard with the lowest possible computing power, so that it is particularly suitable for use in conventional computer equipment, for example laptops or personal computers.

This object is achieved according to the invention by a method according to independent claim 1. The invention has the advantage over the prior art that a method which also meets demanding security requirements is made available, which on the other hand ensures fast encryption of electronic data with the aid of the computing power usually available in a normal personal computer. Despite the high security wire of the process, the encrypted text is generated in very short times. In this way, the method is suitable, for example, for use in connection with the daily exchange of electronic messages (“email”). The method can be implemented as application software with little programming effort, and it can be integrated into standard programs.

Another advantage of the method is that the method according to the invention is an encryption method in which a prefix property is retained, so that unique encryption is made possible, which prevents manipulation of the encrypted text.

Depending on the desired level of security, the expiration can be optimized in an expedient further development of the invention by querying a number of the key elements of the key used for the encryption and automatically entering a user input for specifying the number of key elements. In this way, the user of the encryption method is given an opportunity to freely choose the desired level of security.

In order to further optimize the security of encryption against unauthorized access to the electronic data to be encrypted, in an expedient embodiment of the invention an interleaved encryption is carried out in that the amount of electronic data to be delivered is an encrypted amount of data. This means that the encryption process is carried out several times, so that in the second application the output quantity of electronic data is already an encrypted data quantity.

The invention is explained in more detail below using exemplary embodiments with reference to a drawing. Here show: Figure 1 is a schematic representation of an apparatus for performing a method for encrypting / decrypting an amount of electronic data; and

Figures 2A to 2F representations of a matrix in the course of an encryption process.

The method for encrypting / decrypting or coding / decoding a set V of electronic data (V = {v _ls ..., v _q }, q> 1) is described below. The method is carried out with the aid of a device which is shown schematically in FIG. 1. The quantity V of electronic data is stored in a storage device 1 and is loaded from the storage device 1 for encryption / decryption by a processing module 2. The processing module 2 can be, for example, a conventional microprocessor that is equipped with the aid of suitable software and / or digital hardware technology in order to carry out the method for encryption / decryption or coding / decoding described below. The processing module 2 can be part of a personal computer or another device which has means for processing electronic data, for example a mobile radio telephone or the like.

Encrypted / decrypted data can then be delivered by the processing module 2, for example via an output device 3 to another device 4 and / or to the storage device 1. The delivery to the other device 4 relates, for example, to the transmission of an encrypted electronic message which is then stored in the other device 4 is automatically decrypted. Additionally or alternatively, a direct transmission of the encrypted / decrypted data between the processing module and another data processing device 5 can also be provided.

The data V = {v _ls ..., v _q } are formed using elements of an electronic alphabet data set W (W = {w ₁ , ..., w _n }, n> 1) using a set D.

..., z _μ }, μ> 2) with coding elements Z _j (j = 1, ..., μ), where n = μ + k _c (μ - 1) with k _c eN. If the latter is not the case, then a number n _f with n _f > n is sought, so that the equation actually takes place with a natural number k _c , ie n _f = μ + k _c (μ - 1). Such a number n _f with the associated number c can always be found without difficulty.

The elements of the alphabet data set W can be, for example, the ASCII elements. With the help of the ASCII elements, a message can be written that then to be encoded. The coding elements Z _j are, for example, the numbers 0 and 1 (binary code), which are combined with one another in order to form an associated code word for each ASCII element. The stringing together of the code words for the ASCII elements contained in the message to be coded then forms a coded message which can be processed electronically, for example sent or saved to a recipient.

The following describes the formation of matrix elements a _{v> m} with p = 1, ..., k _c +2 and m = 1, ..., n _{f of} a matrix A = (a _Pjm ), the matrix elements a _{p > m are formed} by means of one or more coding elements Z _j , so that candidate code elements are formed which satisfy a prefix code property. Let φ: 5R ⁺¹ -> ■ 5R ⁺ be any, strictly positive, limited, real function. If using a vector x °

where k ≥ l 2 <μ <n - 32 0 <Xj <1, i = L ..., k,

is given, the sequence {x _v , v> k} becomes iterative

Xv + k + i = φ (λ, Xv + to-, Xv i), v> 0 generated. this means

and thus each symbol v of the ASCII table k + v, d. H. v → k + v, v = l 255

Such an iteration is k + 1 step, because it needs k + 1 initial values to be able to start. Every new number x _{v of} the sequence X = {x _v , v> k} is obtained by the function φ always from k +. 1 arguments is fed. The sequences {x _v , v> k} have the following properties:

(i) They can be generated with little effort.

