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    • 专利摘要:
    The present invention relates to a pseudo-random signal generator and a secure communication system containing said generator. Both the emitter and the receiver of the system contain the pseudo-random signal generator that consists of a phase difference detector fed by the signals of two coupled chaotic oscillators. Encryption consists of masking the message or plain text, divided into blocks, in the difference of phases to form the encrypted message that is sent to the receiver through the communication channel. The receiver uses the same static key as the sender, to synchronize its oscillators with those of the sender by means of a pair of dynamic keys that are generated and sent by the sender through two synchronization channels. Therefore, the phase difference at the receiver will be the same as at the sender and the sender will be able to decipher the message. (Machine-translation by Google Translate, not legally binding)
    公开号:ES2848623A1
    申请号:ES202130538
    申请日:2021-06-11
    公开日:2021-08-10
    发明作者:Alexander Pisarchik；Pasquín Fco Javier Martín；Parth Chholak
    申请人:Smart Human Capital S L；Universidad Politecnica de Madrid；
    IPC主号:
    专利说明:

    [0004] TECHNICAL SECTOR
    [0006] The present invention falls within the field of encryption of information flows in secure communications. Specifically, it is framed within the field of procedures based on chaotic systems.
    [0008] BACKGROUND OF THE INVENTION
    [0010] In a simple case of communication where a message is sent from a sender to a receiver, the message is encoded by the sender by a procedure in such a way that only the receiver is capable of decoding it. The encrypted message is called an encrypted message and it is sent to the receiver through the communication channel. This message consists of a flow of information combined with an encryption token. Sender and receiver generate this signal for the encryption and decryption of the message, respectively.
    [0012] Using encryption, authentication and access control technologies to secure communication systems is an adequate solution to prevent espionage attempts and theft of data transmission. One contribution to solve this problem is to use signals generated by components that operate in the non-linear regime, such as chaotic oscillators. Chaotic cryptography is based on the use of chaos theory on secure communication systems.
    [0014] Chaos theory studies deterministic systems with high sensitivity to small changes in initial conditions and parameters. In general, chaotic systems show sudden and dramatic changes that give rise to a behavior that describes the non-periodic temporal evolution of the system. That is, it never repeats itself and is apparently random, but completely deterministic.
    [0016] In the state of the art of communication systems that use chaotic systems to encrypt information, the transmission of the key is required for decryption. Among the patents that use these methods we can mention: Bianco US5048086A and Weiss US5479512A, which consist of generating a sequence of random numbers in digital format produced by a chaotic system, the message to be encrypted in digital format and the combined signal are attached It is transmitted. The receiver extracts the digital message from the combined signal transmitted using a key that generates the same sequence of random numbers in digital format, produced by a chaotic system. The great disadvantage of this method is the decrease in security as a result of the transmission of the key. Also, this method makes random access to the information channel difficult, that is, the receiver must listen to the channel from the beginning of the transmission by the sender and retrieve the complete message, otherwise they will not be able to access even part of the message that is being transmitted . Random access is necessary for real-time communications.
    [0018] One way to solve this problem using chaotic systems for secure communications where key transmission is not required is shown in Carroll US5473694A and Cuomo US5291555A patents. In summary, they describe a method that consists of modulating a parameter of a chaotic signal with a signal that carries the information or adding a signal that carries information to a chaotic signal. The resulting chaotic signal is transmitted using conventional transmission technologies from a transmitter containing an encoder to a receiver containing a decoder. The decoder in the receiver synchronizes the chaotic signal from the receiver with the original chaotic signal without the need for key exchange. Comparison of the resulting chaotic signal with the synchronized signal makes it possible to extract the original information. Furthermore, this method admits random access to the information channel since the receiver can synchronize with the sender at any moment of the transmission. However, these secure communication systems that use synchronization have a deficiency, if the transmission is intercepted, it is possible to reconstruct the state space to find out the underlying dynamics of the transmission encoder, allowing the information signal to be extracted using another non-linear generator system. chaos or other technology.
    [0020] These secure communication systems based on chaotic signal synchronization have a weakness against attack by synchronization. Synchronization-based secure communication systems use chaotic non-linear systems coupled in a master-slave configuration, where the master represents a transmitter and the slave a receiver, the output signal of the transmitter is used to encrypt or mask the information signal.
