JP2011034397A - Device and method for making random number generated - Google Patents

Device and method for making random number generated Download PDF

Info

Publication number
JP2011034397A
JP2011034397A JP2009180711A JP2009180711A JP2011034397A JP 2011034397 A JP2011034397 A JP 2011034397A JP 2009180711 A JP2009180711 A JP 2009180711A JP 2009180711 A JP2009180711 A JP 2009180711A JP 2011034397 A JP2011034397 A JP 2011034397A
Authority
JP
Japan
Prior art keywords
light
random number
light source
time difference
threshold
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP2009180711A
Other languages
Japanese (ja)
Other versions
JP4759077B2 (en
Inventor
Yasushi Inoue
恭 井上
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nippon Telegraph and Telephone Corp
Original Assignee
Nippon Telegraph and Telephone Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nippon Telegraph and Telephone Corp filed Critical Nippon Telegraph and Telephone Corp
Priority to JP2009180711A priority Critical patent/JP4759077B2/en
Publication of JP2011034397A publication Critical patent/JP2011034397A/en
Application granted granted Critical
Publication of JP4759077B2 publication Critical patent/JP4759077B2/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Abstract

<P>PROBLEM TO BE SOLVED: To provide a random number generation technique that is simpler than conventional techniques. <P>SOLUTION: A device for generating random numbers includes a light source that outputs amplified natural emission light; a branching means for branching the light from the light source; a delay means for providing a time difference between the branched light beams; a combination means for combining the light beams, given the time difference; a detection means for detecting the strength of the light beams combined; and a threshold means for generating random numbers, by comparing the detected strength of the light beams with a threshold. This allows obtaining a noise signal having fluctuations that are three digits or more greater than those obtained by the conventional techniques that utilize electrical noise. Furthermore, the light frequency bandwidth of an ASE light source is as wide as 1 THz or higher, enabling generation of random numbers of high generation speed. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

本発明は、乱数発生装置に関する。より詳しくは、本発明は、ランダムな「0」「1」のビット列を発生する乱数発生装置に関する。   The present invention relates to a random number generator. More specifically, the present invention relates to a random number generator that generates a random bit string of “0” and “1”.

乱数は暗号システムや認証システムなどに用いられる基本要素であり、乱数発生器はこれらのシステムを構築するうえでの基本デバイスである。通常、乱数は{0、1}のランダムなビット列である。乱数を発生させる手法としては、大きく分けて、計算機上のアルゴリズムで作る算術的方法と物理現象を利用する方法があるが、真にランダムなビット列は後者により生成される。   Random numbers are basic elements used in cryptographic systems and authentication systems, and random number generators are basic devices for constructing these systems. Usually, the random number is a random bit string of {0, 1}. Methods for generating random numbers are roughly divided into an arithmetic method using a computer algorithm and a method using a physical phenomenon. A truly random bit string is generated by the latter.

物理的乱数発生法にもいろいろな手法がある。もっとも一般的であり製品化もされているのは、電気回路の雑音を利用する方法である(非特許文献1参照)。電子が導体内を粒子として移動する際、個々の電子に生じるランダムな運動が、電気的な雑音を引き起こす。そこで、この雑音信号を閾値回路に通し、あるレベル以上ならビット「1」、それ以下ならビット「0」を出力することにより、乱数を得る。   There are various physical random number generation methods. The most common and commercialized method is a method using noise of an electric circuit (see Non-Patent Document 1). As electrons move as particles in a conductor, random motion that occurs in individual electrons causes electrical noise. Therefore, a random number is obtained by passing this noise signal through a threshold circuit and outputting a bit “1” if it is above a certain level and a bit “0” if it is below that level.

