Part1:重合指数及其无偏估计值 重合指数：设某种语言由n个字母组成，每个 字母i发生的概率为pi(1≤i≤n),则重合指数就 是指两个随机字母相同的概率，记为C IC=∑p, i=l 般用IC的无偏估计值C来近似计算IC.其中 的xi表示字母i出现的频次，L表示文本长度，n 表示某种语言中包含的字母数。 r-器出
Part1 : 重合指数及其无偏估计值 • 重合指数：设某种语言由n个字母组成，每个 字母i发生的概率为pi(1≤i≤n)，则重合指数就 是指两个随机字母相同的概率，记为IC 1 n i i IC p = = • 一般用IC的无偏估计值IC’来近似计算IC. 其中 的xi表示字母i出现的频次，L表示文本长度，n 表示某种语言中包含的字母数。 1 ( 1) ' ( 1) n i i i x x IC = L L − = −
C'值的特点 ·随机英文文本的1C'总是大约为0.038. ·而一段有意义的英文文本的IC'总是大约为 0.065
IC’值的特点 • 随机英文文本的IC’总是大约为0.038. • 而一段有意义的英文文本的IC’总是大约为 0.065
Example1:随机英文文本明文及其c 随机英文文本为：mooiybyvfnkrvxapqzaeo jvoygudguaymoejvshxwhdkowboea nocqpuuebguddjzankbwqaojiqsamryvduqcynqogosfrmusuu ogiidivjpzdjqtatohyqoukuhukqzfqkvssvnbotuxijieyvaz nrrutuwbnleciqbhtglvluytpqrigyxy jaxuo jzansmstkhdja qkqrcywlrgulsfauilgmmffqkljddogluwgkirkgvzbitxxwtt exjxunxketyazopqmfztsxckdaygexdexouyrcjstsucycpqre pps jwiqmzrxhhmzjevsgtihakmhqkbfmzhqzzjteetzgyydfcs afhdochcbmmqniamahucidpcatxccbkibjwwwzpxdth jdxxqte azrvbqpluzrwbeplqfdfeceggrskzrasw juhagbwgxtohhumir vuqxrptkyavgihalecqcpfxrjdnjbscrahfuaebsobfppnpkyg vkdohloqjteqmnjtyijdmhlsbszheftjcoppxtlbqlhaplbtmf rkfbmipdztutxnudpyeohjjbtxxoykfivqmltddalkwwfixsqx neirtxjrivkifqlhjfhlifpwkfcwcfbniizagvgv 随机英文文本的IC无偏估计值为： 0.0380
Example 1:随机英文文本明文及其IC’
Example1:随机英文文本密文及其Ic (移位加密key=17) 加密后的随机英文文本： dffzpspmwebimorghgrvfamfpxluxlrpdfvamjyonyubfnsfvr efthgllvsxluuagrebsnhrfazhjrdipmulhtpehfxfjwidljll fxzzuzmagquahkrkfyphflblylbhqwhbmjjmesfklozazvpmrq eiilklnsecvtzhsykxcmclpkghizxpoparolfaqrejdjkbyuar hbhitpncixlc jwrlzcxddwwhbcauufxclnxbzibxmqszkoonkk voaoleobvkprqfghdwqk jotburpxvouvoflpita jkjltptghiv ggjanzhdqioyydqavmjxkzyrbdyhbswdqyhqqakvvkqxppuwtj rwyuftytsddhezrdryltzugtrkottsbzsannnqgoukyauoohkv rqimshgclqinsvgchwuwvtvxxijbqirjnalyrxsnxokfyyldzi mlhoigkbprmxzyrcvthtgwoiaueasjtirywlrvsjfswggegbpx mbufycfhakvhdeakpzaudycjsjqyvwkatfggokeshcyrgcskdw ibwsdzguqklkoelugpvfyaaskoofpbwzmhdckuurcbnnwzo jho evzikoaizmbzwhcyawyczwgnbwtntwsezzqrxmxm 加密后的随机英文文本的IC无偏估计值为： 0.0380 注：英文文本中字母的编码为 az….025
Example 1:随机英文文本密文及其IC’ (移位加密key=17) 注：英文文本中字母的编码为 a~z…….0~25
Example2:一个有意义的英文text Differential Privacy is the state-of-the-art goal for the problem of privacy-preserving data release and privacy-preserving data mining.Existingtechniques using differential privacy,however,cannot effectively handle the publication of high-dimensional data.In particular,when the input dataset contains a large number of attributes,existing methods incur higher computing complexity and lower information to noise ratio,which renders the published data next to useless.This proposal aims to reduce computing complexity and signal to noise ratio.The starting point is to approximate the full distribution of high-dimensional dataset with a set of low-dimensional marginal distributions via optimizing score function and reducing sensitivity,in which generation of noisy conditional distributions with differential privacy is computed in a set of low-dimensional subspaces,and then,the sample tuples from the noisy approximation distribution are used to generate and release the synthetic dataset.Some crucial science problems would be investigated below:(i)constructing a low k-degree Bayesian network over the high-dimensional dataset via exponential mechanism in differential privacy,where the score function is optimized to reduce the sensitivity using mutual information,equivalence classes in maximum joint distribution and dynamic programming;(ii)studying the algorithm to compute a set of noisy conditional distributions from joint distributions in the subspace of Bayesian network,via the Laplace mechanism of differential privacy.(iii)exploring how to generate synthetic data from the differentially private Bayesian network and conditional distributions,without explicitly materializing the noisy global distribution.The proposed solution may have theoretical and technical significance for synthetic data generation with differential privacy on business prospects. 其Ic'为：0.0659
Example 2:一个有意义的英文text • Differential Privacy is the state-of-the-art goal for the problem of privacy-preserving data release and privacy-preserving data mining. Existing techniques using differential privacy, however, cannot effectively handle the publication of high-dimensional data. In particular, when the input dataset contains a large number of attributes, existing methods incur higher computing complexity and lower information to noise ratio, which renders the published data next to useless. This proposal aims to reduce computing complexity and signal to noise ratio. The starting point is to approximate the full distribution of high-dimensional dataset with a set of low-dimensional marginal distributions via optimizing score function and reducing sensitivity, in which generation of noisy conditional distributions with differential privacy is computed in a set of low-dimensional subspaces, and then, the sample tuples from the noisy approximation distribution are used to generate and release the synthetic dataset. Some crucial science problems would be investigated below: (i) constructing a low k-degree Bayesian network over the high-dimensional dataset via exponential mechanism in differential privacy, where the score function is optimized to reduce the sensitivity using mutual information, equivalence classes in maximum joint distribution and dynamic programming; (ii)studying the algorithm to compute a set of noisy conditional distributions from joint distributions in the subspace of Bayesian network, via the Laplace mechanism of differential privacy. (iii)exploring how to generate synthetic data from the differentially private Bayesian network and conditional distributions, without explicitly materializing the noisy global distribution. The proposed solution may have theoretical and technical significance for synthetic data generation with differential privacy on business prospects. 其IC’为：0.0659