王龍生趙彤王大銘吳旦昱周磊武錦劉新宇王安幫

1)(太原理工大學(xué),新型傳感器與智能控制教育部重點(diǎn)實(shí)驗(yàn)室,太原 030024)

2)(太原理工大學(xué)物理與光電工程學(xué)院,光電工程研究所,太原 030024)

3)(中國科學(xué)院微電子研究所微波器件與集成電路研究室,北京 100029)

利用混沌激光多位量化實(shí)時(shí)產(chǎn)生14 Gb/s的物理隨機(jī)數(shù)?

王龍生1)2)趙彤1)2)王大銘1)2)吳旦昱3)周磊3)武錦3)劉新宇3)?王安幫1)2)?

1)(太原理工大學(xué),新型傳感器與智能控制教育部重點(diǎn)實(shí)驗(yàn)室,太原 030024)

2)(太原理工大學(xué)物理與光電工程學(xué)院,光電工程研究所,太原 030024)

3)(中國科學(xué)院微電子研究所微波器件與集成電路研究室,北京 100029)

半導(dǎo)體激光器,混沌激光,多位量化,物理隨機(jī)數(shù)

1 引 言

隨機(jī)數(shù)在數(shù)值模擬、加密通信等領(lǐng)域具有重要的應(yīng)用潛力[1,2].根據(jù)產(chǎn)生方式劃分,隨機(jī)數(shù)可分為偽隨機(jī)數(shù)與物理隨機(jī)數(shù)兩大類.偽隨機(jī)數(shù)基于固定的算法與種子產(chǎn)生,實(shí)時(shí)速率可達(dá)數(shù)Gb/s量級(jí),但受限于周期性與可重復(fù)性等固有缺陷,其隨機(jī)性不甚理想.物理隨機(jī)數(shù)基于物理隨機(jī)現(xiàn)象產(chǎn)生,如電阻熱噪聲、振蕩器頻率啁啾等,其隨機(jī)性優(yōu)良可靠[3,4].然而,受限于信號(hào)帶寬,隨機(jī)數(shù)的實(shí)時(shí)產(chǎn)生速率僅為Mb/s量級(jí),難以滿足實(shí)際應(yīng)用.特別是面向信息安全領(lǐng)域,高速物理隨機(jī)數(shù)的實(shí)時(shí)產(chǎn)生顯得尤為重要.

近年來,光子寬帶熵源,如放大自發(fā)輻射、激光相位抖動(dòng)以及混沌激光等被廣泛用于生成高速物理隨機(jī)數(shù).特別是混沌激光因其高帶寬、大幅度等特性,被用作新一代物理熵源以解決物理隨機(jī)數(shù)實(shí)時(shí)生成速率不足的問題,獲得了國際、國內(nèi)學(xué)者的廣泛關(guān)注[5?8].例如,日本Uchida等[5]利用外腔反饋混沌半導(dǎo)體激光器作為熵源,通過1位模數(shù)轉(zhuǎn)換器(ADC)量化與異或邏輯門(XOR)處理之后,實(shí)時(shí)產(chǎn)生了1.7 Gb/s的物理隨機(jī)數(shù);隨后,該課題組利用光子集成外腔反饋半導(dǎo)體激光器作為熵源將產(chǎn)生速率提升至2.08 Gb/s[6];Wang等[7]結(jié)合外腔反饋混沌半導(dǎo)體激光器與1位延遲差分比較以及異或處理,將實(shí)時(shí)速率進(jìn)一步提升至4.5 Gb/s;此外,趙東亮等[8]利用1位差分比較器對(duì)外腔反饋混沌激光的離散脈沖序列進(jìn)行自延遲比較,在線實(shí)時(shí)獲得了7 Gb/s的物理隨機(jī)數(shù).然而,基于外腔反饋混沌激光1位量化的隨機(jī)數(shù)產(chǎn)生速率也面臨瓶頸問題,主要原因是1位量化速率依賴于熵源帶寬,而外腔反饋混沌半導(dǎo)體激光器的熵源帶寬受弛豫振蕩限制幾乎達(dá)到極限[9].通過光注入、光拍頻等方法[10?14]雖然可以增加混沌激光的帶寬以提高1位量化的實(shí)時(shí)生成速率,但速率上升空間有限,同時(shí)會(huì)引入系統(tǒng)復(fù)雜、成本高昂的缺陷,不利于實(shí)際應(yīng)用.