真性乱数(物理乱数)生成IC RPG100/RPG100Bカタログ、[online]、2005年9月、FDK株式会社、[平成21年7月15日検索]、インターネット<http://www.fdk.co.jp/cyber-j/pdf/HM-RAJ001.pdf>True random number (physical random number) generation IC RPG100 / RPG100B catalog, [online], September 2005, FDK Corporation, [July 15, 2009 search], Internet <http://www.fdk.co.jp /cyber-j/pdf/HM-RAJ001.pdf>

このような電気的な雑音信号の振幅は一般に大きくはなく、数十μV程度である。これを閾値処理するためには、4〜5桁ほど増幅しなければならない。特に、速い速度で乱数を発生させたい場合、広帯域な回路及び増幅器が必要となり、回路規模や消費電力が大きくなる。そのため、より簡便な乱数発生器を得るためには、振幅が大きくかつ広帯域な雑音信号を発生させる手段が望まれる。   The amplitude of such an electric noise signal is generally not large and is about several tens of μV. In order to threshold this, it must be amplified by 4 to 5 digits. In particular, when it is desired to generate random numbers at a high speed, a broadband circuit and an amplifier are required, which increases the circuit scale and power consumption. Therefore, in order to obtain a simpler random number generator, a means for generating a noise signal having a large amplitude and a wide band is desired.

本発明は、このような問題に鑑みてなされたもので、その目的とするところは、従来よりも簡便な乱数発生技術を提供することにある。特に、振幅が大きくかつ広帯域な雑音信号を発生させる手段を備えた乱数発生技術を提供する。   The present invention has been made in view of such problems, and an object of the present invention is to provide a technique for generating random numbers that is simpler than before. In particular, a random number generation technique including means for generating a noise signal having a large amplitude and a wide band is provided.

本発明は、このような目的を達成するために、請求項1に記載の発明は、乱数を発生させる装置であって、増幅自然放出光を出力する光源と、前記光源からの光を分岐する分岐手段と、前記分岐した光の間に時間差を与える遅延手段と、前記時間差を与えられた光を合波する合波手段と、前記合波された光の強度を検出する検出手段と、前記検出された光の強度を閾値と比較して乱数を生成する閾値手段とを備えたことを特徴とする。   In order to achieve such an object, the present invention is an apparatus for generating a random number, wherein a light source for outputting amplified spontaneous emission light and light from the light source are branched. Branching means; delay means for giving a time difference between the branched lights; multiplexing means for multiplexing the light given the time difference; detecting means for detecting the intensity of the combined light; Threshold means for generating a random number by comparing the detected light intensity with a threshold is provided.

また、請求項2に記載の発明は、請求項1に記載の装置であって、前記分岐手段は、前記光源からの光を2つに分岐することを特徴とする。   The invention according to claim 2 is the apparatus according to claim 1, wherein the branching unit branches light from the light source into two.

また、請求項3に記載の発明は、乱数を発生させる方法であって、増幅自然放出光を分岐することと、前記分岐した光の間に時間差を与えることと、前記時間差を与えられた光を合波することと、前記合波された光の強度を閾値と比較して乱数を生成することとを備えることを特徴とする。   The invention according to claim 3 is a method for generating a random number, wherein the amplified spontaneous emission light is branched, a time difference is given between the branched light, and the time difference is given. And a random number is generated by comparing the intensity of the combined light with a threshold value.

これまで述べてきたように、本発明によれば、揺らぎ幅が大きくかつ広帯域な雑音信号を発生させることができる。これにより、従来よりも簡便な乱数発生器を提供することができる。より具体的には、本発明によれば、電気雑音を利用する従来技術より3桁以上大きな揺らぎを持つ雑音信号を得ることができる。また、光周波数の帯域が広いASE光源を使用することにより、速い生成速度の乱数発生が可能となる。   As described above, according to the present invention, it is possible to generate a noise signal having a wide fluctuation width and a wide band. Thereby, it is possible to provide a random number generator that is simpler than before. More specifically, according to the present invention, it is possible to obtain a noise signal having a fluctuation that is three orders of magnitude greater than that of the prior art using electrical noise. Further, by using an ASE light source having a wide optical frequency band, it is possible to generate a random number at a high generation speed.

本発明の一実施形態による乱数発生器の構成例を示す図である。It is a figure which shows the structural example of the random number generator by one Embodiment of this invention.