    [0022] The brute force attack by synchronization of these communication systems includes the interception of the communication channel and the simulation of the receiver by a virtual model that adjusts all the parameters until the best synchronization or the smallest synchronization error is reached. When the transmitter and the virtual receiver reach the same parameter values, it is when there is complete synchronization between these two systems and the extraction of the information signal is obtained by comparing the synchronized signal of the virtual receiver with the signal of the transmitter. Synchronization attacks in secure communication systems based on chaotic signals are described in the following articles: M. Zanin, R. Sevilla-Escoboza, R. Jaimes-Reátegui, J. García-López, G. Huerta-Cuellar & AN Pisarchik, "Synchronization Attack to Chaotic Communication Systems", Discontinuity Nonlinearity and Complexity vol. 2, 333 (2013); and JH García-López, R. Jaimes-Reátegui, R. Chiu-Zarate, D. López-Mancilla, R. Ramírez-Jiménez & AN Pisarchik, "Secure Computer Communication Based on Chaotic Rossler Oscillators", The Open Electrical & Electronic Engineering Journal vol. 2, 41 (2008).
    [0023] Synchronization sensitivity to parameter changes in chaotic systems is crucial for communication security. A small variation in one of these parameters can produce such a large timing error that recovery of the information signal is impossible. Likewise, we can consider two types of parameters: the parameters related to the chaotic emitter and receiver systems, and the parameter underlying the synchronization time. The threshold value of this last parameter being essential to achieve complete synchronization. For values less than this synchronization time, complete synchronization is not achieved and information retrieval is impossible.
    [0024] In the following publication, the problem of the synchronization attack is solved by varying one of the parameters of the emitter and receiver oscillators simultaneously in time intervals shorter than the synchronization time: AN Pisarchik, M. Jiménez-Rodríguez & R. Jaimes-Reátegui, "How to Resist Synchronization Attacks", Discontinuity, Nonlinearity, and Complexity vol. 4, 1 (2015). Basically, the parameter is varied using a function that generates a sequence of values from a seed that makes up a secret key known only to the sender and receiver, therefore, only they are capable of synchronizing. An attacker who uses a virtual system to try to synchronize with the emitter's oscillator can never reach it since before he can poll the value of the parameter, it changes and the attacker must restart the process. The disadvantage of this method is that it eliminates the possibility of random access to the information channel by the receiver. This is because the receiver does not know at what moment the sequence of values used to vary the parameter of the oscillators began to be generated, so that, even if it knows the value of the seed, it will not be able to synchronize if it does not start to listen to the communication channel at the moment the transmission begins.
    [0025] The technological references found in the state of the art are based on stream encryption, that is, on combining the information with a pseudo-random signal. This signal is usually one of the signals produced by a chaotic oscillator in the emitter that generally exhibits high autocorrelation for moderately wide time increments. This means that there may be portions of information in the encrypted signal that correspond to more or less similar values of the pseudo-random signal in relatively small time intervals. This behavior leads to the exposure of some of the information to statistical attacks, which results in a significant reduction in the security of the encryption.
    [0027] EXPLANATION OF THE INVENTION
    [0029] The present invention solves all the problems previously posed by means of a new high-security communication system that encrypts the message in blocks using a novel pseudo-random signal generator based on the phase difference between two chaotic oscillators.
    [0030] In recent studies it has been detected that the phase difference between two chaotic oscillators in phase synchronization has properties similar to noise as shown in: AN Pisarchik, G. Huerta-Cuellar & CW Kulp, "Statistical Analysis of Symbolic Dynamics in Weakly Coupled Chaotic Oscillators ", Communications in Nonlinear Science and Numerical Simulation vol.62,134 (2018). In this article it can be seen that it is very difficult to reconstruct chaotic attractors from the difference of phases. In addition, the degree of autocorrelation of the phase difference compared to that of the chaotic signal of one of the oscillators is lower, which brings together some very interesting characteristics to be used as a pseudo-random signal for secure communication systems.
    [0032] Taking the foregoing into account, in the present invention, the emitter and the receiver each have a pseudo-random signal generator. They are twin generators and each one consists of two chaotic oscillators coupled in such a way that they can achieve phase synchronization, and whose output signals feed a phase difference detector. At the transmitter, the output signal of the phase difference detector is combined with the information signal of the message in an encoder to obtain the encrypted signal that will be sent to the receiver through the communication channel. At the receiver, this signal from the phase difference detector is combined with the encrypted signal received at a decoder to extract the information signal from the message. In order for the receiver to be able to correctly decode the message, it must generate the same output signal as the emitter in the phase difference detector. This is achieved by implementing two synchronization channels. Through each of them, the emitter sends a signal from each chaotic oscillator to the receiver, which uses these signals to couple its oscillators with those of the emitter in order to achieve full synchronization. When the receiver reaches synchronization, the signals from its oscillators that feed the phase difference detector are the same as those generated by the emitter's oscillators. Therefore, the receiver will generate the same phase difference signal as the emitter and the decryption will be correct.