更加有效的解決方法是利用多位ADC對(duì)混沌激光進(jìn)行量化,通過抽取多位有效位的隨機(jī)數(shù)來成倍增加生成速率[15?25].例如,以色列Reidler等[15]利用8位ADC對(duì)外腔反饋混沌激光量化,經(jīng)一階求導(dǎo)后續(xù)處理之后,通過抽取低5位有效位獲得了12.5 Gb/s的物理隨機(jī)數(shù);唐曦等[16]利用8位ADC對(duì)互注入混沌激光量化,通過抽取低7位有效位并結(jié)合異或處理獲得了速率為17.5 Gb/s的物理隨機(jī)數(shù);Kanter等[17]利用8位ADC對(duì)外腔反饋混沌激光量化,經(jīng)多階求導(dǎo)后續(xù)處理之后,通過抽取低15位有效位獲得了速率為300 Gb/s的物理隨機(jī)數(shù).Li等[18]利用8位ADC對(duì)外腔反饋混沌激光量化,經(jīng)高階有限差分后續(xù)處理之后,通過抽取低55位有效位獲得了速率為2.2 Tb/s物理隨機(jī)數(shù).值得注意的是,盡管上述多位量化抽取方案能夠獲得超高速物理隨機(jī)數(shù),但均是通過示波器存儲(chǔ)混沌信號(hào)波形后進(jìn)行離線處理得到的,并非在線實(shí)時(shí)產(chǎn)生,在一定程度上限制了實(shí)際應(yīng)用.

本文提出了一種基于混沌激光多位量化的高速物理隨機(jī)數(shù)實(shí)時(shí)產(chǎn)生方法并進(jìn)行了實(shí)驗(yàn)驗(yàn)證.以外腔反饋混沌半導(dǎo)體激光器作為熵源,通過時(shí)鐘速率為7 GHz的6位ADC對(duì)其采樣量化,生成從最高位至最低位6位有效位的0,1序列,利用現(xiàn)場(chǎng)可編程軟件(FPGA)抽取低2位有效位并進(jìn)行自延遲異或處理,最終獲得了實(shí)時(shí)速率為14 Gb/s的物理隨機(jī)數(shù).該隨機(jī)數(shù)具有良好的統(tǒng)計(jì)隨機(jī)性,可成功通過隨機(jī)數(shù)行業(yè)測(cè)試標(biāo)準(zhǔn)(NIST SP 800-22).

2 實(shí)驗(yàn)裝置

基于混沌激光多位量化實(shí)時(shí)產(chǎn)生高速物理隨機(jī)數(shù)的實(shí)驗(yàn)裝置如圖1所示.半導(dǎo)體激光器(DFB)經(jīng)偏振控制器(PC)之后進(jìn)入50:50耦合器(FC)分成兩路,其中一路進(jìn)入鏡面(FM)構(gòu)成的外腔,經(jīng)衰減器(VA)進(jìn)行強(qiáng)度調(diào)節(jié)之后,返回激光器擾動(dòng)產(chǎn)生混沌激光.混沌激光經(jīng)另外一路光纖通道輸出至光電探測(cè)器(PD),轉(zhuǎn)換為電信號(hào),該信號(hào)隨后經(jīng)時(shí)鐘(Clock)與FPGA控制下的6位ADC采樣量化,輸出從最高位至最低位6位有效位的隨機(jī)序列,FPGA抽取低2位有效位并進(jìn)行自延遲異或處理,最終獲得了實(shí)時(shí)高速的物理隨機(jī)數(shù).