(ii) Each initial vector x ° generates a certain sequence of numbers {x _v }, ie to master the whole sequence it is sufficient to know the vector x °.

(iii) Knowing k + 1 elements of the sequence allows the next elements to be generated, but does not provide any information about the previous elements. It is a one-way function.

Since the sequence {x _v , v> k} can diverge quickly, a parameter λ is introduced which has two tasks to perform:

(i) The sequence {x _v } is prevented from quickly converging against a fixed point. From a certain limit to another, empirically determinable limit, which depends on k, an ergodic behavior of the sequence is forced.

(ii) It is the initial value of a small random selection of the initial elements of the code alphabet, because the code alphabet has μ symbols that can be chosen arbitrarily. Each key generates a personal code, ie the code is generated with certain symbols. If you always use the same numbers λ and μ as key part and only these numbers, whereby the other numbers of the vector x ° can be chosen arbitrarily between zero and one, then codes with the same code Symbols. Of course, only the code symbols are the same, but not the code words.

It is preferred to choose the number λ as a parameter such that the sequence {x _v } behaves chaotically, ie that it does not converge to a fixed point.

Then the numbers {x _v } are each assigned a specific ASCII element, namely a specific character of the ASCII code. The numbers are sorted according to size and saved in the last row of matrix A, ie (a _{k + 2J} ). For all elements of the line from i = n +

1 to nf is set & _{kc +} ι, i ~ ^. The following applies: a h + 21 ≥ a 'k _c +2.2 ≥ ... ≥ a _τ , + 2, n _f

The marking must now be carried out. The matrix A looks like this:

Then the following steps are carried out:

(a) Let i = k _c and n _f = μ + z ^' (μ - 1) n = n _f - (μ -1)

(b) The last μ elements of row i + 2 are added:

^S = Σ ^a ^ 2J

One sets: a _{l + 2} ~ =. The elements of this line are to be sorted again up to position ϊϊ. (c) For all j = 1, ..., n set ^a i + l, j ^{~ a} i + 2 ie all elements of the upper row that have been sorted are copied into the lower row of matrix A. Then it applies

^a MΛ ^≥ ≥ S ≥ - ^≥ .n

(d) The new position of the number s is stored in a vector b (i).

(e) Let i = i - 1, and return to (a).

Repeat steps (a) - (e) until row 2 of matrix A is reached, ie until i = 1. Then in the vector b (i), i = 1, ..., k _c , all positions of the sum are obtained, and the formation of the matrix A is thus completed. It follows that for i = 1, ..., k _c the required condition l ≤ b (i) <μ + (i -l) (μ - l)

is satisfied.

The following therefore applies when forming matrix A:

Line 2 a _{2 j} 1 ≤ j <μ

Row 3 a _3J 1 <j <μ + (μ - 1)

Row sa _s j 1 <j <μ + (s - 2) (μ - 1)

Row k _c + la _w 1 <j <μ + (k _c - l) (μ - 1) = n _f - (μ - 1)

In the following, matrix A is to be marked. The following applies: Only one permissible cell is selected in each row, and only from this cell may "children slip into the next row". Mother and child are placed in the μ last permissible cell of the next but one row. Merging rule: Every marked cell of the matrix A has μ children and the next generation occupies the μ last permissible cells, the remaining cells also jump with no changes. For example, let n = 7 and μ = 3 and D = {a, b, c}. Then 7 = 3 + 2 - 2, so k _c = 2. The matrix A in the first and second generation then looks like this:

The next population is then:

After the last propagation you get:

Thus the code for use is in line 4 for coding. If the marking of matrix A is known, the code can be generated with the prefix property. It turns out that the number of different markings for n> 50 is very large. In the case of the ASCII characters, coding is done with n = 255.

The process steps of the coding / decoding process are listed again in the following summaries.

Coding method

The length of the key depends on k and is determined in advance.

(1) Select μ so that 2 <μ <n -32. (2) Choose an iteration function φ: 9? , k + l - »5R.

(3) Determine the range for the parameter λ.

(4) Generation of n elements of the sequence x _v + k + ι = φ (λ; x _{v + k} , ... x _{v + 1} ), v> O and λ suitable.

(5) Sort the numbers {x _{v + k} , 1 <v <n} in size.

(6) Determine k _c and the corresponding number n _f such that n _f = μ + kc (μ-l).