    [0034] To increase security, the present invention provides a new system whereby the message is encrypted in blocks. To do this, the message is divided into information blocks that are encrypted in consecutive cycles. Each cycle consists of the transmitter sending a pair of synchronization signals to the receiver generated from new random initial conditions of the chaotic oscillators. Subsequently, these synchronization signals are stopped and the phase difference signal begins to be generated to combine it with the corresponding block and send it to the receiver. In this way, since each of the blocks corresponds to a different pair of synchronization signals, the receiver must synchronize with the transmitter to decrypt each of the blocks. These synchronization signals have the function of dynamic keys, they are unique for each block and are public.
    [0036] To avoid synchronization attacks, a function is implemented that uses a chaotic map to generate an ordered sequence of values that takes a parameter from the chaotic oscillators at both the sender and the receiver. From the beginning of communication, the haters parameter changes its value in less time than the sync time. So the initial conditions and the parameter of the function form a secret static key that only the sender and receiver should know. This system allows the dynamic keys to be public and, in an attack on the system, they cannot be used to decrypt the message blocks. In addition, the sequence of parameter values generated by the chaotic map is repeated for each block of the message, which solves the problem of random access, that is, if the receiver begins to listen to the communications channel at a time after the start. of the transmission by the sender, the first will be able to unencrypt the blocks after the start of the listening. Another important characteristic of the system due to its special design is that it allows its implementation in parallel, which is important when integrating it into computer architectures with several processing cores.
    [0038] Pseudo-random signal generator (figure 1)
    [0040] The invention comprises a pseudo-random signal generator that is present in both the transmitter and the receiver. This signal generator is one of the claims of the present invention and comprises two chaotic oscillators with a coupling, which allows them to achieve phase synchronization, and a phase difference detector.
    [0041] In a preferred embodiment, the pseudo-random signal generator, (figural), comprises a system of differential equations that represent the dynamics of the chaotic oscillators over time:
    [0046] where the initial states are different, ui (t0) / u 2 (t0) - For simplicity, we consider that both oscillators are identical in master-slave configuration, in such a way that f: R d ^ R d describes the time derivatives of the state variables of each of the isolated oscillators yg: R2d ^ Rd represents the coupling function that allows the oscillators to achieve phase synchronization, where d is the degree of freedom of the system. In a particular embodiment, for the case d = 3, the state variables of the master oscillator can be represented by the state vector u 1 ( t) = [x1 ( t), y1 ( t), z1 (t)] T , and those of the slave oscillator by u 2 (t) = [x 2 (t), y2 (t), z2 (t)] T. The state variables represent the signals that the oscillators generate. The phase difference between the two oscillators 0 ( t) = 02 () - <pi ( t) is a pseudo-random signal, where <pi ( t) and 02 () are the absolute phases of the master and slave oscillators with respect to a reference instant t rcf which can be obtained from the state vectors u 1 (t) and u 2 (t) by means of a conventional transformation carried out in the phase difference detector. Also, if the initial states are chosen to be random, then the phase difference represents a signal random.
    [0048] Block cipher system (figure 2)
    [0050] The purpose of the secure communications system is to be able to send an encrypted message from the sender (10) to the receiver (20) by masking the message or plain text m (r) in a random signal r E (t) generated at the sender . Only the receiver has the ability to reproduce this signal and, therefore, to separate the plaintext from the encrypted message because it can be synchronized with the sender. The message (or plain text) consists of a signal that we can divide into M contiguous blocks m¿ (r) for t¿_ i < t < t , ¿ei = 1, ..., M, where m (r) = U im í ( T) the complete message to be transmitted and A r inf0 = n - r¿_i the duration of the blocks.
    [0052] We define the ith cycle as the time interval during which the dynamic keys and the encrypted block m¿ (r) are sent. A cycle starts at tz0, ends at t ^ n and is divided into two intervals:
    [0054] • The asynchronous interval whose duration is A íasinc = t * cf - tz0 and is wide enough so that the oscillators of the emitter are completely synchronized with those of the receiver. At t z0 , new random initial states are generated for the sender by means of an entropy source (9) and, then, the sending of the dynamic keys begins until instant t * cf is reached.
    [0056] • The synchronized interval whose duration is A tsinc = fñn - t * cf and, during which the block m ^ r) is encrypted, sent and decrypted, so it is necessary that A tsinc> A r inf0. The interval begins at t * cf, which is the reference time for the phase difference in both the emitter and the receiver.
    [0058] The total duration of a cycle is the sum of the durations of the previous intervals, that is, A icici0 = A íasinc A tsinc. Then, to send the complete message, M consecutive cycles are used and a total time of MA iciCi0 is needed (Figure 3 shows the system signals in two consecutive cycles).
