JP2000206472A - Optical chaos random number generating apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an optical chaos random number generating apparatus of high reproducibility in generation of a physical random number and easy in controllability by using a high speed property of light and a deterministic characteristic and a random number property of a system provided in a chaos dynamics system. SOLUTION: An optical demultiplexer 3 divides a beam from a light source 11 into beams of the same power of a prescribed number, and an optical chaos signal generating device 1 consisting of the prescribed number of optical interferometer groups having two optical paths is made incident respectively with the beams divided with the optical demultiplexer 3, and the beams are branched into two parts to be re-multiplexed. An optical path length difference information storage 2 stores the information of an optical path length difference between two optical paths between branching - multiplexing of the prescribed number of optical interferometers, and an optical output signal measuring device 4 measures the energy of prescribed optical chaos output signals outputted from the prescribed number of optical interferometers. An optical output signal processing storage 5 processes and stores the energy values of the optical output signals shown by a constant dimension non-negative real number vector outputted from respective optical interferometers measured by the optical output signal measuring device 4.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a chaotic dynamical system X (n +
1) The present invention relates to an optical chaos random number generator that generates chaotic random numbers satisfying = F [X (n)] by an optical circuit.

[0002]

2. Description of the Related Art Generating a random number sequence is roughly divided into two.
There are two ways. One is generated by a random number generation program stored in a digital computer, and the program is a random number generation algorithm required by the Monte Carlo method, which has many application fields such as device modeling and financial derivative calculation. It corresponds to an existing pseudo-random number generation program such as a congruential random number, an M-sequence which is a random number sequence generated by a shift register required in a spread spectrum communication system, and a gold code, and these have been widely used in the past.

[0003] Another method is to generate a random number from noise that is unavoidable in an electronic circuit or device physically constituted by a physical random number. Because the mechanism is unknown or complicated, there is no reproducibility to generate the same random number sequence when the same initial conditions are given, which is inappropriate for engineering random number applications. There is also a chaotic random number signal method that generates laser chaos by an optical circuit using a laser with a feedback loop with a time delay, but the equation describing the signal is a nonlinear partial differential equation that is difficult to analyze, and the random number It is difficult to quantitatively analyze the nature of the laser, and it is still an experimental stage to incorporate laser chaos into the random noise generation part of the future terabit / second optical communication system.
Due to the complexity of the system, it is difficult to integrate the laser chaos generating portion, and there are great difficulties in practical use and commercialization.

[0004]

The signal transmission speed of a random number on a digital computer or a physical random number by an electronic circuit is such that the operating frequency of a practical electronic device is about 600 MHz.
There is a speed limit due to z. Therefore, it is impossible to directly apply a physical random number generation method based on conventional electronic circuits and devices in order to cope with data transmission at a high bit rate of a T bit / sec class such as a moving image. In addition, the signal generation method using optical laser chaos has poor reproducibility due to the complexity of the system and is generated using a shift register even if it is difficult to design engineering that requires high accuracy. Unlike the M-sequence described above, there is a problem that it is not easy to generate random numbers that are easy to control.

In the conventional Monte Carlo calculation, the calculation speed is obviously determined by the performance of the pseudo-random number generation program used in the Monte Carlo method, and furthermore, the stable operation speed of the semiconductor device constituting the digital computer. For the high-speed calculation of the Monte Carlo method having many applications, the operation limit of an electronic device (about 75 GHz in theory, about 600 MHz in practical use, Nikkei Electronics 1998.
6.29, "Efforts on Switched Light Technology to Enter T Bits / Second, p.109) There was a speed limit coming from.

The present invention has been proposed to solve the problems relating to the limit of the speed of random number generation and the controllability thereof. The main objects of the present invention are to provide high-speed light and a chaotic dynamical system. Using the deterministic properties and randomness of the system,
An object of the present invention is to provide an optical chaos random number generator having high reproducibility and easy controllability in the above-described physical random number generation. It is another object of the present invention to provide an optical chaotic random number generator having a speed capable of supporting data transmission in the class of T bits / second.