(7) At positions i = n + 1 to n _f set x, = 0.

(8) Determine the marking of the matrix A. Determine the values of the vector b (i) with 1 <i <k _c , where l≤b (i) <μ + (il) (μ-l) i = l ₅ . .., k _c

(9) Generation of the vector code (v), with v = 1, ..., n, where in code (v) is the code of the character v to which the number x _{v + k of} the iteration has been assigned.

Decoding method

It is assumed that the following information is available: Let W = {w _ls ..., w _n } be an alphabet, D = {z _1; ..., z _μ } the associated code alphabet with coding elements and the vector

the key. A coded text is to be decoded, which is composed of elements of D. The iteration function φ: 9ϊ ^{k + 1} - 5R as well as the parameter λ are known, ie exactly as with encryption. The decoding is then carried out in the exemplary embodiment with the following steps:

(1) Generation of n elements of the sequence x _{v + k +} = φ (λ, x _{v + k} , ..., x _{v +} ι), v> O and λ suitable. (2) Sort the numbers {x _{v +} , 1 <v <n} in size. (3) Determine k _c and the corresponding number n _f so that: n _f = μ + k _c (μ - 1). (4) At positions i = n + 1 to n _f . Set x, = 0. (5) Determine the marking of the matrix A. Determine the values of the vector b (i) with 1 <i <k _c , where l ≤ b (i) <μ + (i - l) (μ - l), i = 1- .... k _c

(6) Generation of the vector code (v) with v = 1, ..., n, wherein in code (v) is the code of the character v to which the number x _{v + k of} the iteration has been assigned.

The vector code (v) is used as a kind of catalog. The coded text is started to be read character by character from the beginning and each time a comparison is made as to whether the read characters already together represent an encoded word of the vector code (v). If this is the case, decoding is carried out. Then you start to read and compare character by character again. This is only possible thanks to the prefix property of the generated code. The whole process can be carried out very quickly. A large number of operations are not necessary, as is the case with asymmetrical methods.

The method described is further explained below with reference to FIGS. 2A to 2F. An alphabet set W to be encoded comprises the letter set {R, O, M, A}. The set D comprises two symbols as freely selectable coding elements, i. H. D = {0, 1}.

The elements of the matrix A = (a _Pjm ) are considered, the cells or elements of the matrix A, which are identified by the character “0”, having no meaning and being disregarded, ie they are neither used nor used cells of matrix A marked with the symbol "•" indicate the markings of matrix A.

Cell a _{21 is marked} in the second line and cell a ₃₁ in the third line. Only the elements of a selected cell can multiply. When the matrix A is occupied, the following multiplication rules should apply in the exemplary embodiment during the row-by-row coverage: - All symbols that land in a marked cell of matrix A are to be considered as a mother.

- Every mother has as many children as there are symbols in the second line of the matrix.

- Mother and child come into the next generation, i.e. the next line upwards and occupy the last two cells, each like this: mother plus first child and in the next cell mother plus second child. The symbols in the cells without marking continue without changes to the next generation, i.e. the next line.

In the exemplary embodiment, the starting position (line 2) according to FIG. 2A results. The first mother is in cell a ₂₁ , she has two children and goes into the next generation as 00 and 01. The second generation (row 3) then results according to FIG. 2B. In this generation the second mother is in cell a ₃₁ , she has two children and gerxt in the next generation (row 4) as 10 and 11, so that there is a matrix assignment according to FIG. 2C. The desired code words for the letters {R, O, M, A} to be coded then result from line 4.

If, for example, the word AMOR is to be coded, the following code results: 111O0100.

If the marking of the matrix were chosen differently, as is shown by way of example in FIG. 2D, then the assignment of the matrix A in the exemplary embodiment results, taking into account the above rules according to FIGS. 2E and 2F. In this case, if the text "AMOR MORA ROMA" is to be encoded, the following results: AMOR = 001000011 MORA = 000011001 ROMA = 101000001

This then leads to the coded text: 001000011000011001101000001. The decoding is done from left to right and without any problems due to the prefix property of the code. Data compression ierunε Another advantage of the method is that encrypted data compression can be carried out if: 1. The set D is any subset of the set {1, 2, ..., 9} and comprises at least two elements. 2. There is an encrypted file that was created with D as in point 1 and with the method presented above.