    [0060] We call encryption the procedure that consists of masking each of the blocks m¿ (r) in the phase difference 0 ^ ( t) produced in the emitter, and which gives rise to the encrypted signal s ( t) = mE ( t) r E ( t) that is sent to the receiver through the communication channel (22), where
    [0062] mE (t) J m¿ (r) si t) .cf <í <ífln j ^ E (¿)
    [0063] y ^ E (t)
    [0064] and 0 otherwise, 0 otherwise,
    [0066] where mE ( t) is the information signal, which is generated by an input buffer (6), and r E (t) is the random signal generated in the emitter, as mentioned.
    [0068] In a preferred embodiment, the pseudo-random signal generator of the emitter (5) The system comprises differential equations that represent the dynamics of chaotic oscillators over time t e [íq, t zñn]
    [0070]
    [0072] the initial states uEl (io) = uE2 (tO) and a phase difference detector (14), where c is a parameter of the chaotic oscillators that can be adjusted, as discussed below. In this embodiment, the oscillators are coupled using only the state variable yEl.
    [0074] Decryption system
    [0076] We call decryption to the procedure that occurs in the receiver (20) and that consists of bringing each of the blocks m¿ (r) of the encrypted signal s ( t). This process is only possible if, during the synchronized interval, the receiver is capable of generating a phase difference 0lK ( t) that is the same difference 9 ^ ( t) that is generated in the emitter (10), and that of place to the information signal recovered at the receiver mR (t) = s ( t) - r R (t). Consequently, it must be satisfied that r R (t) = r E (t), where
    [0081] It is the random signal reproduced in the receiver thanks to the synchronization between transmitter and receiver.
    [0083] In order to avoid different attacks based on cryptanalysis, it is imposed that the initial states uEl (iO) and uE2 (¿0) in the issuer are random. Therefore, for the condition r R (t) = r E ( t) to be fulfilled, the sender sends, in addition to the encrypted signal, two non-chronization signals, sl (t) and s2 ( t), which contain the dynamic keys. This procedure consists of sending two state variables of the emitter, one of the variables of the master oscillator and the other of the slave oscillator, through two synchronization channels (23, 24). Once at the receiver, these signals are used to couple the master oscillators and slave oscillators during the asynchronous interval, the duration of which must be long enough for them to reach full synchronization.
    [0085] In the previous embodiment, in which the oscillators of the emitter (1, 2) are represented by equations [1] and [2], the pseudo-random signal generator of the receiver (15) comprises the system of differential equations representing the dynamics of the oscillators chaotic over time
    [0090] where the initial states uri (í q) and u R2 (tg) are arbitrary. Furthermore, the receiver (15) comprises a phase difference detector. The function h: R 2d ^ Rd represents the coupling (19, 21) between the emitter and receiver oscillators, and k is the coupling force parameter that takes the necessary value for full synchronization to occur during the asynchronous interval , that is, when si ( t) / 0 and s2 (t) / 0, being null in any other case.
    [0092] Then, in the same preferred embodiment, the synchronization signals consist of
    [0094] P e í (¿) if 4 <i <í * cf
    [0095] (t) J ^ E2 (¿) If 4 < t <t c if (t) and s2
    [0096] 0 otherwise, 0 otherwise,
    [0098] In both cases, for safety, avoid sending the initial conditions x j ^ t g) and x j ^ tg).
    [0099] The system allows random access to channels (22, 23, 24) so that if <* 0 and t'ñn > t¡fn, the receiver can access the complete message m (r). If, on the contrary, t'0> and / or C < tffn, the receiver can still decrypt some blocks and, therefore, access a part of the message depending on the time during which it accesses the channels. In any case, if tr (í) = r E (í), the information signal recovered in the decoder is
    [0101] If t (.cf < t <fñn
    [0105] The output buffer (16) is in charge of concatenating the blocks m ^ r) that make up the decrypted message.
    [0107] Protection against sync attacks
    [0109] To avoid the synchronization attack, both the emitter (10) and the receiver (20) have a generator of the parameter c (8, 18) based on a discrete chaotic map. This device changes the parameter value of the chaotic oscillators in fixed time intervals A tc much smaller than the time that an attacker would need for full synchronization if he had access to the synchronization channels, that is, A tc <A íasinc. So, if we divide the time interval for the ith cycle into N subintervals, such that A tcici0 = NA tc, to each subinterval, from n = 0 to n = N - 1, there corresponds a value of c that is obtained by the function cn + 1 = tp ( cn, vn + i; p), where vn is the nth value of a chaotic map and p a parameter of the same that is part of the static key of the system. Likewise, the initial values c0 and v0 are also part of the static key. The function p produces a sequence of N values of c bounded in such a way that the oscillators always retain their chaotic behavior.
