密码学年会11月2号上午six classical-quantuam variant maps

1、随着墨子号量子卫星成为科技亮点，量子密钥分发BB84等协议优劣 前沿网络安全应用焦点最新谷歌在自然杂志发表的量子霸权论文：量子经典随机序列生成器的取样统计结果比较 国际量子计算前沿从测量的角度，存在随机序列测量协议和方法，区分经典密码序列量子密码序列？已有的NIST800-22及国密统计随机检测协议: P值检测 0,1 基于随机变量的取样统计模式 这些协议，不能满足随机序列动态随机性的测量需求！针对密码序列动态随机性分析，依靠取样统计能获得充分的信息吗？ 引子Q3.：谷歌计划进行或完成了哪些经典计算机很难做到的计算？计算的是：一个“challenger”生成一个随机量子电路C(即一个由 1 个

2、量子比特和最近邻的 2 个量子比特组成的随机序列，深度为 20，作用于n=50 至 60 qubits 的二维网格上)。将C发送到量子计算机，将C应用于全部为 0 的初始状态，以0,1为基础来测量结果，返回所观察到的所有n-bit 字符串，重复数千次甚至数百万次。最后，利用统计检验来检查输出是否与量子计算机所做的一致。不是一个因式分解问题。电路C在n-bit 字符串上产生一些概率分布，称为 DC，问题是从这个分布中输出样本。通常有2n个字符串支持 DC，关键是，DC 的分布不均匀。虽然只会观察到与2n相比很小的样本，但可以检查样本是否优先地聚集，建立起对完成传统棘手事情的信心。一句话：量子计算

3、机被要求应用一个随机(但已知的)量子操作序列不是因为关心结果，而是因为试图证明它能在一些任务上击败经典计算机。The calculation Google chose checking the outputs from a quantum random-number generator has limited practical applications, “the scientific achievement is huge”, says Scott Aaronson, a theoretical computer scientist at the University of Texas a

4、t Austin.Quantum supremacy using a programmablesuperconducting processor 谷歌的量子霸权Jeffrey Zheng（郑智捷）, YM Luo, ZF Li, Chris ZhengSchool of Software, Yunnan University2 November 2019Stationary Randomness of Three Types of Six Random Sequences on Variant Maps中国密码学会年会 ChinaCrypt 2019 陕西 西安 IntroductionBas

5、e ModelTesting SchemesProcessing RoutinesResults of Six SequencesConclusionContentThis talk briefly introduces variant maps and typical applications to identify three types of six random sequences (AES/DES Block Cipher, A5/RC4 Stream Cipher and ANU/USTC Quantum Ciphers)Random sequences under segment

6、s on multiple statistical probability maps Shifting operations to extract Statistical Process MeasurementsTypical ResultsPossible applications:Distinguishing various random number generators Pseudo-random Ciphers or True-random Ciphers (Quantum/Physical Devices)Quality Control: Stronger Stationary R

7、andomness - Better Quality on Random properties IntroductionBase ModelWWW/Cloud Computing/Mobile Communication/ Quantum Satellite Network Security SystemsCore: Random Number Generators QuantumLaser / Thermal sourcesTruly Random Number Generator e.g. Quantum CryptographyPseudo Random Number Generator

8、e.g. Stream ciphersLinear / Nonlinear / Recursive0-1 序列0-1 SequenceNIST 800-22 （Statistical Testing Package）P_Value 0-1 SequenceMultiple Statistical Probability Measures（Variant Schemes）Statistical Probability Spectrum 0-1 SequenceFrequency Transformation/ Analysis（Signal Processing Schemes）Frequenc

9、y SpectrumTime-frequency SpectrumPulses：Frequency/ProbabilitySpectrumSingleContinuumDiscreteDiscrete-continuumSingleContinuumDiscreteDiscrete-continuumSingleContinuumDiscreteDiscrete-ContinuumFrequency Spectrum on Sin/Cos SignalsFrequency Spectrum on PulsesProbability Spectrum on PulsesPulses on Fre

10、quency SpectrumFrequency Spectrum on A Single PulseFrequency Spectrum on A Pulse SequenceA pulse sequence cannot map to a single spectrum A single pulse/ a random sequence can map to continuum spectrumA regular pulse sequence can map to discrete spectrumA pulse sequence with approximate period can m