[0007]

According to the present invention, there is provided an optical chaotic random number generator for obtaining a chaotic random number described by a chaotic dynamical system X (n + 1) = F [X (n)] as an optical output signal. (1) an optical signal demultiplexing device that splits light from a light source into a predetermined number of light beams of the same power, and (2) the light split by the optical signal demultiplexing device is respectively incident and split into two. An optical chaos signal generator comprising the above-mentioned predetermined number of optical interferometers having two optical paths, each of which is re-multiplexed; and (3) the optical path length of two optical paths between the branching and the multiplexing of the predetermined number of optical interferometers. An optical path length difference information storage device for storing difference information, and (4) an optical output signal measuring device for measuring the power of an optical chaos output signal output from the predetermined number of optical interferometers, (5) The predetermined number of non-negative real vectors output from each optical interferometer measured by the optical output signal measuring device. An optical output signal storage device for storing the power value of the optical output signal represented.

As described above, since the optical chaos signal generating means is constituted by an optical circuit in which a plurality of interferometers having two optical paths such as a Mach-Zehnder interferometer are arranged in parallel, they are generated by a conventional shift register. The method uses high-speed light while maintaining desirable random properties, such as equal distribution, as well as pseudo-random numbers such as M-sequences and congruential random numbers. It can generate random numbers at higher bit rates such as seconds, and uses a one-dimensional chaos mapping that laser chaos does not have, so it maintains high speed optical signals. However, the reproducibility and randomness of random numbers required for future spectrum communication and Monte Carlo methods, such as the statistical nature of the random numbers being clearly and clearly understood. Since statistical properties of are given explicitly can freely control the generation of random numbers.

Further, the circuit of the present invention, in which a plurality of interferometers having two optical paths are arranged in parallel, can be formed on a silicon substrate in an integrated and miniaturized form by utilizing a technique for manufacturing a planar lightwave circuit. Can be.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS First, the known facts regarding "solvable chaos" which forms the basis of chaos of the present invention will be described, and then the present invention will be described in comparison with a method of realizing chaos with an electronic circuit.

[0011] Chaos is a phenomenon that has an initial value sensitivity to an initial value X (1) while being given by a deterministic expression of X (j + 1) = F [X (j)]. It is universally found in a wide range of natural phenomena, such as celestial movement, weather phenomena, animal population changes, and input responses to neurons in the brain. The fact that they are chaotic does not only mean that their phenomena have the deterministic nature of having rules behind them, despite their seemingly random appearance, but Lorenz in the 1960s As it was discovered, when trying to simulate these phenomena with a computer, errors due to subtle deviations in initial values and deviations in approximation of differential equations in a digital computer increase exponentially with time. In other words, even though the underlying equation is deterministic, it is difficult to make a long-term prediction substantially, so that it is a phenomenon that makes it difficult to quantitatively analyze and predict the phenomenon.

Attempts to actually apply such chaos to engineering have been made in recent years. The basic idea is to use chaos instead of a pseudo-random number generator that can be obtained by calculation with a digital computer that has been known for a long time, but many chaotic dynamical systems use nonlinear transformation. Because it is the basis, it is difficult to obtain the properties of the solution analytically, and if you try to obtain the qualitative and quantitative properties, you are forced to use a digital computer to calculate in situations where there are large errors Therefore, there is a dilemma that the credibility of the calculation result is diminished. Therefore, from the viewpoint of controllability, which is important for engineering applications,
Before the simulation of the characteristics, the existence and mathematical characteristics of chaos classes whose characteristics are known in advance have been of interest.

[0013] Recently, although one of the present inventors is chaotic, there is a systematic class whose characteristics can be obtained analytically, and the nonlinear mapping of the class by the addition theorem of the elliptic function. It was shown that the class could be composed. (K. Umeno, Method of constructing exactly sol
vable chaos, Phys. Rev. E (1997) Vol.55: 5280-528
4.) Elliptic functions include trigonometric functions. Therefore logistic map that is known to exhibit chaotic behavior [Equation 4], the official double angle of ^{sin 2 (a) sin 2 (} 2a) = 4si
Since n ² (a) (1-sin ² (a)), this logistic map is analytic general solution (X
Since it has (n) = sin ² (2 ^n-1 a)), it is a chaos in the chaos class that can be solved as above.

