WO2006017949A1

WO2006017949A1 - Encryption device and method using global scaling for key distribution

Info

Publication number: WO2006017949A1
Application number: PCT/CH2005/000427
Authority: WO
Inventors: Ralf Otte; Hartmut Müller
Original assignee: Tecdata Ag
Priority date: 2004-08-20
Filing date: 2005-07-20
Publication date: 2006-02-23
Also published as: DE102004040654A1; JP2008511195A; EP1779587A1

Abstract

The invention relates to a method for encrypting data, which is characterized in that all required information is transmitted via random processes on the basis of a global scaling modulation and demodulation, whereby a modulation, injection, extraction and demodulation of resonant frequencies of coupled noise processes is carried out.

Description

DEVICE AND METHOD FOR ENCRYPTION USING GLOBAL

SCALING TO KEY DISTRIBUTION

The invention relates to a device and a method for encrypting messages. The device and the method are suitable for encrypting digital data. The invention is applicable in many areas of information transfer, z. B. in telecommunications, metrology, sensors, medical technology, telecommunications, banking and insurance, and more.

It is customary to apply encryption methods for the secrecy of messages or for the secret transmission of messages. The goal of the encryption is to change a message to be transmitted so that only the recipient, but not a third party, read it, i. can decrypt.

The receiver implements this decryption (deciphering, decoding) with a so-called key, i. information that usually only he and the sender own and which is necessary and sufficient to make the message readable again.

Numerous encryption methods are known for this purpose. In principle, in the case of an encryption from the key k, the plaintext m, a ciphertext c is generated, so that the following applies to the encryption:

c = f (k, m)

For this function f, there must now be a reversible function f, so that the following applies to the decryption:

m = f (k, c) where k is usually the shared, secret key for sender and receiver. An important type of encryption is referred to as symmetric encryption in which both sender and receiver - but in the best case only these - know the secret key k. For symmetric methods, for example so-called block ciphers and stream ciphers are known. Although symmetric encryption methods are very powerful, they are only applicable if both sender and receiver possess the secret key, so that just the transmission, ie the exchange of keys for example by postal or electronic means is a point of attack.

Furthermore, so-called asymmetric encryption methods are known in which each participant in the system is assigned a private (secret) key d and a public key e. The asymmetric encryption algorithm f calculates a ciphertext c for each plaintext m using the public key e

c = f _e (m)

and the inverse function f again assigns the plaintext m to this ciphertext c with the aid of the private key d, whereby the following applies for the correct decryption:

m '= m = f _d (f _e (m))

Both some symmetrical but in particular asymmetrical encryption methods are generally based on mathematical algorithms and are not protected by physical effects or properties. For example, a physically supported, secret transmission of messages would be the use of special ink and the like, as was common in the past. Today's transmission of secret messages is often based on the encryption by means of mathematical algorithms.

In asymmetric encryption methods, the so-called public-key method, the mathematical encryption idea is based, for example, on using so-called mathematical one-way functions, functions which are difficult to reverse. One of the- Such a one-way function is, for example, the factorization of large numbers: While the multiplication of two very large primes p and q is trivial, their inversion, ie the factorization of the resulting number n back into the two primes p and q, is very complex. For example, the largest figure up to the year 2003 had 155 digits and it is estimated that the decomposition of a number n of 220 digits can take several thousands of years with the best methods known today [ibid]. Thus, these public-key methods were considered to be relatively secure until the recent past.

For all encryption methods, attacks are now known which have the goal of decrypting the encrypted message c or of recalculating the key k solely from knowledge of a plain text m and / or a ciphertext c or to intercept the key directly, i. In the case of the known attacks, by intercepting a ciphertext with an associated plaintext, one attempts to calculate the key or intercept the key which must sometime be exchanged in the case of symmetrical methods.

The attacks are typically distinguished in the following ways:

• Ciphertext-only attack: The attacker wants to determine the associated plaintext or the used key k from the knowledge of some home text

• Known-plaintext attack: The attacker wants to determine the key k from some known plaintexts and associated ciphertext

• Chosen-plaintext attack: attacker knows the encryption function f, so it can certainly encrypt plaintext itself, but does not know the key k and wants to calculate k.

• Chosen-ciphertext attack: attacker knows the decryption function f, so he can decode secret texts himself, but does not know the key k and wants to calculate k.

It is known that all asymmetric encryption methods used today can be revealed theoretically, since they are based on mathematical properties that can be exploited by a third party to decrypt, even if The decryption as mentioned above with conventional computers or computer networks can take a very long time, for example, thousands of years.

In particular, initial proposals have been made to accelerate the decryption by the use of so-called. Quantum computers extremely. The theoretical idea behind this is that quantum computers can simultaneously perform millions of arithmetic operations, since quanta, so-called qubits in information theory, simultaneously occupy several states and, in the processing of qubits, several states are simultaneously calculated. This allows mathematical algorithms and thus factorizing large numbers or deciphering procedures to be implemented faster by orders of magnitude.

In 1994, Shor was able to prove that with special mathematical methods that would run on a quantum computer, for example, the RSA algorithm, one of the best known asymmetric encryption methods, is no longer secure and can be deciphered.

Although currently no really powerful quantum computers exist on the z. If, for example, the Shor algorithm can run and which are used to decrypt messages, there is a great need for new encryption methods which decisively increase the security of the message transmission, even in the later use of any quantum computers. This is particularly important, since the first executable quantum computers were realized. For example, in 2001, at the IBM Almaden Research Center, the number 15 was broken down into its prime factors using a 7-bit quantum computer.

The search for new asymmetric encryption methods or new methods for secret key exchange in symmetrical encryption methods is therefore a currently important task, although it was already proved by Mauborgne and Vernam in 1917 that absolute security in the message transmission is achieved by the following three conditions:

1. The length of the key k corresponds to the length of the plaintext m 2. Each key k consists of an absolutely random string

3. Each key k may only be used once and must then be safely destroyed.

A method based on these principles is called one-time pad method. It is well known that these ideal one-time pad methods are perfect methods whose safety can even be proved theoretically.

