Abstract:
A method of generating random numbers comprises: generating a first noise and passing the first noise through a first high pass filter which removes a periodic component contained in the first noise to produce a first noise signal having 1/f characteristic; generating a second noise and passing the second noise through a second high pass filter which removes a periodic component contained in the second noise to produce a second noise signal having 1/f characteristic; supplying the first and second noise signals to a differential circuit to derive a different signal between the first noise signal and said second noise signal; and generating, from the different signal, random numbers which do not have a periodicity due to 1/f characteristics of the first and second noise signals.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method of generating random numbers, and more particularly relates to a method of generating uniform or pure random numbers which do not substantially have a periodicity. 
   2. Description of the Related Art 
   Disordered random numbers having equal frequency of occurrence as a whole has been widely utilized in numerical simulation for analyzing social phenomena and physical phenomena. Coding system with random numbers has been also proposed in order to protect personal information in electronic trading, electronic patient charts and remote electronic diagnoses. 
   In general, random numbers are produced by means of software of electronic computer, in which algorithms for producing numbers with certain distribution properties are utilized. However, in case of generating random number by computer algorithms, since the random numbers are produced in accordance with certain mathematical formulae, pure random numbers having neither periodicity nor regularity could not be generated. Therefore, when important personal date is encoded with the aid of such pseudo-random numbers, encoded data might be easily decoded and no protection could be attained. 
   In order to mitigate the above mentioned drawback, there has been also proposed to generate random numbers on the basis of electric noises produced from electric elements such as resistor and diode. However, noise produced by a resistor has a so-called 1/f characteristic. That is to say, noise components of lower frequency have higher amplitude and noise components of higher frequency have lower amplitude. Therefore, when random numbers are generated on the basis of bivalent signals which are obtained in accordance with amplitude of noise, there is a problem that the thus generated random numbers have a periodicity due to 1/f characteristic. In this manner, uniform or pure random numbers having no periodicity could not be generated. A diode also produces 1/f noise, and therefore random numbers generated from the diode noise might also have a periodicity. 
   SUMMARY OF THE INVENTION 
   The present invention has for its object to provide a method of generating random numbers for generating substantially pure random numbers having no periodicity nor regularity from noise having 1/f characteristic. 
   According to the invention, a method of generating random numbers comprises the steps of:
         producing a first noise having 1/f characteristic from a first noise generator circuit and a second noise having 1/f characteristic from a second noise generator circuit;   supplying said first and second noises having 1/f characteristic produced from the first and second noise generator circuits to a differential circuit to derive a difference signal between said first noise and said second noise; and   generating, from said difference signal, random numbers which have not a periodicity due to 1/f characteristics of the first and second noises.       

   In the method of generating random numbers according to the invention, although the first and second noises produced by the first and second noise generator circuits have 1/f characteristic, the difference signal derived from these noises does not have a periodicity due to 1/f characteristic owing to a fact that a possibility that noise components having higher frequency, i.e. a higher occurrence frequency are cancelled out becomes higher than a possibility that noise components having lower frequency, i.e. a lower occurrence frequency are cancelled out, and thus an occurrence frequency over a whole frequency range of noise becomes uniform. Therefore, in the difference signal produced from the differential circuit a periodicity due to 1/f characteristic has been cancelled out, and the pure random numbers having no periodicity can be generated. 
   In a preferable embodiment of the random number generating method according to the invention, the output signal from the differential circuit is supplied to an analog-digital converting circuit and is converted thereby into a digital signal. The digital signal thus generated from the analog-digital converting circuit is used as random numbers. In this case, various kinds of random numbers may be obtained by changing lengths of sections of the digital signal sequence. 