[0014]

(Equation 4)

Further, this logistic map [Equation 4] has ergodicity [Equation 5] that the spatial average is equal to the temporal average, and there is only one invariant measure which is a distribution that ensemble the spatial average (SMUlam and J. von). Neumann, B
ull. Math. Soc. 53 (1947) 1120 and the above-mentioned literature), and it is also known that it can be written as [Equation 6]. This class of chaotic systems, which has the properties of an ideal random number called ergodicity, can also write down general solutions, and clearly understand the statistical laws, is a chaotic system that is solvable from its outstanding characteristics.
Or a chaotic system that can be solved exactly (Exactly Solvable Chaos)
It has been applied to the Monte Carlo method up to now (“Statistical simulation method and storage medium storing this program”, Japanese Patent Application Laid-Open No. 10-283344).
) And spread code generation in spread spectrum communication.

[0016]

(Equation 5)

[0017]

(Equation 6)

The present invention provides a chaos map (also known as Chebyshev map, RL Adler an
dT.J.Rivlin, Proc. Am. Math. Soc. 15 (1964) 794.
) Is physically realized, and a random number is generated at high speed using an optical circuit instead of the conventional technology using electronic devices. In this case, the double-angle formula corresponds to the logistic map [Formula 7], the triple-size formula corresponds to the cubic map [Formula 8], and the present invention provides a Chebyshev map Fm corresponding to the general m-fold formula including them. This is a physical realization of a chaotic map called.

[0019]

(Equation 7)

[0020]

(Equation 8)

Therefore, the present invention falls into the category of analog computers dedicated to random number generation, in which the phenomenon of chaos is simulated by a physically configured device.

However, the chaotic dynamical system X (n + 1)
Circuits that realize chaos such as = F [X (n)] are limited to those using standard IC technologies such as switched capacitor (SC) circuits and switched current (SI) circuits (Tsuneta, Eguchi, Inoue, "Chaotic Signals and Circuits," IEICE Journal, Vol. 81 No. 6 pp.610-613: 1998). Although the chaotic signal generation circuit was easily realizable and could be integrated, there is no result that can obtain advantages in terms of speed and accuracy compared to the current simulation of chaos on high-performance general-purpose digital computers. Is the current situation. Furthermore, the operating speed limit of electronic devices (theoretically about 7
There is also an inherent speed limit coming from 5 GHz, practically about 600 MHz mentioned above, Nikkei Electronics 1998. 6.29, "Switching Light Technology Approaches T Bits / sec, p. 109).

Accordingly, the present invention uses an optical circuit comprising a plurality of Mach-Zehnder interferometers for performing an input signal and an output signal as optical signals as shown in FIG. The point that it can overcome the speed limit of the device is a significant difference from the chaos circuit based on the conventional electronic device / circuit.

The optical chaos random number generator of the present invention will be described below in detail with reference to the drawings. FIG. 1 shows an example of a schematic configuration of an optical chaotic random number generator for obtaining a chaotic random number described by a chaotic dynamical system X (n + 1) = F [X (n)] as an optical output signal according to the present invention. (1) The light demultiplexing device 3 that divides the light from the light source 11 into a predetermined number of light beams having the same power, and (2) the light split by the light demultiplexing device 3 is incident and split into two. Thereafter, an optical chaotic signal generator 1 comprising a predetermined number of optical interferometers 13 having two optical paths for re-multiplexing, (3)
An optical path length difference information storage device 2 for storing information on an optical path length difference between two optical paths between the branching and the multiplexing of the predetermined number of optical interferometers 13; and (4) output from the predetermined number of optical interferometers. An optical output signal measuring device 4 for measuring the energy of a predetermined optical chaotic output signal, and (5) the constant dimension non-negative real number output from each optical interferometer measured by the optical output signal measuring means. A light output signal processing and storage device 5 for processing and storing the energy value of the light output signal represented by a vector.