Due to the prefix property, such coding is unique and can be represented with symbols from an extended ASCII table. In an extended ASCII table, each symbol is represented with two bytes, ie 2 ^Λ 16 bits, which means that the table contains 65536 symbols.

The following steps must be carried out for data compression: 1. Determine z = max {z ₁ , ..., z _μ }, 2 <μ <9, Z _j e {1, ..., 9}. 2. The basis of the numerical representation is then b = z + 1. 3. Select G ^* = 2 ¹⁵ - 1 4. From left to right, read the symbols Z _{j of} the encrypted message: a. Setting j = 0 and s = Z _j • b ¹ . b. If s <G, then read the next symbol and set:

1- j = j + l 2. s = s + z, b ⁱ c. If s> G, save the symbol that is in the extended ASCII table.

Because the system changes from a smaller ASCII table to a larger one, the end result is an encrypted file that is smaller than the original file.

Datendekomprimieruns

The decoding is done analogously: 1. There is an encrypted message which has been represented with the extended ASCII table and which has been encrypted using the method presented above. 2. The key to the process is known. There is thus information about the set D that was used as the code alphabet. The decompressed file is then obtained as follows: 3. Read each symbol and determine its numerical representation in the extended ASCII table. 4. Each number obtained in 3. is shown in the numerical representation according to base b according to 2.. 5. After step 4. there is an encrypted file. 6. Use the procedure outlined above.

The procedure presented here was implemented in the programming language Visual Basic with the EXCEL interface. Because of the simplicity of the method, it can of course be implemented in any programming language.

Those disclosed in the foregoing description, claims and drawings

Features of the invention can be important both individually and in any combination for realizing the invention in its various embodiments.

Claims

Expectations

Method for encrypting a quantity V of electronic data (V- {v ₁ , ..., v _q }, q> 1) to be delivered from a transmitting device to a receiving device, which can be transmitted using elements of an electronic alphabetical data quantity W (W = {W _j , ..., w _n }, n> 1), with the help of a processing module comprised by a computer and using a set D (D = {z _1} ..., z _μ }, 2 <μ <n -32) with coding elements Z _j (j = 1, ..., μ), where n = μ + k _c (μ - 1) with k _c eN and the method comprises the following steps:

- Reading of the electronic alphabet data W by the processing module from a memory module;

- taking into account key elements of an electronic key, the coordinates x; form a vector x ° with

in which

0 <i <1 i = 1.2 k

Execution of a mapping φ: 9ϊ ^{k + 1} - »5R ^{+ of} the elements w, (i = 1, ..., n) of the electronic alphabet data set W with the help of an irreversible, real function φ according to

Xv + k + i = φ (λ, x _{v + k} , ..., Xy + i), with v> 0 for iteratively forming sequence elements x _{v of} a sequence

X = {x _v , v> k} with the help of the processing module, where λ lies in an interval dependent on k, so that the sequence X is chaotic and a sequence element x, e X is assigned to each element Wj; - Sorting the sequence elements x _{v in} terms of size, a largest sequence element forming a first sequence element of a sorted sequence X '= {x' _v }, v>k; - _{Forming matrix} elements a _Pjirι with p = 1, ..., k _c +2 and m = 1, ..., n _{f of} a matrix A = (a _P) m), the matrix elements a _p , _m using one or more coding elements Z _{j are} formed so that candidate code elements are formed which satisfy a prefix code property; - Selecting at least one code element in each line p with 2 <p <k _c + 1 of matrix A from the candidate code elements; Assigning each selected code element to each of the elements w; the electronic alphabet data set W; and encrypting the quantity V of electronic data to be dispensed with the processing module in accordance with the previously made association between the selected code elements and the elements Wj of the electronic alphabet data quantity W.

2. The method according to claim 1, characterized g ekennz ei chn et that before executing the mapping φ: 5R ^{k + 1} -> SH ^{+ of} the elements Wj of the electronic alphabet data set W a number of the key elements is queried and a user input for specifying the Number of key elements is recorded automatically.

3. The method according to claim 1 or 2, characterized g ekennz ei chnet that depending on μ an interleaved encryption is carried out by the amount V of electronic data to be delivered is an encrypted amount of data.

4. The method according to any one of the preceding claims, characterized in that the quantity V to be dispensed is compressed.

5. Use of the method according to one of claims 1 to 4 for encrypting an electronic file.

6. Use of the method according to one of claims 1 to 4 for encrypted data archiving.

7. Use of the method according to one of claims 1 to 4 for encrypting an electronic file with a mobile radio telephone.