図1に、本発明の一実施形態による乱数発生器の基本構成を示す。乱数発生器100は、増幅自然放出(Amplified Spontaneous Emission:AES)光を発生する光源101と、AES光源101の出力と結合された光カップラ102と、光カップラ102の一方の出力と結合された遅延手段103と、光カップラ102の他方の出力および遅延手段103の出力と結合された光カップラ104と、光カップラ104の出力と結合された光強度検出器105と、光強度検出器105の出力と接続された閾値回路106とを備えている。   FIG. 1 shows a basic configuration of a random number generator according to an embodiment of the present invention. The random number generator 100 includes a light source 101 that generates amplified spontaneous emission (AES) light, an optical coupler 102 that is coupled to the output of the AES light source 101, and a delay that is coupled to one output of the optical coupler 102. Means 103, an optical coupler 104 coupled to the other output of optical coupler 102 and the output of delay means 103, an optical intensity detector 105 coupled to the output of optical coupler 104, and an output of optical intensity detector 105 And a connected threshold circuit 106.

ASE光源101は、増幅自然放出(AES)光を発生する。具体的には、信号光が入力されていない光増幅器やスーパールミネッセントダイオード(Super Luminescent Diode:SLD)などがこれにあたる。ASE光源からの出力光は、光カップラ102により2分岐され、一方に対して遅延手段103により時間遅延が与えられた後、光カップラ104により再び合波される。合波された光は、光強度検出器105により電気信号に変換され、光強度検出器からの電気信号は、閾値回路106により電気信号のレベルに応じてビットが判定される。そして、閾値回路106からのビット列は、乱数発生器100の出力となる。なお、光強度検出器105からの電気信号は、必要に応じて増幅器により増幅してもよい。   The ASE light source 101 generates amplified spontaneous emission (AES) light. Specifically, an optical amplifier to which signal light is not input, a super luminescent diode (SLD), or the like corresponds to this. The output light from the ASE light source is branched into two by the optical coupler 102, one of which is given a time delay by the delay means 103, and then multiplexed again by the optical coupler 104. The combined light is converted into an electric signal by the light intensity detector 105, and the bit of the electric signal from the light intensity detector is determined by the threshold circuit 106 according to the level of the electric signal. Then, the bit string from the threshold circuit 106 becomes an output of the random number generator 100. Note that the electrical signal from the light intensity detector 105 may be amplified by an amplifier as necessary.

このような構成における信号の流れを、式を使用して説明する。   The signal flow in such a configuration will be described using equations.

まず、ASE光源からは広い波長範囲にわたって位相がランダムな光(自然放出光)が出力される。出力光の波長範囲を微小単位の波長域に区切り、k番目の波長域の出力光をAkexp[i(ωkt+θk)]と表わすと、全出力光はそれらの足し合わせとして次のように表される。 First, light having a random phase (spontaneously emitted light) is output from an ASE light source over a wide wavelength range. When the wavelength range of the output light is divided into minute wavelength ranges, and the output light in the kth wavelength range is expressed as A k exp [i (ω k t + θ k )], the total output light is the sum of the following: It is expressed as follows.

Figure 2011034397
Figure 2011034397

ここで、ωkはk番目波長域の光の角周波数、θkはその位相、Akはその振幅であり、ΣはASE光源の出力波長範囲の和を表す。Akは時間的に一定である一方、位相θkはランダムに変動する。 Here, ω k is the angular frequency of light in the kth wavelength region, θ k is its phase, A k is its amplitude, and Σ represents the sum of the output wavelength ranges of the ASE light source. While A k is constant over time, the phase θ k varies randomly.

ASE光源からの出力は2分岐され、一方に遅延時間τが与えられた後に再び合波される。合波後の光は次のように表わされる。   The output from the ASE light source is branched into two, and after being given a delay time τ, it is combined again. The combined light is expressed as follows.

Figure 2011034397
Figure 2011034397

第1項が短い経路を経た光、第2が長い経路を経た光を表わしている。長い経路を経た光は、遅延を受けた分、時間がτだけシフトしている。 The first term represents light passing through a short path, and the second term represents light passing through a long path. The light passing through the long path is shifted by τ by the amount of delay.