FIG. 2 shows an example of the optical demultiplexer 3 for the optical chaotic signal generator 1 shown in FIG. 3. In the illustrated embodiment, seven light beams from a light source 11 such as a laser are arranged in three stages. The optical signal is divided into eight optical signals of the same power by the coupler 12 and incident on the eight interferometers 13 constituting the optical chaotic signal generator 1, respectively. However, eight separate light sources may be connected by optical fibers to the input ports of each interferometer 13 and connectors.

The optical chaos signal generator 1, which divides the incident light into two light beams and combines them again, produces an optical interference effect due to the difference in optical path length between the two optical paths from the branching to the multiplexing. An example of the optical interferometer is a Mach-Zehnder interferometer. As shown in FIG. 3, a plurality of Mach-Zehnder interferometers are arranged in parallel to realize a chaotic signal generator 1 by an optical circuit. In the embodiment of FIG. 3, an optical circuit is configured using four interferometers MZI (1) to MZI (4). In this case, the dynamic variable X (i) is the power of light, and normal square detection is possible. The optical path length difference of each of the interferometers 13 is determined by the heat coupled to the optical path of each interferometer of the optical path length difference information storage device 2.
In order to generate a predetermined phase difference between the two optical paths by the optical phase shifter 14, this is realized by heating one of the optical paths to a predetermined temperature by a signal from the temperature control unit 15. The temperature signal from the temperature control unit 15 is displayed on the temperature display unit 16 and stored.

Each interferometer 13 of the chaos signal generator 1
The output optical signal (optical chaos signal) is sent to the fort detector 17 constituting the optical output signal measuring device 4 by an optical fiber, and the optical signal is converted into an electric signal corresponding to the energy (output power) and measured. . Therefore, the numerical value is non-negative, and the measured signal is represented by the predetermined number of non-negative real vectors.

The output electric signal from the measuring device 4 is sent to the input device 18 of the optical output signal processing storage device 5. The signal input to the input device 18 stores the optical signal energy value of each interferometer 13 via the central signal processing device 19 in the external storage device 2.
2, and displayed by the display device 23 as necessary. The illustrated optical output signal processing and storage device 5 also includes a central signal processing device 19, a storage device 20, and a main storage device 21, so that general signal processing can also be performed.
The elements of the stored non-negative real vector of the predetermined number dimension are obtained by arranging chaotic sequences X (1), X (2), X (3),... X (N) in parallel. Therefore, it is possible to freely generate a new chaotic random number by using the optical chaotic signal obtained by the optical chaotic random number generator as a “seed”. The optical chaotic signal generator 1 including a plurality of optical interferometers described above can be integrated and formed by utilizing a planar lightwave circuit manufacturing technique for forming an optical waveguide on a silicon substrate.

The plurality of Mach-Zehnder interferometers in FIG. 3 are symbolized as MZI (1), MZI (2),..., MZI (N) from above, and each Mach-Zehnder interferometer MZI (j) has Two input ports and two
There are two output ports, and the difference in optical path length of each MZI (j) is set to ΔL (j). However, it is assumed that 1 ≦ j ≦ N. Let n be the effective refractive index and let the wavelength of the input light be λ. The scattering matrix of the Mach-Zehnder interferometer at that time is represented by the optical path length difference Δ as shown in [Equation 9].
It is uniquely determined by L (j), effective refractive index n, and light wavelength λ (Paul E. Green, “Fiber Optic Networks” (Prentice
Hall, 1993), p.124. ). In _Equation 9, H _ik
(Λ) indicates a complex electric field output to the output port k when a unit electric field is input to the input port i. Here, 1 indicates an upper port, and 2 indicates a lower port.

[0030]

(Equation 9)

Here, each Mach-Zehnder interferometer MZI
It is assumed that there is no input from the input port (j) (see FIG. 3). Then, the complex electric field vector received at the output side of the Mach-Zehnder interferometer MZI (j) is uniquely determined as in [Equation 10].

[0032]

(Equation 10)

Therefore, the optical power received at the output side is given by a non-negative trigonometric function as shown in [Equation 11].