However, it is currently practically impossible to generate a new random key for each message transmission between transmitter and receiver and to exchange it between transmitter and receiver.

In some areas, such as banks, abbreviated keys, e.g. TAN numbers, which become invalid after each transmission. However, the exchange of the new keys, which must permanently take place between transmitter and receiver in this way, could be intercepted under certain circumstances, so that the security is impaired.

Since messages that are encoded, for example, with one-time pad methods, are not or at least very difficult to decipher, an attacker must and will focus in particular on getting to the possession of the key k. The generation and exchange of the keys between transmitter and receiver is thus the most critical point of the entire message transmission, which is why newer methods such as quantum cryptography have been developed for the tap-proof transmission of keys.

In the field of quantum cryptography it is known that, for example, the polarization states of photons transmitted through fiber optic cables are suitable for performing quantum cryptographic tasks. A disadvantage of these known methods is the high technical complexity and the basic limitation of the possibilities of message transmission, since the transmitter and receiver must be connected to a fiber optic cable in order to evaluate the polarized photons. Special quantum cryptography protocols have been developed for the quantum-mechanical and tamper-proof key transmission between a transmitter and a receiver. Known is the so-called. BB84 protocol for quantum cryptography.

The basic idea of quantum cryptography is to skilfully exploit properties of quanta, such as the polarization direction of photons, and their superposition. From the quantum theory it follows that, for example, photons which have been polarized vertically pass with a 50 percent probability also a polarization grid rotated by 45 degrees thereto, i. In fact, 50% of the photons following the vertical grating pass the subsequent rotated grating. This property of quanta is exploited in the well-known BB84 protocol, simplified as follows:

By a random selection of a Polarisationsschemasi (vertical, horizontal) and Schemas2 (45 degrees right, left) at the transmitter and the measurement of Polari¬ sationsrichtung the passed photons and assignment of the polarization direction to the numbers zero or one - for example at Schemal: vertical = 1, horizontal = 0; and Scheme 2: right = 1, left = 0 - the transmitter produces a random number sequence of zeros and ones. For its part, the receiver then uses two detectors, which it randomly alternates, to measure the polarization direction of the received photons. Da¬ detector corresponds to the Schemal and Detektor2 the Scheme2. This also creates a random sequence of zeros and ones at the receiver, depending on which polarization direction was measured.

After that transmitter and receiver communicate via a normal public line at which photon which scheme was used. All photons and thus results that have used different schemes in the transmitter and receiver, which inevitably has to happen, since both the transmitter and the receiver randomly selected each other, are discarded. What is left is a sequence of numbers of zeroes and ones, which are identical for sender and receiver. Should a third party monitor the transmitted photons, the sender and receiver will recognize that the remaining qubits, of which S and E happen to select some for comparison, are not identical. For example, assume that if there are more than 14% of erroneous qubits between transmitter and receiver (with the same schemes), a third one has been listening. This can be used to detect the interception and the key must be discarded. Based on these and other similar methods, devices and methods for quantum cryptography have been developed.

In addition to the BB84 protocol, there are other protocol methods in which an external source supplies both transmitters and receivers with entangled photons.

However, in all methods there remains a significant range limitation.

The quantum cryptographic transmission using optical fiber cables over 67 kilometers between Geneva and Lusanne is known.

Other known methods are the use of radio links, so the transmission by air, which further increases the application possibilities.

The problem with these known methods is that one can not amplify the qubits because the gain changes the quantum state. It is therefore customary to send the qubits through fiber-optic cable between transmitter and receiver. As a result, however, the distances between transmitter and receiver are limited, currently the maximum distance is about 100 km.

A disadvantage of all the known quantum cryptographic methods, in addition to the very high technical outlay for fiber optic cables or microwave links, is the basic distance limitation, which is due to the fact that qubits have to be exchanged between the transmitter and the receiver since these contain the information for the key. However, the known methods are thus not suitable for transmitting keys over very large distances using small technical means.

Another disadvantage of classical quantum cryptography is the verification of the schemes between sender and receiver in order to determine the random string. and in determining the acceptable error rate to detect if third parties have been listening to the key.

The approach of the tap-proof transmission of messages by the use of one-time pad methods based on the quantum cryptographic Schlüsselüber¬ transmission is thus currently still insufficiently resolved.

Due to the upcoming use of quantum computers for the extremely rapid decoding of public-key methods, there is still a very great need for further developed encryption methods, in particular the simple, fast and reliable key exchange for symmetrical encryption methods.

The object of the invention is to develop a method for encryption in which a simple, faster, always possible, permanent and interceptable exchange of keys takes place between the sender of a message and the recipient of the message, for example by means of a so-called. One-time pad method to ensure transmission with maximum security. A further object of the invention is that the recipient should automatically recognize when the key was received without authorization by a third party.

The object is solved with the features of Anspruchsi.

Another object is to provide a device for encrypting messages, resp. Data, in particular for GS cryptography GS - Global Scaling). This object is achieved with the features of claim 13.

Based on a GS synchronization, a secret, random and arbitrarily long one-time key is synchronously generated or exchanged between transmitter and receiver, in which coupled local random processes are used to generate a key which is then suitable, for example based on a One-time pad method to exchange encrypted messages via conventional media. Advantageous embodiments are specified in the respective subclaims.

A very simple example of the use of the key k is described using the example of a special symmetric encryption method, the stream cipher.

It is known that in a stream cipher the plaintext m is encrypted character by character by generating a keystream k having the same length as the plaintext m. The encryption is realized in such a way that in each case a plain text character from m is linked to a key character from k. In the known one-time-pad method, the prototype of the stream cipher, both the message m and the key k are present as a sequence of bits of the same length.