實(shí)驗(yàn)中,半導(dǎo)體激光器(Eblana,EP1550-DM-B05-FM)閾值電流為13.68 mA,電流源(ILX Lightwave,LDX-3412)調(diào)節(jié)激光器工作電流為34 mA,溫控源(ILX Lightwave,LDT-5412)調(diào)節(jié)激光器工作波長為1550.486 nm;外腔反饋延遲為107.9 ns,衰減器調(diào)節(jié)外腔反饋強(qiáng)度為總輸出強(qiáng)度的?10.2 dB;光電探測(cè)器(BPDV2120R)帶寬為45 GHz;多位ADC為自主研發(fā),由四個(gè)6位子ADC構(gòu)成[26],實(shí)驗(yàn)中利用其中一個(gè)6位子ADC進(jìn)行采樣量化,采樣頻率為7 GHz,由時(shí)鐘(Agilent,E8257D)控制;FPGA(Virtex-7 XC7 VX690 T)對(duì)6位ADC進(jìn)行實(shí)時(shí)同步控制并抽取低2位隨機(jī)序列進(jìn)行自延遲異或處理,延遲長度為70 bit.此外,混沌激光的光譜、功率譜以及時(shí)序分別由光譜儀(YOKOGAWA,AQ6370C,0.02 nm)、頻譜儀(Agilent,N9030A,43 GHz)以及示波器(LeCroy,SDA806Zi-A,16 GHz,40 GS/s)測(cè)量.

圖1 基于混沌激光多位量化實(shí)時(shí)產(chǎn)生高速物理隨機(jī)數(shù)的實(shí)驗(yàn)裝置Fig.1.Experimental setup of real-time high-speed physical random number generation based on multi-bit quantization of laser chaos.

3 實(shí)驗(yàn)結(jié)果

3.1 混沌激光特性分析

圖2(a)為混沌激光的功率譜(黑線所示),灰線為頻譜儀的噪聲基底,按照功率譜能量80%計(jì)算[27],混沌激光的帶寬約為10 GHz,大于實(shí)驗(yàn)中ADC的采樣速率.圖2(b)為混沌激光的時(shí)序,從時(shí)序可知,外腔反饋半導(dǎo)體激光器輸出具有高速的類噪聲振蕩,且振蕩幅度可達(dá)上百毫伏,如此大幅度振蕩有助于ADC的采樣與量化.圖2(c)為混沌激光的幅值分布,可以看出分布函數(shù)呈現(xiàn)明顯的不對(duì)稱,其偏斜度為1.74,該不對(duì)稱性將導(dǎo)致0,1 bit的比例不均衡,降低隨機(jī)數(shù)的隨機(jī)性.圖2(d)為混沌激光的自相關(guān)曲線,零峰處的相關(guān)系數(shù)迅速衰減至噪聲基底附近,而在外腔周期處(107.9 ns)又會(huì)出現(xiàn)另外一個(gè)相關(guān)峰,該峰是由于外腔諧振導(dǎo)致,稱為時(shí)延特征[28].該特征將會(huì)導(dǎo)致混沌激光時(shí)域波形與之前的狀態(tài)存在周期性的弱相關(guān)(弱周期性),惡化了生成隨機(jī)數(shù)的隨機(jī)性.值得注意的是,有效位抽取可在一定程度上削弱非對(duì)稱幅值分布與時(shí)延特征帶來的影響,但通常需要結(jié)合其他后續(xù)處理,如異或、求導(dǎo)以及比特反轉(zhuǎn)等來徹底消除[29].

圖2 混沌激光特性 (a)功率譜;(b)時(shí)序;(c)幅值分布;(d)自相關(guān)曲線Fig.2.Characteristics of laser chaos:(a)Power spectrum;(b)time series;(c)amplitude distribution;(d)autocorrelation trace.