[0034]

[Equation 11]

Now, the optical path difference ΔL (j + 1) of the j + 1-th Mach-Zehnder interferometer MZI (j + 1) is m of the optical path difference ΔL (j) of the j-th Mach-Zehnder interferometer. ([Equation 1
2)). However, the conditions of the wavelength λ and the effective refractive index n are the same for each Mach-Zehnder interferometer, and m is 2
An integer greater than or equal to.

[0036]

(Equation 12)

Therefore, the optical power received by the interferometer MZI (j) is given by the same non-negative trigonometric function as in [Equation 12], and becomes as shown in [Equation 13].

[0038]

(Equation 13)

Now, as in [Equation 14], the optical power of the upper output port of each interferometer MZI (j) is read as a dynamic variable X (j).

[0040]

[Equation 14]

When m = 2, the optical output powers X (j + 1) and X (j + 1)
(j) is the double angle formula of sin function sin (2a) = 2cos (a) sin (a)
Thus, a logistic mapping is formed in the same manner as in [Equation 1]. When m = 3, both powers form a cubic mapping in the same manner as in [Equation 2] by the triple angle formula of the sin function. Similarly, for certain integers where m is 2 or more, both powers become a chaotic map called a Chebyshev map (m-th order polynomial) given by a formula of m times the sine function (RL Adler and TJ Rivlin, Proc. A
m. Math. Soc. 15 (1964) 794). If the optical power at the lower output port of each Mach-Zehnder interferometer is read as a dynamic variable Y (j), the optical output powers Y (j + 1) and Y (j) are the mappings given by the formula of m times cos ² θ. Which is equivalent to the rational transformation of the above Chebyshev mapping.

These mappings are all mappings from the unit interval [0,1] to the unit interval [0,1], and the remarkable fact is that the spatial average is equal to the temporal average. have. In this case, the spatial average is given by an invariant measure [Equation 15] common to all these mappings.

[0043]

(Equation 15)

Therefore, when N Mach-Zehnder interferometers satisfying the above-mentioned properties are prepared, the respective outputs have the same optical power values as those calculated for these chaotic dynamical systems measured at each output side. It is possible to obtain as. Given the initial conditions for these chaotic dynamical systems, the chaotic random numbers have a deterministic property that the sequence of chaotic random numbers is determined by the repetitive transformation of a certain map (chaotic map) and the ideal random number The chaotic random number generator has ergodicity, which is a characteristic, and can be used as a random number generator that guarantees general ergodicity. Accordingly, the calculation of the Monte Carlo method based on the ergodic property [Equation 16] can also be performed by using the Monte Carlo calculation algorithm using chaotic random numbers (see Japanese Patent Application Laid-Open No. 10-283344).

[0045]

(Equation 16)

Here, A (x) is a function belonging to the class L1 (P) of an integrable function in which the right side of [Equation 16] converges.

If the threshold value is set to 0.5 and the conversion is performed according to the rule of “1” when the threshold value is larger than the threshold value and “0” when the threshold value is smaller than the threshold value, the probability that “0” and “1” are the same as in an ideal coin tossing game. Independent distribution with 0.5 (ii
d.:independent and identically distributed) binary sequence can be obtained. Further, by preparing a large number of threshold values, a more general multi-valued sequence can be obtained. (In the case of the cubic mapping in FIG. 5, a ternary sequence)

When the threshold value is set to 0.5, there is a real trajectory corresponding to an arbitrary binary sequence code, so that the apparatus of the present invention is suitable as a binary sequence random number generating apparatus. this is,
It applies the concept of symbol dynamics, in which a dynamical system is observed with a code sequence. That is, in this way, an ideal digital random number sequence can be extracted from the chaotic random number generator of the present invention having an analog value.

In order to change the initial condition of the obtained chaotic random numbers, the wavelength of the light source may be changed. With the current technology, the output characteristics such as the loss characteristics of the Mach-Zehnder interferometer can keep the energy loss rate close to zero independent of the wavelength, resulting in an interferometer with excellent stability. In the chaotic dynamical system, if the initial value is slightly shifted, it largely rebounds (exponentially with respect to the number of mapping repetitions) as an output error. Therefore, the device of the present invention is a device in which the consequence of the chaotic nature of the chaotic dynamical system used therein appears as the light source wavelength dependence of the random number sequence, which enhances the confidentiality of the random numbers used in cryptographic communication and the like. Becomes

Here, the Mach-Zehnder interferometer is an interference device that splits incident light into two light beams and then multiplexes the light beams again, and produces an optical interference effect due to the optical path length difference between the two optical paths from the branching to the multiplexing. It is total.