    [0111] BRIEF DESCRIPTION OF THE FIGURES
    [0113] To complement the description that is being made and in order to help a better understanding of the characteristics of the invention, according to a preferred example of a practical embodiment thereof, a set of figures is attached as an integral part of said description. where, with an illustrative and non-limiting nature, the following has been represented:
    [0115] Figure 1: Diagram of the pseudo-random signal generator in which the chaotic oscillators are identical and are coupled in a master-slave configuration.
    [0117] Figure 2: Diagram of the secure communication system based on masking by means of the phase shift between chaotic oscillators.
    [0119] Figure 3: Represents the time series for the first two encryption cycles of the image in figure 4: (a) and (b) synchronization signals, (c) random signal generated in the transmitter and receiver, (d) signal encrypted and (e) information signal retrieved at the receiver.
    [0121] Figure 4: Image of a person that is used as a message in the preferred embodiment for a demonstration of encryption.
    [0123] Figure 5: Result of the encryption of the image of figure 4 in the preferred embodiment.
    [0124] Figure 6: Standard deviation of the bits that make up the floating point numbers of a sequence of random numbers obtained from the transmitter's pseudo-random signal generator. The least significant bit corresponds to position 1.
    [0126] PREFERRED EMBODIMENT OF THE INVENTION
    [0128] The implementation of the present invention is directly related to the field of secure communication systems, analog and digital electronic devices and computer programs, more specifically it refers to a highly secure communication system based on chaotic systems. Additionally, the present invention can be implemented in electronic circuits as well as in wireless communication systems.
    [0129] The present invention is further illustrated by the following application example, which is not intended to be limiting of its scope. In this application example, a computational method is developed for the implementation of the invention using software, hardware, re or a mixture of both. To do this, a discretization of the time domain t is established in such a way that tj = t0 jh with j = 0, 1, ... and t0 = 0 are the instants of an equispaced discretization with time step h = 0.1.
    [0131] This embodiment implements the invention by employing identical Rossler oscillators as chaotic oscillators in the pseudo-random signal generators. In addition, the logistic map is used as a chaotic map for its implementation in the generators (8, 18) of the parameter c.
    [0133] Chaotic emitter oscillators
    [0135] In this preferred embodiment, the pair of chaotic oscillators (1,2) of the pseudo-random signal generator of the emitter (5) consists of identical Rossler oscillators with diffusive coupling (3) represented by the differential equations that describe their dynamics along over time t e [ig, tzñn]
    [0137] dvE1 ddV viE2 _ ni „i
    [0138] dt —2 / ei - ZE1 ' dt - ~ yE2 - ZE2)
    [0139] d ^ E 1 dyE 2
    [0140] dt vEi a yE i, [3] dt - XE2 + a yE2 + K ' ( .VEI ~ 2 / E2)) [4] dz> E 1 dzE 2
    [0141] dt b + ^ ElX ^ El - c)) dt = b Z ^ 2 ( XE2 ~ c))
    [0143] where a = 1.65 and b = 0.2 are fixed parameters of the oscillators, while c is an adjustable parameter that maintains the chaotic behavior of the oscillators if it takes values in the interval [8.5,12]. The system of equations [3] corresponds to the master oscillator (1) and the system [4] to the slave (2). In order for the oscillators to achieve phase synchronization intermittently, the coupling force parameter k '= 0.001 is set. The initial states u ^ 1 (t0) = u ^ 2 (t0) are random, so that each of the initial conditions is obtained from a uniform distribution U (0,1) using the entropy source (9 ).
    [0144] We call time series to the values that a system variable takes in the instants of a discretization of the time domain like the one previously described. In order to obtain the time series of the state variables of the Rossler oscillators, a numerical integration scheme is used for initial value problems. In this embodiment, a fourth-order Runge-Kutta scheme is used. These schematics provide . f j 5 an approximation of the variable at the calculated instant, so that
    [0149] are an approximation of the state vectors of the master and slave oscillators respectively at time tj , obtained from the numerical integration scheme.
    [0151] Chaotic receptor oscillators
    [0153] In this preferred embodiment, the identical Rossler oscillator pair of the receiver with diffusive coupling (13) is represented by the differential equations that describe their dynamics over time.