合波後の光は光強度検出器により電気信号に変換される。この電気信号は、次のように表わされる。   The combined light is converted into an electrical signal by a light intensity detector. This electrical signal is expressed as follows.

Figure 2011034397
Figure 2011034397

各微小波長域の位相θkは、時間的にランダムに変動し、また異なる波長域間の相対位相(θk−θk')もランダムである。したがって、式(1)の第2〜4項はランダムに変動する。そこで、この電気信号を閾値回路に入力し、あるレベル以上ならビット「1」、それ以下ならビット「0」とすれば、乱数を得ることができる。 The phase θ k of each minute wavelength region varies randomly with time, and the relative phase (θ k −θ k ′ ) between different wavelength regions is also random. Therefore, the second to fourth terms of Equation (1) vary randomly. Therefore, if this electric signal is input to the threshold circuit and the bit is “1” if it is above a certain level and bit “0” if it is less than that level, a random number can be obtained.

式(1)において、第1項以外は全てランダムに変動する項となっている。各項の大きさはほぼ同じオーダーである。したがって、式(1)で表わされる電気信号は、信号全体が大きく変動する。ところで、一般的な光強度検出器であるアバランシェフォトダイオード(APD)の光-電気変換効率は、1A/W程度である。つまり、数mWの光信号から数mAの電気信号が発生する。これは、50Ω回路系では100mV以上に相当する。また、光増幅器やスーパールミネッセントダイオードから数mW程度のASE光を得るのは容易である。これらのことより、本実施形態では、電気雑音を利用する従来技術より3桁以上大きな揺らぎを持つ雑音信号が得られることが分かる。   In the formula (1), all except the first term are terms that randomly vary. The size of each term is almost the same order. Therefore, the entire signal of the electrical signal represented by Equation (1) varies greatly. By the way, the photoelectric conversion efficiency of an avalanche photodiode (APD), which is a general light intensity detector, is about 1 A / W. That is, an electric signal of several mA is generated from an optical signal of several mW. This corresponds to 100 mV or more in the 50Ω circuit system. Moreover, it is easy to obtain ASE light of about several mW from an optical amplifier or a super luminescent diode. From these facts, it can be seen that in the present embodiment, a noise signal having a fluctuation that is three orders of magnitude larger than that of the prior art using electrical noise can be obtained.

さらに帯域についてみてみると、式(1)の信号の周波数帯域は、ASE光の光周波数帯域にわたっている。上記ASE光源の光周波数帯域は1THz以上であり、式(1)の信号周波数帯域も同じ程度と考えられる。これを利用すると、速い生成速度の乱数発生が可能である。   Further, regarding the band, the frequency band of the signal of the formula (1) covers the optical frequency band of the ASE light. The optical frequency band of the ASE light source is 1 THz or more, and the signal frequency band of Expression (1) is considered to be the same level. By using this, it is possible to generate random numbers at a high generation speed.

以上、本発明について、特定の実施形態について具体的に説明したが、本発明の原理を適用できる多くの実施可能な形態に鑑みて、ここに記載した実施形態は、単に例示に過ぎず、本発明の範囲を限定するものではない。ここに例示した実施形態は、本発明の趣旨から逸脱することなくその構成と詳細を変更することができる。さらに、説明のための構成要素および手順は、本発明の趣旨から逸脱することなく変更、補足、またはその順序を変えてもよい。   Although the present invention has been specifically described above with reference to specific embodiments, the embodiments described herein are merely illustrative in view of the many possible embodiments to which the principles of the present invention can be applied. It is not intended to limit the scope of the invention. The configuration and details of the embodiment exemplified here can be changed without departing from the spirit of the present invention. Further, the illustrative components and procedures may be changed, supplemented, or changed in order without departing from the spirit of the invention.