In each interferometer, it is assumed that there is a difference between the two optical path lengths by ΔL (j). Now, since the scattering matrix of each interferometer is given by [Equation 9], the power of the input light entering the upper input port of each Mach-Zehnder interferometer is set to 1, and the power of the input light entering the lower input port is set to zero. At this time, the power X (j) of the optical signal output from the upper output port of each interferometer is given by [Equation 14]. Now, since it is assumed that the optical path length difference ΔL (j) of each interferometer satisfies the linear relational expression given by [Equation 3] with respect to an integer of 2 or more, the j + 1-th Mach-Zehnder interference The relational expression between the optical output X (j + 1) of the total MZI (j + 1) and the optical output X (j) of the j-th Mach-Zehnder interferometer MZI (j) is m times the sin ² (x) Equals the formula That is, when the output of each Mach-Zehnder interferometer is m = 2, si
The logistic map [Formula 1] given by the double-angle formula of n ² (x) is satisfied. If m = 3, the cubic map [Formula 2] given by the triple-size formula of sin ² (x) is satisfied, For general m, a relational expression given by an m-th order Chebyshev map Fm that is equal to the formula of m times the angle of sin ² (x) [Equation 1
7].

[0052]

[Equation 17]

Since this is a mapping dynamical system that gives the above-mentioned solvable chaos, it can be seen that this system is realized by an optical circuit of solvable chaos. As described above, the present invention can provide an apparatus for generating random numbers used in a wide range of application fields, such as the Monte Carlo method, the spread spectrum communication system, the optical communication system, and the encryption key generation, using the high speed of light.

[Embodiment 1] In Embodiment 1, an optical chaos circuit using a variable wavelength laser as a light source will be described. Further, the initial value X (1) can be set to any real value from 0 to 1. The effective refractive index is n, and the initial value X (1)
Is the optical path length difference of the first Mach-Zehnder interferometer MZI (1), ΔL (1) = ΔL. At that time, X
(1) = since sin ² becomes [(πnΔL / λ)], at least the value of the case, from X (1) is always 0 to 1 range of wavelengths of the light source move between λ _s ≦ λ ≦ λ _l To take once, [Equation 18]
Condition is required.

[0055]

(Equation 18)

[0056] Thus, as the optical path length difference MZI (1) is [Equation 19], formula is derived which depends on the upper limit lambda _l and lower lambda _s wavelength.

[0057]

[Equation 19]

That is, the optical path length difference of the interferometer MZI (1) is expressed by the following equation.
9] or an integer multiple thereof. Here, the value of ΔL is estimated from an actual example. The wavelength range is 1450-1590 [nm], that is, λ _s = 1450 [nm], λ _l
In the case of a wavelength tunable laser light source (product number HP8168F) manufactured by Hewlett-Packard Co., Ltd. = 1590 [nm], ΔL = 16467.8 / n [nm] can be estimated from [Equation 19]. In this case, ΔL = It is understood that it is desirable that an integral multiple of 16.5 / n [um] be the optical path length difference of the Mach-Zehnder interferometer MZI (1). Of course, when another tunable laser light source is used, the above formula [Equation 19] can be used similarly to the above example.
By applying to the Mach-Zehnder interferometer MZI
The optical path length difference ΔL (1) of (1) can be estimated, and further, the optical path length difference ΔL (j) of all Mach-Zehnder interferometers can be estimated according to the equation (19).