3.2 隨機(jī)數(shù)提取與測(cè)評(píng)

混沌激光經(jīng)6位ADC采樣量化之后生成多位有效位的隨機(jī)比特,通過FPGA抽取其中低2位并進(jìn)行自延遲異或處理之后作為最終隨機(jī)序列.實(shí)驗(yàn)中得到的次低位(2nd least significant bit 2nd LSB)與最低位(LSB)隨機(jī)比特的碼型圖與眼圖分別如圖3(a)與圖3(b)所示.由碼型圖可知,隨機(jī)碼為非歸零碼,7 bit位于1 ns之內(nèi),表明1位有效位抽取時(shí)隨機(jī)數(shù)的生成速率為7 Gb/s.眼圖張開良好,眼圖交叉點(diǎn)之間的間隔為143.4 ps(23.9×6),等于一個(gè)碼型寬度.

為了分析隨機(jī)數(shù)的統(tǒng)計(jì)隨機(jī)性,定性研究了隨機(jī)數(shù)經(jīng)數(shù)模轉(zhuǎn)換之后十進(jìn)制波形的均衡性與相關(guān)性.圖4為低2位有效位隨機(jī)數(shù)對(duì)應(yīng)的十進(jìn)制波形,左側(cè)縱軸為十進(jìn)制水平(0—3),右側(cè)縱軸為對(duì)應(yīng)的二進(jìn)制水平(00—11),十進(jìn)制水平0代表二進(jìn)制00,十進(jìn)制水平3代表二進(jìn)制11;其中二進(jìn)制水平的左邊一位代表2位有效位中的2nd LSB,右邊一位代表LSB.

圖3 隨機(jī)比特的碼型圖與眼圖 (a)2nd LSB;(b)LSBFig.3.Temporal waveforms and eye diagrams of random bits for(a)2nd LSB and(b)LSB.

圖4 低2位有效位隨機(jī)數(shù)對(duì)應(yīng)的十進(jìn)制波形Fig.4.Decimal waveforms of binary sequence with 2LSBs.

圖5(a)與圖5(c)分別為異或處理之前十進(jìn)制波形的幅值分布與自相關(guān)曲線,圖5(b)與圖5(d)分別為異或處理之后十進(jìn)制波形的幅值分布與自相關(guān)曲線.如圖5(a)所示,異或之前十進(jìn)制波形的幅值分布呈現(xiàn)非均衡性,主要體現(xiàn)在不同幅值的出現(xiàn)概率不同:幅值2出現(xiàn)的概率明顯高于其他幅值的出現(xiàn)概率;異或之后,如圖5(b)所示,各個(gè)幅值的出現(xiàn)概率幾乎相等,有利于生成0,1 bit均衡的物理隨機(jī)數(shù).此外,如圖5(c)所示,異或之前十進(jìn)制波形的自相關(guān)曲線在外腔周期處仍存在相關(guān)峰,表明波形之間依然具有周期性的相關(guān).異或之后,如圖5(d)所示,該相關(guān)峰消失,表明十進(jìn)制波形得到了優(yōu)化,有利于生成隨機(jī)性優(yōu)良的物理隨機(jī)數(shù).

進(jìn)一步定量研究了生成隨機(jī)數(shù)的均衡性與相關(guān)性.均衡性與相關(guān)性可分別通過計(jì)算0,1 bit的偏斜函數(shù)|e[N]|與自相關(guān)函數(shù)C[K]來衡量,定義如下:

其中,a[N],a[N+K]均為長度為N的0,1隨機(jī)序列,K為延遲比特的長度,〈·〉為統(tǒng)計(jì)平均運(yùn)算.對(duì)于一列有限長度的隨機(jī)序列,通常利用高斯統(tǒng)計(jì)分布估計(jì)N[0,σ2]來評(píng)估其統(tǒng)計(jì)隨機(jī)性.對(duì)于高斯分布,其偏斜函數(shù)|e[N]|的標(biāo)準(zhǔn)偏差σe和自相關(guān)函數(shù)C[K]的標(biāo)準(zhǔn)偏差σc分別為(N?1/2)/2和N?1/2.當(dāng)|e[N]|和C[K]分別小于對(duì)應(yīng)的三倍標(biāo)準(zhǔn)偏差,即3σe與 3σc,隨機(jī)序列可被認(rèn)為是統(tǒng)計(jì)無偏和內(nèi)部獨(dú)立的[7].