For the implementation of the method, the message m is converted into a sequence of bits and the key k is a secret random sequence of bits known only to the transmitter and receiver. The encryption f is carried out, for example, such that corresponding bits of the plaintext and of the key are added to one another modulo2 or XOR (0 + 0 = 0, 1 + 0 = 1, 0 + 1 = 1, 1 + 1 = 0).

The decryption takes place, for example, in that the receiver adds the encrypted message c with its key k, which is identical to that of the transmitter, modulo2 (XOR) and thus obtains the plaintext m back.

m = f (k, c) = mod ₂ (mod ₂ (k, m))

If the key k is used in each case for only a single encryption and decryption message, then all known attacks are not able to carry out sustained decryption, because even if the key k can be calculated by intercepting a plaintext m and ciphertext c, then it is unsuitable for the next message transfer for decoding because a completely new key k is used.

The key exchange is based on Global Scaing. Global Scaling (GS) is an established physical term that illustrates that frequency distributions of physical quantities such as masses, temperatures, weights and frequencies of real systems are logarithmically scale-invariant. The publications by Hartmut Müller in Ehlers-Verlag on Global Scaling are hereby expressly included in the disclosure content of this patent application.

With the aid of the GS, it is thus possible in particular to calculate those physical values which are preferably taken up in real processes, in particular random processes.

These preferred values can be determined by a continued fraction decomposition according to L. Euler, since according to Euler it is known that every real number x can be represented by its chain break according to equation (1):

x = n ₀ + z / (Π _T + z / (n ₂ + z / (n ₃ + z / (n ₄ + z / (n ₅ + ..))))) (1)

In this case, the large z represents the so-called partial counter whose value is set to the value 2 according to GS for subsequent frequency analyzes.

Since the scale invariance occurs in logarithmic scales, all analyzes of large logarithmized to base e are performed in the GS method. This produces equation (2)

In x = n ₀ + 2 / (m + 2 / (n ₂ + 2 / (n ₃ + 2 / (n ₄ + 2 / (n ₅ + ..))))) (2)

The respective numerical values depend on the underlying units of measure. In GS the magnitudes to be evaluated are set in relation to physical constants y, the so-called calibration masses. However, these constants are known only within a given precision, which is why there are upper and lower limit values for these constants. This produces the equation (3) as the most important basic equation of the GS, which can be expanded by a phase shift of φ = 3/2, which is not relevant for the explanation of the invention, however:

In (x / y) = n ₀ + 2 / (ni + 2 / (n ₂ + 2 / (n ₃ + 2 / (n ₄ + 2 / (n ₅ + ..))))) (3)

The integer part denominators [no, ni, r) ₂ ...] must always be greater than the numerator in terms of their absolute value due to the convergence condition for continued fractions and are always divisible by 3 integers.

By applying equation (3), a given physical quantity, e.g. a frequency is decomposed according to the GS chain fraction method and converted into a so-called chain break code. This is to be described by way of example by a GS fraction breaking fraction decomposition for a frequency fo.

In GS the value 1, 4254869e24 Hz is used as the physical constant y for the calculation of frequencies.

Equation (3) results in a fraction breakage decomposition and the calculation of the partial denominators n ₀ , n i, n ₂ , n ₃ , n ₄ , etc. The calculation of the frequency values by chain breakage according to equation (3) was carried out by way of example with the GSC3000 professional tool of FIG Institute for Space Energy Research GmbH, Wolfratshausen, performed and is shown in Fig. 1 by way of example for the frequency f _o = 2O32 Hz. The frequency 2032 Hz corresponds to the so-called GS chain fraction code [-48; 9086]. The subnouncer n ₀ = - 48, the subnumer ni = 9086 or ni = 9036, depending on the limit of the Kon¬ used constant y for the frequency.

Since the divisional ni in this example (ni = 9086) is large and thus the entire quo tient vanishes from ni is low, the frequency 2032 Hz is in the vicinity of the value no (n ₀ = -48) and is therefore also known as GS node frequency be¬ draws. Further DC node frequencies according to equation (3) are for example 5 Hz, 101 Hz, 40804 Hz, 16461 kHz. A device for information processing, for example of data or signals, consists of a transmitter S and a receiver E for the analysis and manipulation of a coupled random process.

The device and the method use coupled random processes, in particular coupled noise processes as information carriers

There are a large number of possibilities for designing or developing the method according to the invention, the device and the assemblies or units. For this purpose, reference is made both to the claims subordinate to the independent patent claims and to the description of the preferred embodiments shown in the drawing.

According to S. Shnoll, more or less strong coupling effects of random processes occur when they are executed simultaneously and synchronously, i. With simultaneous measurements of random processes, the frequency distributions of the physical measured values have identical fine structures. The patterns of (non-smoothed) histograms of the measurements of several concurrent random processes are the same or similar. The representation of non-smoothed histograms is also referred to as a fine structure of the histogram in Global Scaling.

A high degree of correspondence of the fine structure can be recognized from the fact that the histograms of the underlying random processes are very similar even in their smaller expressions, so that not only their statistical parameters such as mean values, variances, etc. agree, but also the frequencies of certain Measured values in the respective histograms very often coincide. However, according to GS, this overlap is only analyzed for non-smoothed histograms.

The similarity of the fine structures of histograms or the similarity of the time course or the similarity of the rate of change of the time course of two additional processes is now defined as a measure of the actual synchronicity of random processes. In the following, random processes with a high degree of agreement are referred to as coupled random processes. The invention will be described in two embodiments with reference to a drawing closer be¬ written. In the drawing show the

Fig. 1: Tool GSC 3000 for GS analysis of frequencies

Fig. 2: Scheme for data transmission

Fig. 3: transmitting and receiving unit

Fig. 4: Background noise of a semiconductor device

Fig. 5: Harmonic components of the background noise

Fig. 6: Synchronous harmonic components of background noise in

Transmitter (upper cell) and receiver (upper cell)

Fig. 7: transmission of an encrypted message (example character "E").