   In another preferable embodiment of the random number generating method according to the invention, a single digit is obtained from a single bit or a plurality of bits of the digital signal generated from said analog-digital converting circuit, and then this digit is compared with a predetermined threshold level. When a digit is equal to or larger than the threshold level, “1” of a binary number is allocated and when a digit is smaller than the threshold level, “0” of binary number is allocated. In this case, probabilities of occurrence of “1” and “0” are detected, and said threshold level may be adjusted such that the probabilities of occurrence of “1” and “0” become 0.5 or about 0.5. Alternatively, terms during which probabilities of occurrence of “1” and “0” are detected may be adjusted, for instance by means of the generated random numbers. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a circuit diagram showing an embodiment of a noise generating circuit used in the random number generating method according to the invention; 
       FIG. 2  is a block diagram illustrating an embodiment of the random number generating circuit according to the invention; 
       FIG. 3  is a flow chart representing the operation of the random number generating circuit shown in  FIG. 2 ; 
       FIG. 4  is a diagram showing a distribution of random numbers generated by the method according to the invention; and 
       FIG. 5  is a diagram representing a distribution of random numbers generated by a known method. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1  is a circuit diagram illustrating an embodiment of a noise generating circuit which is used in the random number generating method according to the invention. In the present embodiment, a diode is utilized as a noise source. Since noise generated by the diode is very weak, the noise is amplified. At the same time, a periodic hum which might be contained in a DC supply source is removed. A terminal  11  to which is applied a DC voltage of 12 volts is connected to a positive input terminal of an amplifier  16  by means of resistors  12 ,  13  and electrolytic capacitors  14 ,  15 . A common connection point between the resistor  13  and the electrolytic capacitor  14  is connected to an anode of a noise generating diode  17 , and a cathode of this diode is connected to the ground. Capacitors  18  and  19  are connected between the ground and a junction point between the resistors  12  and  13 . 
   An output terminal of the amplifier  16  is connected to the ground via feedback resistors  21  and  22 , and a junction point between these feedback resistors is connected to a negative input terminal of the amplifier  16 . An output terminal of the amplifier  16  is connected via a coupling capacitor  23  to a high pass filter  24 . A junction point between the coupling capacitor  23  and the high pass filter  24  is connected to the ground by means of a resistor  25 . By providing the high pass filter  24 , a periodic component such as hum contained in the noise can be removed. Therefore, at an output terminal connected to the high pass filter  24 , there is obtained a noise generated by the diode  17  and amplified by the amplifier  16 . This noise has 1/f characteristic and is called noise signal. In  FIG. 1 , values of the resistors and capacitors are shown for the sake of reference, and it should be noted that the present invention is not limited to these values. 
     FIG. 2  is a block diagram showing an embodiment of the random number generating circuit according to the invention. There are provided first and second noise generating circuits  31  and  32  each being constructed by the noise generating circuit shown in FIG.  1 . Noise signals having 1/f characteristic generated from the first and second noise generating circuits  31  and  32  are supplied to a differential circuit  33  and a difference between these noise signals is derived. The noise signal generated from each of the first and second noise generating circuits  31  and  32  has 1/f characteristic, in which a noise component having a lower frequency has a larger amplitude and a noise component having a higher frequency has a smaller amplitude. Therefore, when the noise signal having such 1/f characteristic is subjected to the analog-digital conversion, a frequency of occurrence of a smaller digital signal becomes higher than that of a larger digital signal. This results in a periodicity in the converted digital signal. Therefore, if random numbers are generated from such a digital signal having a periodicity, the random numbers also have a periodicity. In this manner, pure random numbers could not be obtained. 
   In the present invention, in order to suppress the above mentioned periodicity, the noise signals generated from the first and second noise generating circuits  31  and  32  are supplied to the differential circuit  33  and a difference therebetween is derived. Then, a probability that noise components having higher frequencies is higher than a probability that noise components having lower frequencies, and a frequency of occurrence of noise components having higher frequencies is reduced much more than a frequency of occurrence of noise components having lower frequencies. Therefore, a periodicity of the difference signal produced from the differential circuit  33  is reduced, and random numbers having no periodicity due to 1/f characteristic can be generated by the difference signal from the differential circuit  33 . 