    [0158] where the parameters a, b, c and k ' take the same values as in the emitter equations. The system of equations [5] corresponds to the master oscillator (11) and the system [6] to the slave (12). The initial states take the arbitrary values u R i (tg) = uR2 (t (,) = [0, 0, 0] T. The coupling force parameter k takes the following values
    [0160] 1.75 if if ( tj ) = 0 and S2 ( tj ) = 0
    [0164] in such a way that 1.75 is the value with which the sender and receiver reach complete synchronization during the asynchronous interval, that is, when integrating the systems [5] and [6] they will produce the same time series during the synchronized interval as the systems of emitter equations [3] and [4] respectively. The numerical integration scheme used to obtain the time series is the same as that used to integrate the emitter equations, so that uR1 ( tj) ps uri * ^ and uR2 ( tj) ps u R2 ^, where
    [0166] ^ R i (j) '' ^ R2 (j) '
    [0167] URi d U) j = yRi (j) and uR2 * -j ^ = yR2 (j)
    [0168] , ¿R2 ^,
    [0170] they are an approximation of the state vectors of the master and slave oscillators respectively at time t j, obtained from the scheme.
    [0172] Phase difference detector
    [0174] Both transmitter and receiver have a phase difference detector (4, 14) that is part of their pseudo-random signal generators. Next, the implementation of these detectors is detailed using the time series generated by numerically integrating the equations of the chaotic oscillators.
    [0175] The representation of a Rossler oscillator in state space is a spiral-type chaotic attractor. The calculation of the relative phase at an instant tj can be carried out by measuring the phase of a vector that follows the projected trajectory of the attractor in the XY plane. So the relative phases of each oscillator at time tj can be approximated by
    [0180] where
    [0182] Then, the absolute phase difference can be approximated at time t j by means of the expressions
    [0187] being
    [0192] In the same way, for the receiver you have to
    [0195] Emitter-receiver synchronization
    [0197] Taking into account all the above, the synchronization signals consist of
    [0199] X (j)
    [0200] E1 If % <tj <t * .cf X (j
    [0201] E2 ) If ^ <tj <t [.cf if (tj) = ys 2 (tj) =
    [0202] 0 otherwise, 0 otherwise.
    [0204] In both signals it is avoided to send the value of the random initial conditions x ^ 1 ( ti) and xE2 (tg). This situation allows the encryption cycles to be concatenated so that the final instant of each of them coincides with the initial instant of the next, that is, ¿fln = ¿or + 1 ■ Figure 3 shows the two signals synchronization for the first two cycles of the encryption of the image of Figure 4.
    [0206] The synchronization between sender and receiver is reached when neither 00 nor 00 < e for all tj e (írCf, í f ln], where e represents the machine error that depends on the computing architecture.
    [0208] Generator of the c parameter of chaotic oscillators
    [0210] Both transmitter and receiver have a generator of the parameter c (8,18). In this embodiment, the logistic map vn + 1 = pvn (1 - vn) with parameter p and initial condition v0 is used so that both start from the static key. In this embodiment of the system, the parameter c changes in each integration step, then A tc = h = 0.1 and c = for t, _ i < t < tj and tj> ti . For the emitter and receiver oscillators to retain their chaotic behavior, c must be contained in the interval [8.5,12]. Then, in this preferred embodiment, the sequence of values of the parameter c that makes up the generator output is described by
    [0211] cn + vn + 1 if cn + vn + 1 <12
    [0215] where n = 0,1, ... and ci e [8.5,12] is the initial condition of the generator that is also part of the static key. In order for the system to retain the property of random access, this procedure is restarted for each encryption / decryption cycle, that is, c (j) = c1 if tj = ti h and, consequently, c (j + n) = cn + 1 for the successive integration steps of the ith cycle.
    [0217] Encryption and decryption of an image
    [0219] As an example, a 512 x 512 pixel image of a person (figure 4) is used as a message or plain text. Each pixel is represented by 24 bits, 8 bits to represent the intensity of each of the three colors: red ( R), green ( G), and blue ( B). To send the message, the bits of each pixel of the image are reordered into a vector as follows:
    [0220] m = [# 1,1 , G 1,1, # 1I1, ..., # 1,512, G i , 512, # 1,512, • ••, # 512,512, ^ 512,512, # 512,512]
    [0221] where the subscripts of each color indicate the position of the pixel to which they correspond on Cartesian axes. Therefore, message m contains a total of 512 x 512 x 24 = 6291456 bits.
    [0222] The random signal at the emitter is the sequence of random bits
    [0227] and, in the same way, the receiver reproduces the random signal
    [0232] In figure 3 it can be seen that the signals rE ( tj ) and r K ( tj) coincide. This is because the sender and receiver use the same static key values shown in Table 1, which causes them to be able to synchronize their oscillators.
    [0234] As it is desired to decrypt the complete message, it is assumed that the receiver begins to listen to the channels at the same moment that the sender begins to generate the dynamic keys of the first block. Then, by convention it is established that t'0 = t¿ = t0 = 0.