Here it uses

Embodiment I Phenomena of coupled local random processes taking advantage of findings of the GS theory for transmitting and receiving a key k from a transmitter S to a receiver E, which can be explained in accordance with the prior art with a quantum physical mode and the

Exemplary embodiment II coupled local random processes at the transmitter and receiver using the findings of the GS theory for the synchronous readout of an external source, for example the global white noise with which the local random processes in S and E are synchronized under suitable conditions.

Embodiment I

For the transmission of a key from a transmitter S (1) to a receiver E (2) random processes are generated in both technical terminals S and E, which - if they run simultaneously or synchronously - Shnoll and o.g. Definition as coupled random processes.

In this method, the transmitter and the receiver are implemented by technical terminals, which firstly contain a technical noise source or the connection of a allow technical noise source and secondly, the subsequent processing steps 1-8 can perform in real time. Between transmitter and receiver is a transmission path 5 for coupled random processes.

Transmitting and receiving unit are executed in more detail in Fig. 3.

For the transmitter device 3, 4, 6, 7 and receiver device 8 to 11, a commercially available computer, for example a laptop, is used in each case. This means that in the further course the generation 3, 4, GS modulation 6, coupling 7, coupling 8 and GS demodulation 9 and information 10 of the output signal 11 of coupled random processes in a transmission path 5 for coupled random processes based on the noise processes the sound card of two commercially available computers (transmitter 1 and receiver 2) shown, see also specific disclosure of DE 102004008444.0 the applicant.

The transfer of keys k via coupled random processes is now achieved according to the invention with subsequent method steps 1 to 8. The terminals are commercially available computers. The method is abe ^"r to other devices, other sampling frequencies f ₀ and other random processes applicable. The method is falling process in particular for each technically produced and manipulable supply, for example, devices based on external or internal noise generators, Halbleiter¬, processors, modems, etc. . applicable.

The number after the subheadings of the method steps indicates the relevant reference numeral according to FIG. 3, in which the method step is executed in detail.

The exemplary embodiment I can furthermore be implemented in various technical variants, of which two methods, example la and example 1b are shown in detail by way of example: Exemplary embodiment la

In the exemplary embodiment 1 a, a commercially available computer, for example a laptop with integrated sound card, is used for receiver 1 and receiver 2, respectively. This means that in the further course the generation (3, 4) and processing (6) of coupled random processes (5) based on the noise processes of the sound card are represented by two commercially available computers S (1) and E (2).

1. coupling to a noise process (3, 4)

Tuning a transmitter and receiver to a common frequency band (e.g., from 5Hz to 16.4MHz) of a technical noise process.

To generate the noise process, for example, the sound card of a commercial computer or laptop can be used. The frequency band of the noise is thereby for example between 100 Hz and 15 kHz. Other technical noise sources would be e.g. Semiconductor elements or computer processors. A typical noise signal from a technical noise source is shown in FIG. 4 over its time course.

The noise signals of the sound card are accessed by means of software, for example by means of Windows commands, and the respective noise levels are made available to a subsequent evaluation software.

2. Sampling the Noise Process to Generate Random Numbers (3, 4) To further process the noise process, random numbers are generated by sampling the noise signal. The sampling of the noise processes at the transmitter and receiver takes place according to the invention with a GS node frequency f _o and thus leads to the generation of a GS time sequence of random numbers Z.

A suitable node frequency for the sampling of noise signals of the sound card is fo = 2031, 55 Hz, for example. Other node frequencies can be determined by means of equation (3). Thereafter, the conversion of the GS-Abtastsignales into a normalized, unitless sequence of numerical values (Z) optionally of the range N, for example, by residual class formation R modulo N (modulo operator) according to the formula Z ≡Z modulo N ₁ where N is an integer ,

This results in the transmitter S, the random number sequence Zs and the receiver E, the random number sequence Z _E. By sampling, for example, a succession of random numbers is created and displayed on the monitors of the transmitter and receiver ange¬ shows:

Zs = {... 10 23 2500 249 28 378 40456 ...} Z _E = {... 45 789 4581 45 3 6782 2360 ...}

However, the two random number sequences Zs or Z _E at the transmitter or receiver are usually not synchronized in time without technical precautions.

In order to achieve a synchronicity and thus coupling of both random processes, an exact temporal synchronicity of both processes in the transmitter and receiver must be established - as shown in Shnoll. Therefore, the noise processes at the transmitter and receiver become synchronous in time, i. always scanned at the same time.

This creates the random numbers at the transmitter and receiver synchronously in time. Technically, the synchronous sampling can be realized for example by the control of an external radio clock on both terminals. The precision of the synchronous clock should be at least an order of magnitude more accurate than the sampling frequency.

This results in the transmitter and receiver in the synchronous cycle of the period Δts = 1 / fo ⁼ tj + i-tj, for example, the following random numbers, which can be displayed by software technology on the computer screen:

Zs = {... 11 (W 80 (ti ₊₁ ) 3421 (W) .345 (t _{i + 3} ) 245 (t _{i + 4} ) 4512 (t _{i + 5} ) 5071 (t _{i + 6} ). } Z _E = {... 2345 (t _{i + 0} ) 479 (tj _{+ 1} ) 23 (t _{i + 2} ) 346 ( _{i + 3} ) 11U) 6593 (t _{i + 5} ) 5031 (t, ₊₆ ) ...} The further description of the invention is set forth in the following method steps 3-8, wherein these steps according to the invention must be realized within the sampling period Δts.