[Embodiment 2] Logistic mapping [Equation 1]
Will be described with reference to an optical circuit. This is designed so that m = 2 in the relational expression [Equation 3] of the optical path length difference of each interferometer. The condition of the port where the input light of the N Mach-Zehnder interferometers enters is determined from only the upper port as described above, and j
In the case of the Mach-Zehnder interferometer MZI (j), the energy X (j) of the output light 1 exiting from the upper output port is [Equation 20].
Holds, the power X (j) of the output light obtained by each interferometer of FIG. 3 satisfies the logistic mapping [Equation 1] from the formula of the double angle of the sin function. This realizes a logistic mapping dynamics system by an optical circuit using an optical Mach-Zehnder interferometer. Since the property of the logistic map dynamics is known to be chaos, this optical circuit is a chaos random number generator. In this case, the Lyapunov exponent indicating the degree of chaos and the Kolmogolf-Sinaintropy become Log2, which can be regarded as a random number generator that generates one bit of information per Mach-Zehnder interferometer. However, Log represents natural logarithm.
When the obtained output value X (j) is assigned a code “0” or “1” depending on whether the value is 0.5 or more, the probability that the code is “0” is 1/2. , The probability of becoming a code “1” becomes と な り, and this device becomes a binary random number sequence generator having a length N (see FIG. 4). The binary random number sequence generator that physically operates in this manner maintains the same properties as an ideal coin game.

[0060]

(Equation 20)

[Embodiment 3] Optical cubic mapping [Equation 2]
Will be described with reference to an optical circuit. The conditions of the input light entering the N Mach-Zehnder interferometers are the same as in the second embodiment. In this case, the design is made such that m = 3 in the relational expression [Equation 3] of the optical path length difference of each interferometer. The energy X (j) of the output light 1 emitted from the upper output port of the j-th Mach-Zehnder interferometer MZI (j) satisfies [Equation 21].
From the formula of the triple angle of the sin function, the power X (j) of the output light obtained by each interferometer in FIG. 3 satisfies the cubic mapping [Equation 2]. This realizes a cubic mapping dynamics system by an optical circuit using an optical Mach-Zehnder interferometer. Since it is known that the property of the cubic mapping dynamics is chaos, this optical circuit is a chaos random number generator. (In this case Lyapunov exponent and Kolmogorov = Sinai entropy representing the degree of chaos can be regarded as a random number generator for generating a Log3 next, 1 Mach-Zehnder interferometer per Log ₂ 3-bit information.) The obtained output The value X (j) is “0” if the value is smaller than 0.25, and “1”, 0.75 if the value is 0.25 or more and smaller than 0.75.
If the above is assigned to each of them as "2",
The probabilities of the signs “0”, “1”, and “2” are each 1/3
Thus, this device becomes a ternary random number sequence generator of length N (see FIG. 5).

[0062]

(Equation 21)

Fourth Embodiment In the first to third embodiments, the optical output signal X (j) of the upper output port of each Mach-Zehnder interferometer is extracted, but the power of the optical output signal from the lower output port is obtained. Even if Y (j) is extracted, if the optical path length difference ΔL (j) of each Mach-Zehnder interferometer satisfies the condition [Equation 3], the relational expression between the optical output power Y (j + 1) and Y (j) Is m of cos ² (x)
The double angle formula Y (j + 1) = Gm [Y (j)] is satisfied. This function Gm (•) is also a chaotic map, and the Chebyshev map
An mth-order polynomial that satisfies the relational expression of Fm (·) and [Equation 22] is obtained. The shape of the chaotic map can be changed by adjusting the relationship between the input port and the output port that are actually used, but the form of these chaotic maps is the function form given by the formula of m times the trigonometric function. It is limited to.

[0064]

(Equation 22)

It should be noted that the present invention is not limited to the above-described embodiment, and it is needless to say that various modifications can be made without departing from the spirit of the present invention.

[0066]

The random number generation exceeding the current speed limit of about 75 GHz in theory, practically about 600 MHz, which is the operation limit of the conventional electronic device, can be realized by using the characteristics of the optical circuit of the present invention. Further, the present invention makes it possible to provide an integrated and miniaturized device that cannot be realized by a conventional optical laser chaos system by using the present quartz-based planar lightwave circuit (PLC) manufacturing technology. Also, since the present invention uses random numbers that use chaos with high initial value dependence, it is more confidential than random numbers generated from shift registers such as conventional M-sequences. Is a random number suitable for use in.