    [0236] An upper bound on the time required for complete synchronization between the emitter and receiver Róssler oscillators is A tasinc = 100 time units, or what is the same, 103 iterations of the integration scheme are needed in the emitter and receiver . Then the reference time for the computation of y 9 ¿J> is t * cf = tg 100.
    [0238] For a 64-bit architecture and floating point arithmetic, it is possible to analyze which bits change most frequently in a sequence of random numbers corresponding to 6 * E by measuring the standard deviation of the representation of the numbers in binary code. In figure 6 the standard deviation of each of the 64 bits of a random sequence generated in the emitter can be observed. In this embodiment, it is avoided to use the most significant bits that correspond to those located in the last positions to encode the information, so that the band of bits between positions 6 and 45 both included is chosen, which allows to use 40 bits for each value of the phase difference generated at the sender to mask the message.
    [0240] To obtain the duration of the synchronized interval, it is arbitrarily set that 104 iterations of the numerical integration schemes are performed in a cycle. Then, A tcici0 = Aiasinc A tsinc = 100 900 = 1000 units of time and, therefore, 4n = ¿0 1000 = t * cf 900. Then, if we have 9 x 103 values of 6 ^ for each cycle and of 40 bits per each of these values, then the message m must be divided into M = 18 blocks mj (j) of 36 x 104 bits each, so that each value of tj e (írCf, ífln] corresponds to a sequence of 40 bits of the message. Then, the information signal generated in the sender corresponds to
    [0241] J m¿Ü) if fTCÍ < tj <4 n
    [0242] mE ( tj )
    [0243] and 0 otherwise,
    [0245] where i = 1,2, ..., 18. To mask the information signal in the random signal, the emitter applies the logical operator XOR, represented in this embodiment by the symbol ©, between the values of the sequence mE (t j ) and the 40 useful bits of each value of the sequence r E (t j ). So the encrypted signal sent to the receiver through the communication channel is s ( tj) = mE ( tj) 0 r E (t, -).
    [0247] Since each cycle requires 104 iterations of the numerical integration schemes, the emitter and receiver generators of the c parameter must calculate 104 values of c from the values of c0, v0 and p contained in the static key. The values included in the static key are shown in Table 1. If sender and receiver use the same static key, then they can be synchronized via dynamic keys. In such a case, the information signal recovered at the receiver is
    [0249] JO. , .0 m¿Ü) 0 ... 0 If t * cf < tj <4 n
    [0250] m R ( tj) = s ( tj) © r R ( tj)
    [0251] 0 otherwise,
    [0253] where, again, the symbol © represents the logical operator XOR and is the 40-bit sequence of the message sent at time tj that is preceded and followed by the zeros that complete the 64 bits of the floating point number. Figure 3 shows the signal m R ( t) for the first two encryption cycles of the image.
    [0255] Finally, the receiver can recompose the message knowing that m = U¿ m, (j), that is, by concatenating the successive blocks. Figure 5 shows the result of encrypting the image of figure 4. The result of decrypting the image using the keys from table 1 is exactly that shown in figure 4.
    [0260] Table 1: Table of static keys for the sender and receiver that produce a correct decryption of the message.
    权利要求:
    Claims (8)
    [1]
    1. Generator of pseudo-random signals, characterized in that it comprises two chaotic oscillators configured with different and random initial state vectors, at the initial instant in which they begin to oscillate, and with a coupling configured to achieve phase-free synchronization of the oscillators, the output of the oscillators being connected to a phase difference detector, configured to calculate the absolute phase difference d ( t) between the two oscillators with respect to a reference instant t rcf, t 'whose calculated phase difference constitutes the generator output.
    [2]
    2. Secure communications system that sends encrypted information on a message from a sender (10) to a receiver (20), where the sender is configured to divide said information from the message m (r) into M contiguous blocks, where each block m ¡(r) is encrypted during an i-th cycle that is divided into two time intervals: an asynchronous interval, which spans from the initial instant tz0 to the reference instant t * cf; and a synchronized interval, which spans from t * cf to the final instant fñn, also comprising the system:
    • two twin pseudo-random signal generators (5, 15), according to claim 1, one contained in the transmitter and the other in the receiver, the pseudo-random signal generator (15) of the receiver (20) being configured so that its oscillators reach the full phase synchronization with the oscillators of the pseudo-random signal generator (5) of the emitter (10) during the asynchronous interval, using a pair of public dynamic keys, each one contained in a synchronization signal Si (t) and s2 (t) generated by the transmitter, and that sends through two synchronization channels (23, 24),
    • two couplers (19, 21) included in the receiver, each of which receives one of the synchronization signals, to synchronize each oscillator of the receiver with its corresponding twin in the transmitter,
    • an encoder (7), contained in the transmitter, configured to combine the pseudo-random signal r E (t) from the output of its phase difference detector (4) with the information signal mE (t) containing the message m (r) divided into blocks by an input buffer (6), and generate at its output the encrypted signal s (t) that is sent to the receiver through the communication channel (22),
    • a decoder (17), contained in the receiver, configured to combine the pseudo-random signal from the output of its phase difference detector (14) with the received encrypted signal s (t) and generate the recovered information signal at its output m R (t), which contains the sequence of blocks m¿ (r) that are concatenated by an output buffer (16) of the receiver to form the decrypted message m (r),
    • two generators of a parameter (8, 18), one contained in the emitter and the other in the receiver, which contain a chaotic map that are twins in the sender and receiver to generate the same sequence of values of a parameter of each oscillator of the sender and receiver, which is repeated in each encryption cycle of the message blocks.