For example, if at the transmitter and receiver the last random numbers were determined from the noise at the same instant t _n- i, the processing steps must be performed on the transmitter side before the determination of the current random number from the noise Z _E (t _n ). at the receiver at time t ". Therefore the following equation applies:

For the above-mentioned sampling frequency fo of 2031, 55 Hz, the sampling period Δt _s = 1 / fo = 4.92e-4 seconds, within which the processing steps must be carried out, results in the example. This is possible with commercially available computers.

EMBODIMENT Lb

The exemplary embodiment Lb uses the timer function of a computer and can alternatively be used to implement the described steps 1 and 2. That is, the generation and processing of coupled random processes can be realized based on the temporal fluctuations of the timer function of a computer.

The basic input output system (BIOS) of a computer implements the interface between hardware and operating system (Windows, Dos). The BIOS data area 0040: 0000 - 0040: 00FF can be read directly via command lines of the operating system. At 006C in segment 0040, the BIOS stores the 32-bit value of the counter of the system clock.

This value is incremented several times per second in the BIOS each time a timer is called. The speed of this accumulation process (accumulation rate) is subject to temporal fluctuations which generate a physical noise process. The processing According to the invention, this noise process takes place in the already described steps 1 and 2.

3. Derivation of the random number sequence (3, 4)

In the further course, in the transmitter and somewhat later in the receiver according to L. Euler, a derivation of the GS time series of random numbers Z _s and Z _{E of} the form f (x) = lim ((f (x + dx) -f (x)) / dx) realized with dx -> 0.

For nonanalytical functions, as represented by the random number sequences Z _s and Z _E , however, according to Euler, dx = 1 is set, which results in equation (4).

f (x) = lim ((f (x + dx) -f (x)) / dx) with dx = 1 (4)

This results in the transmitter and receiver a new random sequence fs {} or f _E {} of rates of change of the random numbers from Z _s or Z _E. These rates of change of random numbers can also be interpreted as frequency f, wherein the sampling period Δt _s for generating Zs or Z _{E determines} the time scale.

FIG. 5 shows a possible result fs {} of the derivative of the signal Zs from a noise process according to FIG. 4.

For example, within a given frequency band from [no, ni-1] to [no, πi + 1] by a derivation according to equation (4) on the sequence Z _s at the transmitter the following series of rates of change or frequencies:

fsö = {- 1883.93 (tk _{+ 0} ) 1885.15 (tk _{+ 1} ) 1889.87 (tk _{+ 2} ) 1885.51 (tk _{+ 3} ) ...}.

For the receiver, a similar sequence of frequency values f _E {} is calculated within the same given frequency band.

4. Search for GS frequencies (3, 4) In this sequence of frequency values f _s {} or f _E {}, the sender is searched for a global scaling frequency which can be represented by a GS chain fraction code of the structure [no, ni, n ₂ ].

This is realized by performing a chain fraction analysis for each frequency determined from the sequence f _s {} at the transmitter according to equation (3) and determining the associated partial denominators n ₀ , n _1t n ₂ and so forth.

For example, within the given frequency band from [-48, -26] to [- 48, -28], ie from 1881, 13 Hz (continued fraction code: [-48, -26]) to 1891, 50 Hz (Ketten¬ break code: [-48, -28]) in the sequence f _s {} determines the frequency f _R = 1889.87 Hz for which a continued fraction code of structure [n ₀ , ni, n ₂ ] exists.

The continued fraction code for f _R = 1889.87 Hz is equal to [-48, -27, -3].

Partnumber n ₂ in this example is -3.

According to GS, the same frequency f _{R is} found at the transmitter and receiver within the frequency band, ie both original random number sequences Zs and Z _E have exactly one common GS change rate of their random numbers in the given frequency band.

This is referred to below as the resonant frequency f _{R of} both random number sequences Zs and Z _E.

5. GS modulation on transmitter side (6)

At the transmitter, the GS modulation takes place, for example, by a change of the partial denominator n ₂ , for example by a sign reversal of n ₂ . This results in the following new chain fraction code [no, rii, -n ₂ ] on the sender side and a new frequency f _R 'by reversing Equation (3).

In the example, the GS chain fraction [-48, -27, -3] belonging to f _R = 1889.87 Hz is changed to [-48, -27, +3], ie, the partial denominator n ₂ = -3 is replaced by sign reversal on n ' ₂ = + 3 set. This results in the new frequency f _R = 1882.97 Hz after application of Equation (3).

Also, this frequency f _R ¹ mathematically represents a rate of change of the random numbers and by reversing the derivation according to L. Euler from equation (4) the new random number Z _s (t _n ) is calculated in the sender based on this ¬ which is coupled to the transmitter at time t _n in the noise process.

Since all method steps were carried out within the sampling period Δts, the manipulated random number Z's (t _n ) were calculated on the transmitter side, before a new random number was generated at the transmitter or receiver via the noise process.

The inverse of equation (4) is possible because the derivation of equation (4) represents a unique deterministic method. For the same reason, equation (3) is also reversible.

In the example, the new random number Z's (t _n ) = 192 has arisen and, at time t _{n, the} following series of random numbers result:

Zs = {... 11 (U) 80 (t _{l + 1} ) 3421 (t _{i + 2} ) 345 (U) 245 (t _{l + 4} ) 4512 (U) 50712 (U) ... 192 (t) )}

6. Coupling or Physical Generation of the Newly Computed Noise Value (7) The newly calculated random number Z ' _s (t _n ) is converted into a dimension-dependent noise signal value and coupled into the random process within the sampling period. This conversion is possible since the method of converting the noise spectral value into random numbers from the preceding method steps is known and reversible.

In the example of generating the random numbers by means of the noise of a sound card, the new random number (Z's (t _n ) = 192) is thus converted into a noise value on the transmitter side and physically output via the sound card. Due to this coupling in of the noise level value belonging to Z ' _s (t _n ), the noise was modulated on the transmitter side.