圖6(a)為隨機(jī)數(shù)異或前后偏斜函數(shù)的變化情況,異或之前(綠色曲線所示),在不同樣本容量下(1—16 Mbits),隨機(jī)數(shù)偏斜量明顯高于對(duì)應(yīng)的三倍標(biāo)準(zhǔn)偏差(紅色曲線)且基本保持不變.相比之下,異或之后(藍(lán)色曲線所示),不同樣本容量隨機(jī)數(shù)的偏斜量均小于對(duì)應(yīng)的三倍標(biāo)準(zhǔn)偏差.圖6(b)為16 Mbits隨機(jī)數(shù)異或前后自相關(guān)函數(shù)的變化情況,異或之前(綠色曲線所示),隨機(jī)數(shù)的相關(guān)系數(shù)高于對(duì)應(yīng)的三倍標(biāo)準(zhǔn)偏差(紅線所示),更加明顯的是,在1511個(gè)延遲比特附近出現(xiàn)了大幅值的相關(guān)峰,此峰是由外腔時(shí)延導(dǎo)致,位置與外腔周期呈對(duì)應(yīng)關(guān)系:1511/14=107.9 ns.對(duì)比之下,異或之后隨機(jī)數(shù)自相關(guān)系數(shù)(藍(lán)色曲線所示)低于對(duì)應(yīng)的三倍標(biāo)準(zhǔn)偏差.以上結(jié)果表明,本實(shí)驗(yàn)最終得到的由低2位有效位構(gòu)成的隨機(jī)序列是無偏且內(nèi)部獨(dú)立的.

圖5 低2位隨機(jī)數(shù)異或前后十進(jìn)制波形的幅值分布與自相關(guān)曲線Fig.5.Amplitude distribution and autocorrelation trace of decimal waveforms of 2-LSBs random bits with and without XOR operation.

圖6 (網(wǎng)刊彩色)低2位有效位隨機(jī)數(shù)異或前后0,1比特偏斜與獨(dú)立性的定量評(píng)估 (a)0,1偏斜|e[N]|隨樣本量N的變化曲線;(b)自相關(guān)函數(shù)C[K]隨延遲比特K的變化曲線Fig.6.(color online)Quantitative verification of bias and independence for 2-LSBs random bits with and without XOR operation:(a)Bias|e[N]|as a function of sample size N;(b)autocorrelation function C[K]as a function of delay bit K.

進(jìn)一步采用國際行業(yè)測(cè)試標(biāo)準(zhǔn)(NIST SP800-22)對(duì)產(chǎn)生的隨機(jī)數(shù)進(jìn)行測(cè)試[30].該測(cè)試包含15個(gè)子測(cè)試項(xiàng),在顯著水平大于0.01的基礎(chǔ)上,對(duì)1000組1 Mbits的隨機(jī)數(shù)進(jìn)行測(cè)試.為了通過測(cè)試,測(cè)試結(jié)果的一致性(P值)應(yīng)大于0.0001,且通過百分比在0.99±0.0094392的范圍之內(nèi).表1為隨機(jī)數(shù)的NIST測(cè)試結(jié)果,對(duì)于具有多個(gè)P值和通過百分比的測(cè)試項(xiàng),本文只給出了最差的測(cè)試情況.從測(cè)試結(jié)果來看,該隨機(jī)序列能夠通過所有15項(xiàng)隨機(jī)性測(cè)試,說明其具有良好的統(tǒng)計(jì)隨機(jī)性.