[Brief description of the drawings]

FIG. 1 is a schematic configuration diagram illustrating an example of an optical chaos random number generator according to the present invention.

FIG. 2 shows an optical chaotic signal generator of the apparatus of FIG. 1 and an optical demultiplexer for an interferometer.

FIG. 3 shows an example of the optical chaotic signal generation device of the device of FIG.

FIG. 4 is a logistic map that is an example of the Chebyshev map Fm when m = 2.

FIG. 5 is a cubic mapping which is an example of the Chebyshev mapping Fm when m = 3.

[Explanation of symbols]

 Reference Signs List 1 optical chaos signal generator 2 optical path length difference information storage device 3 optical demultiplexer 4 optical output signal measuring device 5 optical output signal processing storage device 11 light source 12 optical coupler 13 optical interferometer 14 heat-optical phase shifter 15 temperature controller 16 Temperature display unit 17 Fort detector 18 Input device 19 Central signal processing device 20 Storage device 21 Main storage device 22 External storage device 23 Display device

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Ken Umeno 4-2-1 Nuki Kitamachi, Koganei City, Tokyo Post Office Within the Communications Research Laboratory (72) Inventor Kenichi Kitayama 4-2-1 Nuki Kitamachi, Koganei City, Tokyo Post Office Within the Ministry of Communications Research Laboratory

Claims (5)

[Claims] 1. An optical signal demultiplexing means for splitting light from a light source into a predetermined number of light beams having the same power;
An optical chaos signal generating means comprising an optical interferometer having a predetermined number of two optical paths which are recombined after branching into two, respectively; an optical path length of two optical paths between the branching and multiplexing of the predetermined number of optical interferometers; Optical path length difference information storage means for storing difference information; optical output signal measurement means for measuring the power of optical chaos output signals output from the predetermined number of optical interferometers; Optical output signal storage means for storing the power value of the optical output signal represented by the predetermined number-dimensional non-negative real number vector output from each optical interferometer measured by the signal measurement means, Chaotic dynamical system X
An optical chaotic random number generator for obtaining a chaotic random number described by (j + 1) = F [X (j)] as an optical output signal. 2. The predetermined number of optical interferometers comprises an optical Mach-Zehnder interferometer, and an optical path length difference Δ of a j-th (where j is a natural number less than or equal to the predetermined number) Mach-Zehnder interferometer.
(j) satisfies the predetermined relationship, the output optical power X (j) is a mapping obtained from the addition formula of the trigonometric function.
The optical chaos random number generator according to claim 1, wherein a dynamical system X (j + 1) = F [X (j)] generated by F (•) is satisfied. 3. The predetermined number of optical interferometers comprises an optical Mach-Zehnder interferometer, and outputs when the optical path length difference Δ (j) of the j-th Mach-Zehnder interferometer satisfies a predetermined relationship. The optical power X (j) includes at least a logistic map [Equation 1] and a cubic map [Equation 2]. For m of 2 or more, the m-th order Chebyshev map Fm
(•) or the mapping that is to be rationalized
The optical chaos random number generator according to claim 1, wherein a dynamical system X (j + 1) = F [X (j)] generated by F (•) is satisfied. (Equation 1) (Equation 2) 4. The apparatus according to claim 1, further comprising a signal modulator for changing an optical output signal represented by the non-negative real vector of the constant dimension stored in the optical output storage. Optical chaos random number generator. 5. The Mach-Zehnder interferometer according to claim 1, wherein the predetermined number of optical interferometers comprises an optical Mach-Zehnder interferometer, and for the m, the j + 1-th (j is a natural number less than or equal to the predetermined number) Mach-Zehnder interferometer. The optical path length difference ΔL (j + 1) stored in the optical path length difference information storage means is m times the optical path length difference ΔL (j) stored in the optical path length difference information storage means of the j-th Mach-Zehnder interferometer. 2. The optical chaos random number generator according to claim 1, wherein a relational expression [Equation 3] that satisfies (m ≧ 2) is satisfied. (Equation 3)