7. Decoupling or Demodulation on the Receiver Side (8, 9) Since the random processes of the transmitter and receiver were synchronized by the DC node frequency and are coupled to one another by temporal synchronicity and have very specific, identical resonance frequencies or rates of change For a short time, the noise process on the receiver side also changes.

In particular, they are physically coupled to one another by entangled quantum states, since the resonance frequencies of both random processes correspond to a quantum of the frequency f _R.

The noise signal in the receiver is coupled out by sampling with f ₀ at time t _n and converted into random numbers by the same method as on the transmitter side.

It appears on the receiver side at the sampling time f _n with high probability the fed into the transmitter random number (in the example Z ' _E (t _n ) = 192), but in any case a random number ZΕ (t _n ), which in the subsequent derivation of the sequence Z _E according to L. Euler (equation (4)) at the receiver causes the defined resonance frequency f _R '.

In the following it will be described how this transmitter-side manipulated resonant frequency f _R ^! is found and decoded on the receiver side.

According to the invention, the receiver analyzes all available frequencies for the frequency band from [n ₀ , π _1-1 ] to [n ₀ , ni + 1] previously determined by the transmitter and based on the newly determined random number Z ' _E (t _n ) within the frequency band by a GS analysis and determines the unique frequency f _R for which the continued fraction code [n ₀ , ni, -n ₂ ] exists.

For this frequency f _R , the divisional n _{2 is} determined. For example, based on the last random number received within the band of frequencies agreed with the transmitter from 1881, 13 Hz (continued fraction code: [- 48, -26]) to 1891, 50 Hz (continued fraction code: [-48, -28] ) of the sequence f _E {} has the common frequency f _R = 1882.969 Hz, for which a continued fraction code of the structure [n ₀ , ni, n ₂ ] exists. The continued fraction code for f _R = 1882.969 Hz is equal to [-48, -26, +3]. The participant n ₂ is +3.

8. Decoding the transmitted information (10)

By comparing the determined continued fraction code with the code determined according to GS, the receiver can now detect whether the n ₂ value has been manipulated on the transmitter side.

For example, according to GS, the expected sign of n _{2 can} be determined mathematically solely from the combination of sampling period Δts, no and ni, since the frequency band is uniquely determined by no and ni by the expected global scaling resonance frequency f _{R of} the random process got to.

In the example of Δt _s = 4.92e-4 seconds, n ₀ = -48 and n- _t = -27, a frequency f _R with the associated continued fraction code [-48, -27, -n ₂ ] is expected on the receiver side, which for the non-modulated case in the transmitter on the receiver side also applies.

In the example of the modulation shown in the receiver, however, the analysis of all frequencies within the frequency band agreed with the transmitter only gave the frequency f _R = 1882.969 Hz, for which a continued fraction code of the structure [nθ, n1, n ₂ ] exis ¬ tiert. And the continued fraction code for f _R = 1882.969 Hz is [-48, -26, +3]. Partnumber n2 is +3.

However, since an n ₂ value of -3 was expected on the receiver side, the receiver has learned that the n ₂ value of the resonant frequency f _{R has been} modulated on the transmitter side. Thus, the receiver recognizes the manipulation on the transmitter side, if it is present. According to the invention, the manipulation from the transmitter side is coded with the bit value 1 and the non-manipulation with the bit value 0.

Thus, a bit of information has been transmitted between transmitter and receiver via the underlying, coupled noise process by GS modulation and GS demodulation of a common resonant frequency f _R.

Due to the possibility of transmitting a bit of the key k thus arbitrarily long key from the sender S to the receiver E are transferable.

The technical transmission rate via the random process shown here is determined and limited by the processing speed of method steps 1-8 and the sampling frequency f ₀ . An increase in the transmission rate is possible, for example, through the use of other sampling frequencies fo, faster computers, improved GS modulation of the continued fraction n ₂ (or higher elements of the chain fraction n ₃ , n ₄ , etc.) or the parallel use of multiple transmission channels.

Embodiment II

The coupling of transmitter S and receiver E to a local random process, for example a thermal noise process of a semiconductor component, takes place according to exemplary embodiment I, method steps 1-3.

This results in the transmitter and receiver again a new random sequence fsO or fε {} of random numbers or rates of change of random numbers from Z ₃ and Z _E. These rates of change of random numbers can also be interpreted as frequency f, the sampling period Δt _s for generating Z _s or Z _{E determining} the time scale.

FIG. 5 again shows a possible result f _s {} of the derivative of the signal Zs from a noise process according to FIG. 4. The receiver is calculated within the same predetermined frequency band, a similar sequence of frequency values fE {}, based on a local random process.

By way of example, this results in the following almost synchronous random process at the transmitter and receiver, which corresponds to a synchronous rate of change of its underlying noise processes and can be understood as a consequence of numbers. The ordinate contains the frequency values which can be abstracted as numbers (FIG. 6).

By defining suitable threshold values, it is possible to calculate from the synchronous harmonic components identical numerical sequences fs and fΕ which can be output as decadic numbers or as bit patterns, see FIG. 6:

Thus, in this embodiment, both in the transmitter S and in the receiver E arbitrarily long, identical numerical sequences are generated, which are used in the other as the key k.

By means of the method according to the invention, which has been described in two exemplary embodiments, a key can be exchanged between a transmitter S and a receiver E, which key is known only to the transmitter and receiver and can therefore be used for symmetrical encryption.

In the receiver, the key k is used for encrypting the message m according to c = f (k, m) and in the sender for decryption according to m = f (k, c). This allows messages m between transmitter and receiver to be exchanged via conventional media and yet can not be deciphered. In particular, they can not be deciphered if the key ki is used only for a single transmission and thereafter a renewed key k ₂ is used.

Since the key exchange of k in the exemplary embodiments can be understood as a physical model of the entanglement of quantum states, for example of photons, since they have the same physical effects, the sensor recognizes catcher in the event that the transmitter is not synchronized with the desired recipient E but a third party E 'and exchanges the key with this.