   In the present embodiment, the difference signal from the differential circuit  33  is supplied to an analog-digital converting circuit  34  and is converted into a digital signal. The thus generated digital signal is supplied to a calculating circuit  35 . In the calculating circuit  35 , the digital signal supplied from the analog-digital converting circuit  34  may be outputted as random numbers, or another random numbers may be outputted by changing sections of the digital-converted value. In the present embodiment, in the calculating circuit  35 , a numerical value is formed from a single bit or a plurality of bits of the digital signal, and the thus formed numerical value is compared with a predetermined threshold value to generate bivalent bits “1” and “0” of random numbers. 
   When “1” and “0” bits generated by a comparison with the threshold value in the calculating circuit  35  are outputted as random numbers, random numbers might differ from pure random numbers owing to a reason that frequencies of occurrence of these “1” and “0” are not controlled. In the present embodiment, in the calculating circuit  35 , frequencies of occurrence of “1” and “0” bits are calculated and the threshold level is adjusted such that frequencies of occurrence become 0.5 or about 0.5. 
     FIG. 3  is a flow chart showing a process of generating pure random numbers by calculating frequencies of occurrence of “1” and “0” bits and by adjusting the threshold level such that frequencies of occurrence become 0.5 or about 0.5. In a step S 1 , a magnitude of a digital signal supplied from the analog-digital converting circuit  33  is compared with the threshold level, and “1” bit is produced when the digital signal is not less than the threshold level and “0” bit is generated when the digital signal is less than the threshold level. Next, in a step S 2 , frequencies of occurrence of “1” bit and “0” bit are calculated for a predetermined period. 
   Furthermore, in a step S 3 , it is judged whether or not the calculated frequencies of occurrence of “1” bit and “0” bit come closer to 0.5. If it is judged that the frequencies of occurrence do not come closer to 0.5, in a step S 4 , the threshold level is changed. In this case, when a frequency of occurrence of “1” bit is higher than a frequency of occurrence of “0” bit, the threshold level is increased, but when a frequency of occurrence of “1” bit is lower than a frequency of occurrence of “0” bit, the threshold level is decreased. 
   By repeating the above mentioned steps, frequencies of occurrence of “1” bit and “0” bit becomes closer to 0.5, and when it is judged in the step S 3  that frequencies of occurrence of “1” bit and “0” bit becomes closer to 0.5, data of random numbers consisting of “1” bit and “0” bit is recorded in a step S 5 , and when it is confirmed in a step S 6  that a required number of random numbers have been recorded, the recording of random numbers is finished in a step S 7 . 
     FIG. 4  is a diagram showing a distribution of random numbers generated by the method according to the invention. In  FIG. 4 , there are plotted 3000 points each of which is determined such that a generated binary number is divided by every 16 bits and values defined by first and last eight bits are plotted on vertical and horizontal axes, respectively.  FIG. 5  is a diagram illustrating a distribution of random numbers of known method in which only a single noise generating circuit is used. In the method according to the invention, 3000 points are distributed uniformly, and therefore it is understood that random numbers do not have a periodicity due to 1/f characteristic of a noise generating source. However, in the known method shown in  FIG. 5 , points are collected in certain regions to form splashed patterns, and thus random numbers have a periodicity. 
   The present invention is not limited to the embodiment explained above, but many alternations and modifications may be conceived by a person skilled in the art within the scope of the invention. For instance, in the above embodiment, the noise generating source for generating noise having 1/f characteristic is constituted by the diode, but it may be formed by another element such as a resistor. 
   As explained in detail, in the method according to the invention, 1/f characteristic of noise can be suppressed by obtaining a difference between two noises generated from the two noise generating circuits and pure random numbers having no periodicity can be generated from said difference. When codes are generated by using such random numbers, they could not be decoded easily. This contributes to an improvement of a security of important information and a social value of the present invention is very large. Moreover, according to the invention, character of random numbers can be adjusted by controlling frequencies of occurrence of binary numbers “1” and “0”, and therefore information encoded in accordance with such random numbers could not be decoded much more easily.