100 乱数発生器
101 AES光源
102 光カップラ
103 遅延手段
104 光カップラ
105 光強度検出器
106 閾値回路
DESCRIPTION OF SYMBOLS 100 Random number generator 101 AES light source 102 Optical coupler 103 Delay means 104 Optical coupler 105 Optical intensity detector 106 Threshold circuit

Claims (3)

乱数を発生させる装置であって、
増幅自然放出光を出力する光源と、
前記光源からの光を分岐する分岐手段と、
前記分岐した光の間に時間差を与える遅延手段と、
前記時間差を与えられた光を合波する合波手段と、
前記合波された光の強度を検出する検出手段と、
前記検出された光の強度を閾値と比較して乱数を生成する閾値手段と
を備えたことを特徴とする装置。
A device for generating random numbers,
A light source that outputs amplified spontaneous emission light;
Branching means for branching light from the light source;
Delay means for providing a time difference between the branched lights;
A multiplexing means for multiplexing the light given the time difference;
Detecting means for detecting the intensity of the combined light;
An apparatus comprising: threshold means for comparing the detected light intensity with a threshold to generate a random number.
請求項1に記載の装置であって、
前記分岐手段は、前記光源からの光を2つに分岐することを特徴とする装置。
The apparatus of claim 1, comprising:
The branching means branches the light from the light source into two.
乱数を発生させる方法であって、
増幅自然放出光を分岐することと、
前記分岐した光の間に時間差を与えることと、
前記時間差を与えられた光を合波することと、
前記合波された光の強度を閾値と比較して乱数を生成することと
を備えることを特徴とする方法。
A method for generating random numbers,
Branching the amplified spontaneous emission; and
Providing a time difference between the branched lights;
Combining the light given the time difference;
Comparing the intensity of the combined light with a threshold to generate a random number.
JP2009180711A 2009-08-03 2009-08-03 Apparatus and method for generating random numbers Active JP4759077B2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP2009180711A JP4759077B2 (en) 2009-08-03 2009-08-03 Apparatus and method for generating random numbers

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP2009180711A JP4759077B2 (en) 2009-08-03 2009-08-03 Apparatus and method for generating random numbers

Publications (2)

Publication Number Publication Date
JP2011034397A true JP2011034397A (en) 2011-02-17
JP4759077B2 JP4759077B2 (en) 2011-08-31

Family

ID=43763397

Family Applications (1)

Application Number Title Priority Date Filing Date
JP2009180711A Active JP4759077B2 (en) 2009-08-03 2009-08-03 Apparatus and method for generating random numbers

Country Status (1)

Country Link
JP (1) JP4759077B2 (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20170024327A (en) * 2015-08-25 2017-03-07 에스케이텔레콤 주식회사 Apparatus for generating random number based on quantum shot noise of multiple light sources
US10019235B2 (en) 2011-09-30 2018-07-10 Los Alamos National Security, Llc Quantum random number generators
JP2018528520A (en) * 2015-07-29 2018-09-27 ロスアラモス・ナショナル・セキュリティ,エルエルシー Quantum random number generator
CN109828745A (en) * 2019-02-25 2019-05-31 华中科技大学 A kind of quantum random number generator

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110632764B (en) * 2019-10-31 2021-05-25 太原理工大学 Chaotic light generating device based on TOAD ring

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000276329A (en) * 1999-03-26 2000-10-06 Takeshi Saito Device for generating very high speed physical random number
JP2009070009A (en) * 2007-09-12 2009-04-02 Sony Corp Random number generation device and random number generation method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000276329A (en) * 1999-03-26 2000-10-06 Takeshi Saito Device for generating very high speed physical random number
JP2009070009A (en) * 2007-09-12 2009-04-02 Sony Corp Random number generation device and random number generation method

Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10019235B2 (en) 2011-09-30 2018-07-10 Los Alamos National Security, Llc Quantum random number generators
US10564933B2 (en) 2011-09-30 2020-02-18 Triad National Security, Llc Quantum random number generators
US11442698B2 (en) 2011-09-30 2022-09-13 Triad National Security, Llc Quantum random number generators
JP2018528520A (en) * 2015-07-29 2018-09-27 ロスアラモス・ナショナル・セキュリティ,エルエルシー Quantum random number generator
JP2020074152A (en) * 2015-07-29 2020-05-14 トライアド ナショナル セキュリティ リミテッド ライアビリティ カンパニー Quantum random number generator
JP2021180038A (en) * 2015-07-29 2021-11-18 トライアド ナショナル セキュリティ リミテッド ライアビリティ カンパニー Quantum random number generator
JP7025458B2 (en) 2015-07-29 2022-02-24 トライアド ナショナル セキュリティ リミテッド ライアビリティ カンパニー Quantum random number generator
JP7264949B2 (en) 2015-07-29 2023-04-25 トライアド ナショナル セキュリティ リミテッド ライアビリティ カンパニー quantum random number generator
KR20170024327A (en) * 2015-08-25 2017-03-07 에스케이텔레콤 주식회사 Apparatus for generating random number based on quantum shot noise of multiple light sources
KR101880520B1 (en) * 2015-08-25 2018-07-20 에스케이텔레콤 주식회사 Apparatus for generating random number based on quantum shot noise of multiple light sources
CN109828745A (en) * 2019-02-25 2019-05-31 华中科技大学 A kind of quantum random number generator

Also Published As

Publication number Publication date
JP4759077B2 (en) 2011-08-31

Similar Documents

Publication Publication Date Title
JP4759077B2 (en) Apparatus and method for generating random numbers
US20200233645A1 (en) Quantum random number generators
EP3329359B1 (en) Quantum random number generators
Tanner et al. High-resolution single-mode fiber-optic distributed Raman sensor for absolute temperature measurement using superconducting nanowire single-photon detectors
Yuan et al. Robust random number generation using steady-state emission of gain-switched laser diodes
Zhang et al. Note: Fully integrated 3.2 Gbps quantum random number generator with real-time extraction
CN106354476B (en) Quantum random number generator based on laser phase fluctuation and quantum random number generation method
Modena et al. Observation of Raman forward scattering and electron acceleration in the relativistic regime
Shi et al. Random numbers from vacuum fluctuations
CN103793198B (en) Based on quantum random number generator and the method for amplifying vacuum state
US8554814B2 (en) Random signal generator using quantum noise
US10585645B2 (en) Quantum random number generator
EP3423935B1 (en) Method and system for random number generation
WO2010029638A1 (en) Photon detector
CN108037907B (en) Quantum random number generation method based on vacuum parallelism
Li et al. Analysis of the effects of temperature increase on quantum random number generator
Kodet et al. Note: Optical trigger device with sub-picosecond timing jitter and stability
Wei et al. Compact quantum random number generator based on superluminescent light-emitting diodes
CN108536424A (en) A kind of quantum random number generator based on vacuum fluctuation
RU2450287C1 (en) Nonlinear radar positioning method
Biewer et al. Initial implementation of a Thomson scattering diagnostic for Proto-MPEX
CN107817967B (en) SFP (Small form-factor pluggable) based integrated quantum random number generator
JP5654509B2 (en) Fluorescence detection apparatus and fluorescence detection method
JP2009236496A (en) High-frequency band noise-producing device
WO2014010056A1 (en) Photon detection device and method

Legal Events

Date Code Title Description
TRDD Decision of grant or rejection written
A01 Written decision to grant a patent or to grant a registration (utility model)

Free format text: JAPANESE INTERMEDIATE CODE: A01

Effective date: 20110527

A01 Written decision to grant a patent or to grant a registration (utility model)

Free format text: JAPANESE INTERMEDIATE CODE: A01

A61 First payment of annual fees (during grant procedure)

Free format text: JAPANESE INTERMEDIATE CODE: A61

Effective date: 20110603

R150 Certificate of patent or registration of utility model

Ref document number: 4759077

Country of ref document: JP

Free format text: JAPANESE INTERMEDIATE CODE: R150

Free format text: JAPANESE INTERMEDIATE CODE: R150

FPAY Renewal fee payment (event date is renewal date of database)

Free format text: PAYMENT UNTIL: 20140610

Year of fee payment: 3

S531 Written request for registration of change of domicile

Free format text: JAPANESE INTERMEDIATE CODE: R313531

R350 Written notification of registration of transfer

Free format text: JAPANESE INTERMEDIATE CODE: R350