In the embodiment I, the synchronicity is created by targeted manipulation of the selected chain fraction code [n ₀ , n ^ n ₂ , ...], which mathematically corresponds to a manipulation of entangled quantum states and therefore can not be bugged unnoticed.

In the exemplary embodiment II, the synchronicity is created by high precision when ausle¬ sen the local random processes. Only if the times of the read-out at the transmitter and at the receiver take place exactly at the same time, wherein the term "exact" is to be selected depending on the application and bandwidth, a synchronization arises as a result of the method steps from step 3.

The exact read-out thus represents a quantum-physical measurement process. For example, if 3 or more devices are used which scan the exact same time of the noise processes, then there are exactly two that achieve the synchronicity. These processes then remain in sync to generate the key until the abort is enforced by the user.

The third or further measuring process can not be synonymous with the two. Thus, should an unauthorized third party intentionally synchronize with the transmitter because it knows the exact time of scanning, the receiver receives a non-synchronous sequence of numbers which can not be used as a key. By using the protocol GSKT04 described below, the sender and receiver are recognized and the synchronization process would have to be restarted.

He can then inform the sender immediately and start a new key exchange.

If S and E have exchanged a common, secret and sufficiently long key k, numerous encryption algorithms can be implemented, whereby the GS 004-P / WO

The simplest variant is the modulo2 or XOR operation between key k and plaintext m.

At an agreed point in time t ₀ , the key k = {11001011} is generated at the sender and receiver with which the message is encoded, in the example the letter "E", m = {E} = {10100101} By f = XOR (k , m) the secret message c = {01101110} is generated and is decoded at the receiver with the function f = XOR (k, c), resulting in the original message m '= {E} again, see FIG here the key to the enciphering and the decoding key 40. The plaintext 31 of the letter "E" in ASCII is to be transmitted. The encrypted text 32 is deciphered and is again read as plain text 41 of the letter in ASCII.

Further possibilities of the encryption with the key k are not to use this key XOR to the message m, but to use the key for a function f, for example, for byte substitution or cyclic shift of bits or bytes of the message or any other transformations that in Emp¬ catchers are reversible.

Since the synchronous key k for transmitter and receiver arises only when two devices process the random processes synchronously at the same time and synchronously, the time and the sampling frequency must be known for both devices. However, the first agreement on the time could possibly be intercepted, so that a third party can try at exactly this time to intercept or read out the key.

According to the invention replace the transmitter and receiver, therefore, at the beginning of Schlüssel¬ transmission based on agreed i bits of the key K of a two-known message ΓTIK _ENNUNG that, when k is identical with encryption by k to be identical at the transmitter and receiver must.

If the receiver was or was not in sync with the sender during the key transmission, it has another random number sequence k ', which it interprets as key k'. By decoding the secret message C _KENN U _NG transmitted by the sender, is then not the agreed plain text ΓΠKENN _U N _G, ie ITIKENNUNG) <> f (k \ C «ENN _UNG ). SO that the receiver notifies the sender to stop the synchronization via conventional forward paths. After this, the sender and the receiver again try to generate a key synchronously until the receiver receives the agreed clear text ΓΠK _ENNUNG . Thus, the key k is synchronous between transmitter and receiver and can no longer be intercepted by third parties.

The generation of the key k can take place immediately before or during the message transmission or at any other time known to both parties.

At the end of the k-encrypted message transmission, the next exact time of synchronous key generation is transmitted so i.a. only sender and receiver know the exact coordinates of the next key generation and the likelihood of external synchronization can be reduced. Otherwise, according to the o.g. The key exchange process is repeated until the sender and recipient exchange the known and agreed clear text ITICENCE and thus the key k is identical to both.

If a third party receives the key k that he believes he has received the sync key of the transmitter, because the received represents according to the quantum physical model a measurement process that is no longer reversible. Thus, the above-mentioned method is also suitable for realizing the first and thus critical start of a key generation, even if unauthorized persons have experienced the exact time of the synchronization, which with exactly the same frequency [no, ni, n ₂ ,...] would have to take exactly the same time points, which is unlikely. If such an unauthorized person receives the key, the receiver notices it according to the above-mentioned method of identification transmission and the key exchange starts again. The next exact times of the key generation are transmitted in deciphered form, so that listening is no longer possible.

To improve the security of the key exchange, a GSKT04 protocol is defined in which the sender continues and cyclically after an agreed cycle time a defined plaintext IΎI _KENNUNGI . For example, sends the name of the sender, who must ent¬ the recipient after decrypting with his key as plain text and gives the recipient the security to decrypt with the correct key k. Since there can only ever be a single pair of transmitters and receivers which receive the same key k through the GS synchronization, this ensures that if the plaintext is correctly recognized ITI _KENN U _NGI = f (k, c) within transmitter and receiver continue to use the same key for a short cycle time and therefore, from a physical point of view, no third party can possess this key and decrypt the message.

Another possibility is the direct comparison of selected bits between sender and receiver. If the error rate exceeds a previously defined value, the entire key is discarded.

Thus, a currently known method - physically justified - fully wireless and wireless, non-decipherable message transmission guaranteed.

The generation of secret, unique keys between transmitter and receiver is realized by effects based on the GS communication, and the message transmission of the payload is then carried out by conventional means, but encrypted with the secret key k, which, since i.a. is used only once, which makes decryption impossible or almost impossible.

The low complexity of the key transmission and thus of the encryption spielsweise as described in the exemplary embodiment of only two commercially available laptops, allows an efficient encryption of messages and thus a wide range of applications, for example in industry and banking.