以上結(jié)果表明,利用混沌激光多位量化可實(shí)時(shí)產(chǎn)生14 Gb/s的物理隨機(jī)數(shù).我們也曾通過1位量化實(shí)時(shí)產(chǎn)生了14 Gb/s的物理隨機(jī)數(shù)[31],其關(guān)鍵在于利用兩個(gè)外腔半導(dǎo)體激光器的光外差來優(yōu)化混沌激光的信號(hào)特征:增加帶寬與平坦度、改善幅值分布以及消除時(shí)延特征.需注意,1位量化速率主要依賴于混沌信號(hào)帶寬,在熵源帶寬有限的條件下,隨機(jī)數(shù)的生成速率也受到了限制.對(duì)比之下,本方案僅需一個(gè)外腔半導(dǎo)體激光器作為生成隨機(jī)數(shù)的信號(hào)源,系統(tǒng)結(jié)構(gòu)簡單、操作靈活.更加重要的是,無需增加熵源信號(hào)帶寬,通過多位量化與有效位抽取便可成倍增加隨機(jī)數(shù)的生成速率,獲得實(shí)時(shí)高速的物理隨機(jī)數(shù).

表1 NIST隨機(jī)性測(cè)試結(jié)果Table 1.Results of NIST statistical test.

4 結(jié) 論

提出了一種基于混沌激光多位量化的高速物理隨機(jī)數(shù)的實(shí)時(shí)產(chǎn)生方法.利用采樣率為7 GHz的6位ADC對(duì)外腔混沌激光采樣量化,生成多位有效位的隨機(jī)比特.通過FPGA實(shí)時(shí)抽取低2位有效位并進(jìn)行自延遲異或處理,實(shí)驗(yàn)中獲得了14 Gb/s的物理隨機(jī)數(shù).該隨機(jī)數(shù)具有良好的0,1均衡比與內(nèi)部獨(dú)立性,可通過國際行業(yè)標(biāo)準(zhǔn)測(cè)試(NIST SP800-22).本項(xiàng)研究可為高速物理隨機(jī)數(shù)的實(shí)時(shí)產(chǎn)生提供一種更加有效的解決途徑,促進(jìn)物理隨機(jī)數(shù)在信息安全領(lǐng)域的應(yīng)用.

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14-Gb/s physical random numbers generated in real time by using multi-bit quantization of chaotic laser?

Wang Long-Sheng1)2)Zhao Tong1)2)Wang Da-Ming1)2)Wu Dan-Yu3)Zhou Lei3)Wu Jin3)Liu Xin-Yu3)?Wang An-Bang1)2)?

1)(Key Laboratory of Advanced Transducers and Intelligent Control System,Ministry of Education,Taiyuan University of Technology,Taiyuan 030024,China)
2)(Institute of Optoelectronic Engineering,College of Physics and Optoelectronics,Taiyuan University of Technology,Taiyuan 030024,China)
3)(Microwave Devices and Integrated Circuit Laboratory,Institute of Microelectronics of Chinese Academy of Sciences,Beijing 100029,China)

12 July 2017;revised manuscript

4 August 2017)

Real-time high-speed physical random numbers are crucial for a broad spectrum of applications in cryptography,communications as well as numerical computations and simulations.Chaotic laser is promising to construct high-speed physical random numbers in real time bene fitting from its complex nonlinear dynamics.However,the real-time generation rate of physical random numbers by using single-bit extraction is confronted with a bottleneck because of the bandwidth limitation caused by laser relaxation,which dominates the laser chaos and then limits the effective bandwidth only to a few GHz.Although some bandwidth-enhanced methods have been proposed to increase the single-bit generation rate,the potential is very limited,and meanwhile the defects of system complexity will be introduced.