    [3]
    3. System according to claim 2, wherein the generator of pseudo-random signals (5) of the emitter comprises an entropy source (9), configured to generate the different initial random states u ^ 1 (t0) and u ^ 2 (t0) of the oscillators at the beginning of the encryption cycle of each block m ¡(r) of the message, the generator being a parameter (8) of the sender, configured to vary a parameter c of the oscillators (1, 2) during the encryption process , and where each one of the emitter's oscillators is configured to generate one of the synchronization signals, each one of which forms a unique public dynamic key for each message block, which are sent during the asynchronous interval to the receiver (20 ) through the synchronization channels (23, 24), where the emitter's phase difference detector (4) is configured to start calculating the phase difference 0lE (t) from the reference instant t * cf taking as phase reference the relative phase of c Each oscillator at that instant, the output of the phase difference detector (4) of the emitter forming the random signal defined by

    [4]
    4. Communications system, according to claim 3, wherein each dynamic key of each message block comprises a signal from each transmitter oscillator excluding random initial conditions, and the receiver being configured to synchronize its oscillators with those of the transmitter from of said dynamic keys of the synchronization signals, and generate the same signals as the emitter during the synchronized interval.
    [5]
    Communication system, according to claim 2, wherein the chaotic oscillators (11, 12) of the pseudo-random signal generator (15) of the receiver, have arbitrary initial states uR i (tg) and uR2 (t'0) at the instant initial t'0 in which the receiver begins listening to the communication (22) and synchronization (23, 24) channels, the generator of a receiver parameter (18) being configured to vary a parameter c of the oscillators during the decryption process, and where the receiver's phase difference detector is configured to start calculating the phase difference 6 ^ (t) from the reference instant t * cf taking as the reference phase the relative phase of each oscillator at that moment, the output of the receiver's phase difference detector (14) forming a replica of the random signal that is generated in the emitter defined by

    [6]
    6. Communications system, according to claim 2, wherein the information signal generated by the input buffer (6) of the sender comprises the sequence of blocks into which the message is divided to be sent during the synchronized interval, being defined by
    j mAT) if 4 f <í <4 i
    mE (i) = <
    ^ 0 otherwise,
    where the block m ^ r) defined in the interval i <r < t does have a duration A r inf0 n - tí - i that must be less than or equal to the duration of the synchronized interval A tsinc = í ^ n- t i rcf , the complete message being m (r) = | J¿ m ¡(r) with i = 1, ..., M.
    [7]
    Communication system, according to claim 2, where the decoder (17) of the receiver is configured to generate the recovered information signal and recover the complete message, only when listening to the synchronization and communication channels starts at the beginning. of transmission, t'0 <and continuously until, at least, the instant tffn, and when the listening time is less than the transmission time of the message, it performs a partial recovery of the message, leaving the signal defined by
    mR (i) J m ¿(r) If t (.cf <í <ífln
    and 0 otherwise.
    [8]
    8. Secure communications system, according to claim 2, where the chaotic map of the generators of parameter c 8, 18) of the oscillators of the emitter (10) and receiver (20), are configured to change the value of parameter c in fixed time intervals A tc smaller than the asynchronous interval, where the time interval of each ith cycle is divided into N subintervals, such that the total duration of a cycle is A tcici0 = NA tc, in which at each subinterval from n = 0 to n = N - 1, it corresponds to a value of c that is obtained by the function cn + 1 = ip ( cn, vn-, p), where vn is the nth value of the chaotic map and p is parameter of the same that is part of a secret static key stored in the sender and receiver and of which the initial values c0 and v 0 are also part, and the function ip being a sequence of N values of the parameter c so that the oscillators preserve always its chaotic behavior, the receiver being configured to synchronize its s oscillators completely with those of the sender only when its secret static key matches that of the sender, allowing the message blocks to be decrypted.
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