In order to avoid the disadvantage of the long keys, since with the one-time pad, the key must be just as long as the message, the method can also be expanded and used, for example, for block ciphers. The method thus has all the advantages of the most modern known quantum cryptographic methods and in comparison to these the additional advantage that it aus¬ without any cabling between the transmitter and receiver, ie without fiber connection aus¬, since the key exchange via coupled random processes, such as the coupling of local thermal noise processes with the global Hintergrundrau¬ rule takes place.

Since the transmission via the background noise by means of coupled random processes can also be explained by quantum physical models, in particular the entanglement of quanta, and uses these effects or has the same phenomenological effects, any eavesdropping can be recognized by third parties, since the result the key changed and this can be detected at any time via the GSKT04 protocol.

Claims

claims

1. A method for encrypting data in which the secret key by Global Scaling cryptography based on resonant frequencies coupled Zu¬ case processes are transmitted and these keys are used to encrypt messages.

2. The method according to claim 1, characterized in that the modulation, data transmission and demodulation takes place on the basis of technical noise processes.

3. The method according to claim 1, characterized in that for the modulation, transmission and demodulation stationary or mobile digital transmission and reception devices are used.

4. The method according to claim 1 to 3, characterized in that on the Modulati on, transmission and demodulation stationary or mobile, commercially available Com¬ computers are used with integrated or external noise source.

5. The method according to claim 1, characterized in that the transmission via stationary or mobile analog and derived therefrom transmitting and Empfangsgerä¬ te takes place.

6. The method according to any one of the preceding claims, characterized in that the transmission is used for medical purposes.

7. The method according to any one of the preceding claims, characterized in that the transmission is used for the transmission of passwords, PIN codes or other security relevant applications.

8. A method for encrypting data or signals according to claim 1, using a transmitting unit with a modulator for modulating the Informa¬ tion and with a Einkoppler for coupling the information into a random process, a receiving unit with a demodulator for demodulating the Infor¬ mation and an output coupler for decoupling the information from the random process, characterized in that the data transmission via coupled random processes takes place.

9. The method according to claim 8, characterized in that a global scaling modulator or a global scaling demodulator is used as modulator and demodulator.

10. Method according to claim 8, characterized in that a noise or random signal of a noise or random signal generating element or process is used as the signal or signal generating element for the input and output coupler and / or the modulator / demodulator, preferably technical noise or random signals or processes such as thermal or white noise or noise or random signal elements such as a noise diode.

11. The method according to claim 8, characterized in that at least one element of the continued fraction code [no, n ^ n ₂ , n ₃ , ..] of the resonant frequency f _{R is} modulated, for example by sign reversal.

12. The method according to any one of the preceding claims, characterized in that it comprises the following method steps:

Generation of a noise signal in the transmitting and receiving unit (S, E), preferably an electrical noise signal Sampling of the noise signal with a GS node frequency f ₀ , preferably a nO frequency for generating a sampling signal conversion of the GS-Abtastsignales in a normalized, unitless sampling signal in the form of numerical values (Z), preferably by residual class bildunq R modulo N (modulo operator) according to the formula Z ≡Z mod G, where G is an integer and can represent the measured noise level.

Derivation of the numerical sequences Z _s and Z _E according to L. Euler for the generation of a sequence of frequencies fs and h-

Determining the resonant frequency f _R within a given Frequenz¬ band

Modulation of the resonant frequency f _R, for example by sign reversal of the element n ₂ from the chain fraction code [no, ni, n2] demodulation and decoding of the changes made in the receiver unit on the transmitting side.

13. Device for encrypting data or signals, consisting of a transmitting unit with a modulator for modulating the information and with a Einkoppler for coupling the information into a carrier wave, a Empfänger¬ unit with a demodulator for demodulating the information and a decoupler for decoupling the Information from the random processes, in particular for a method according to one of claims 1 to 12, characterized in that the transmission takes place via coupled random processes.

14. Device according to claim 13, characterized in that the modulator and demodulator is a DC modulator or a DC demodulator.

15. Device according to claim 13, characterized in that the transmitting unit and / or the receiving unit has a noise or random signal generating unit, preferably an electrical or electronic noise signal generating element, e.g. a noise diode.

16. A device according to claim 13, characterized in that the noise or Zufallssignaierzeugungseinheit or their signals are part of the modulator and / or the Einkopplers.

17. Device according to claim 13, characterized in that it comprises a GS scanning unit, so that the noise signal can be sampled with a GS frequency in order to obtain a GS-clocked random process.

18. Device according to claim 17, characterized in that the sampling frequency is a GS node frequency, preferably a pure nO frequency.

19. Device according to claim 13, characterized in that it contains a commercial device, preferably a stationary computer (computer), a mobile computer, e.g. Laptop or a mobile phone.

20. Device according to claim 13, characterized in that the receiving unit contains a medical, therapeutic or diagnostic device, preferably a pacemaker.

21. A modulator or demodulator for modulating or demodulating the information for a device for encoding data or signals, comprising a transmitter unit with a modulator for modulating the information and with a coupler for coupling the information into a random process, a receiver unit with a demodulator for demodulating the information and an output coupler for decoupling the information from the random process, ins¬ particular for a method according to any one of claims 1-12, characterized gekenn¬ characterized in that the modulator or demodulator is a global scaling modulator or Global scaling demodulator is

22 modulator or demodulator according to claim 21, characterized in that it is a device or a unit that GS modulated natural noise or random signals or GS-dernoduliert, preferably at least one global-scaling resonance frequency of two coupled random processes.

23. Use of a noise or random process, noise or Randallsprozess¬ signal or device for noise or random signal generation for wireless sen information transmission of a useful signal by means of coupled Zufallsprozes¬ se.

24. Use of a process according to claim 23, characterized in that the noise or random process or the noise or random process signal or the device for noise or random signal generation for input or Auskopp¬ development of the random processes and / or modulation or demodulation of Useful signals is used.

Use according to claim 23, characterized in that the noise or random signal of a mobile telephone or of a stationary or mobile computer, e.g. a laptop, is used.