An alternative method is to construct high-speed physical random numbers by using the multi-bit extraction.In this method,each sampling point is converted toNdigital bits by using multi-bit analog-to-digital converter(ADC)and theirM(M≤N)least significant bits are retained as an output of random bits,whereNandMare the numbers of ADC bits and retained bits,respectively.The generation rate of random numbers is thus equal toMtimes sampling rate and can be greatly increased.Whereas,in the multi-bit extraction demonstrations,the intensity output of chaotic laser is usually digitized by the commercial oscilloscope and then processed with least-significant-bit retention followed by other postprocessing methods such as derivative,exclusive-OR,and bit-order reversal.These followed post-processing operations have to be implemented off-line and thus cannot support the real-time generation of random numbers.Resultantly,it is still an ongoing challenge to develop high-speed generation schemes of physical random numbers with the capability of real-time output.

In this paper,a real-time high-speed generation method of physical random numbers by using multi-bit quantization of chaotic laser is proposed and demonstrated experimentally.In the proposed generation scheme,an external-cavity feedback semiconductor laser is utilized as a source of chaotic laser.Through quantizing the chaotic laser with 6-bit ADC,which is triggered by a clock at a sampling rate of 7 GHz,a binary sequence with six significant bits can be achieved.After the selection of the two least-significant bits and self-delayed exclusive-OR operation in the field-programmable gate array(FPGA),a real-time 14-Gb/s binary stream is finally achieved.This binary stream has good uniformity and independence,and has passed the industry-standard statistical test suite provided by the National Institute of Standards and Technology(NIST),showing a good statistical randomness.It is believed that this work provides an alternative method of generating the real-time high-speed random numbers and promotes its applications in the field of information security.

semiconductor laser,laser chaos,multi-bit quantization,physical random number

PACS:42.55.Px,05.45.Gg,05.45.VxDOI:10.7498/aps.66.234205

*Project supported by the National Nature Science Foundation of China(Grant Nos.61475111,61671316),the Natural Science Foundation for Excellent Young Scientists of Shanxi,China(Grant No.2015021004),the International Science and Technology Cooperation Program of Shanxi Province,China(Grant No.201603D421008),and the International Science and Technology Cooperation Program of China(Grant No.2014DFA50870).

?Corresponding author.E-mail:xyliu@ime.ac.cn

?Corresponding author.E-mail:wanganbang@tyut.edu.cn

(2017年7月12日收到;2017年8月4日收到修改稿)

提出了一種基于混沌激光多位量化的高速物理隨機(jī)數(shù)實(shí)時(shí)產(chǎn)生方法.利用外腔反饋混沌半導(dǎo)體激光器作為物理熵源,通過時(shí)鐘速率為7 GHz的多位模數(shù)轉(zhuǎn)換器對(duì)其采樣量化,生成6位有效位的二進(jìn)制隨機(jī)比特,然后利用現(xiàn)場(chǎng)可編程軟件抽取低2位有效位的隨機(jī)序列并進(jìn)行自延遲異或處理,獲得了實(shí)時(shí)速率為14 Gb/s的物理隨機(jī)數(shù).該隨機(jī)數(shù)具有良好的統(tǒng)計(jì)隨機(jī)性,可成功通過隨機(jī)數(shù)行業(yè)測(cè)試標(biāo)準(zhǔn)(NIST SP 800-22).

10.7498/aps.66.234205?國家自然科學(xué)基金(批準(zhǔn)號(hào):61475111,61671316)、山西省優(yōu)秀青年自然科學(xué)基金(批準(zhǔn)號(hào):2015021004)、山西省國際科技合作項(xiàng)目(批準(zhǔn)號(hào):201603D421008)和國際科技合作項(xiàng)目(批準(zhǔn)號(hào):2014DFA50870)資助的課題.

?通信作者.E-mail:xyliu@ime.ac.cn

?通信作者.E-mail:wanganbang@tyut.edu.cn