11、ap to discrete-continuum spectrumStatistical Probability MapsSub-PoissonianPoissonianSuper-PoissonianNon-StationaryStationaryPhase ChangesMultiple Dimensional Distribution and Various ProjectsStandard DistributionsGenerating Quantum Random Number Sequence2 sets of quantum cryptographic data streams:

12、USTC 100MB，ANU 100MBTesting Schemes: Five Variant MapsInput: A 0-1 sequence with N bits Output: Five variant mapsTwo 1D maps: 1DP and 1DQThree 2D maps: 2DP, 2DQ and 2DPQProcess: The input sequence is divided as M segments and each segment with m bitsFor each segment, two measures are determined.p -

13、the number of 1 elementsq the number of 01 patternsMapping all M measures on relevant positionsTesting SchemesInput: A 0-1 sequence with N lengthTwo measures on each segmentForming M segmentsSegmented as m bitsTwo measures: p, q, p 1 numbers， q 01 patterns in a segmentThe i-th segment forms a pair o

14、f measures (pi, qi), 2PQ: (pi, qi), 0= i M, a measuring sequence in M elementsSeparating a pair of measures to be two measuring sequences1D sequence, 1Q: qi, 0= i M1D sequence, 1P: pi, 0= i MApplying Poincare maps to transfer 1D measures into a pair of measures i-1 mod M2D sequence, 2Q: (qi-1,qi), 0

15、= i M2D sequence, 2P: (pi-1,pi), 0= i MMapping measure sequences into mapsThree 2D variant maps, 2P: 2DP; 2Q: 2DQ; 2PQ:2DPQTwo 1D variant maps, 1P:1DP; 1Q:1DQOutput: Five variant mapsProcessing RoutineData stream：USTC key lab of quantum information21 sets of quantum cryptographic sequencesUsing vari

16、ant measures to select maximal values as control parametersEach Sequence generates a set of five distributions as 1DP, 1DQ, 2DP, 2DQ and 2DPQ mapsModel 1 Segmented measuresFive VariantMaps for Quantum Sequences 1DP1DQ2DP2DPQ2DQResults on sequential orderVariant Mapminimalmaximalerrorrationotice1DP0.

17、0690.0710.0020.032DP200230300.14Largest2DPQ780850700.092DQ780850700.091DQ0.1390.1420.0030.02SmallestError analysis for 21setsFrequency Spectrumfor quantum sequencesShifting r bits on X to form X(r)From 0= r =m, calculating m+1groups of sequences to generate relevant mapsFor one group, m=128, N = 100

18、MB, a total number of 13GB data is involved to make one set of measures Model II Shifting measures X(r)Extracting Stationary Randomness Measurements from Statistical ProcessesUSTC quantum random sequence 数据来源：中国科学技术大学量子信息重点实验室 ANU quantum random sequence 数据来源：澳大利亚国立大学量子物理学院量子光学实验室Each Sequence 100MB

19、, m=128Stationary Randomness Measurements on Two Quantum Random Sequencesr=0-128 USTC : ANUUSTC ANU 1DPUSTC ANU 2DPQUSTC ANU 1DQr=0-128 USTC : ANU maximals USTC: 1DP 2DPQ 1DQ ANU: 1DP 2DPQ 1DQStationary randomness on two quantum sequences r=0-128USTC data streamANU data streamThree Variations in Com

20、parisonQx Qx QRx ANUUSTCANUUSTC13.961 13.944 0.0170.177610.196640.019031.27221.41020.1380 Px Px PRx ANUUSTCANUUSTC7.0352 7.0289 0.00630.154720.135420.019302.19921.92650.2727PQx PQx PQRx ANUUSTCANUUSTC0.99245 0.98675 0.005700.047910.046910.001004.82764.75440.0732AES Block CipherDES Block Cipher A5 St

21、ream Cipher RC4 Stream Cipher USTC quantum random sequence ANU quantum random sequence Each Sequence 100MB, m=128Stationary Randomness Measurements on Six Random SequencesThree Maps on Six Random SequencesSix Variant Maps of 2DPQ MeasuresSix MapsRefined3 * 6 MapsSix MeasuringResultsOrders of Six Mea

22、surements平均值区间变化值区间变化值平均值 2019 Open Access Editors: Zheng, Jeffrey (Ed.)This open access book presents theoretical framework and sample applications of variant construction. The first part includes the four components: variant logic, variant measures, variant maps and meta model, while the second part covers sample applications such as variation with functions, variant stream ciphers, quantum interference, classical/quantum random sequences, whole DNA sequences, and mu