CN107347061A - Left side servomechanism 1 and right side power-assisted - Google Patents

Left side servomechanism 1 and right side power-assisted Download PDF

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CN107347061A
CN107347061A CN201710458154.9A CN201710458154A CN107347061A CN 107347061 A CN107347061 A CN 107347061A CN 201710458154 A CN201710458154 A CN 201710458154A CN 107347061 A CN107347061 A CN 107347061A
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CN107347061B (en
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张春慨
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Shenzhen Graduate School Harbin Institute of Technology
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Shenzhen Graduate School Harbin Institute of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
    • H04L63/1408—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic by monitoring network traffic
    • H04L63/1425—Traffic logging, e.g. anomaly detection

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Abstract

The present invention proposes a kind of time series abnormality detection system and method based under Secure, and the system includes service end and user terminal, wherein, service end at least two servers：Server C and server S；The service end distributed storage the time series for forming a complete data set；Server C is the server that service is provided for user terminal, carries out the multi-party shared of time series based on BCP encryption systems between server S and server C, server S is half honest, possesses the master key available for decryptionmk, disturbance is all added in the computing that all S are participated in, prevents S from obtaining the relevant information of relevant user；Server C and server S initialization BCP encryption systems；Server C is supplied to server S after the time series being stored thereon is encrypted；Server S carries out the abnormality detection of time series under security protocol.Time series abnormality detection proposed by the present invention based under Secure has great practical value.

Description

Based on the time series method for detecting abnormality and system under Secure
Technical field
The present invention relates to abnormality detection technical field, more particularly to a kind of time series based under Secure is examined extremely Survey method and system.
Background technology
In real life, every field all includes substantial amounts of time series data, such as the ECG data of patient, brain Supplemental characteristic and network flow data of the big quantity sensor in electromyographic data, power plant etc..And the abnormal subsequence of time series (pattern) detection is a highly important field, and the time series major part Data Representation containing abnormal patterns is normal morphology, The abnormal patterns frequency of occurrences is few, but the abnormal patterns seldom occurred include considerable information.Abnormal electrocardiogram (ECG) data Mean that patient may suffer from certain type of heart disease, abnormal eeg data is probably to be drawn by epilepsy Deng Nao sections disease Rise, find that the abnormal electrocardiogram of patient or eeg data can play directive function to follow-up treatment in time；And factory senses Device data exception might mean that failure occurs in some part of system, notes abnormalities in time and carries out maintenance energy to the system failure Reduce loss.Therefore, great realistic meaning is studied in the abnormal subsequence detection of time series data.
Related scholar had done substantial amounts of work both at home and abroad for research on time series abnormality detection.Dasgupta It is proposed to apply to the thought in immunology among the detection of time series abnormal patterns.This method can using self immune system The characteristics of distinguishing own cells, molecule and external cellular, molecule, negative itemsets original is utilized after time series is carried out into coded treatment Reason difference itself and external cellular or molecule, so as to carry out time series abnormal patterns detection.Junshui Ma propose to utilize One-Class SVM carry out the abnormal patterns detection of time series, and its thought, which comes from One-Class SVM, can detect vectorial number According to the abnormity point of concentration, after time series data is transformed into phase space, model is trained using positive class training data, The model finally come using training carries out detection to time series and sees whether deviate model, can thus carry out time series Abnormal patterns detect.Keogh proposes the abnormal subsequence that HOT SAX methods are come in discovery time sequence, and this method is by the time The Sequence Transformed detection ordering for being SAX method for expressing, time series subsequence being improved using heuristic, so as to greatly carry High time series exception subsequence detection efficiency.Izakian proposes to carry out time sequence using the method for fuzzy C-means clustering Abnormal subsequence detection is arranged, its thought is is clustered time series subsequence using fuzzy C-means clustering method, clustering cluster Center reflects the mode configuration of time series, and original sub-sequence is rebuild with cluster centre, normal sub- sequence Row mode configuration can preferably be reconstructed by clustering cluster center, and abnormal subsequence is difficult to reconstruct by cluster centre, passes through The subsequence being compared with after clustering cluster center reconstructs and atomic series otherness, to find abnormal subsequence.Sivaraks It is proposed to detect the abnormal heartbeats in electrocardiogram (ECG) data using the method for motif discovery, when such a thought can also apply to other Between sequence abnormal subsequence detection among.This method by analyzing electrocardiogram (ECG) data feature and extracting the pattern repeated, And by the similitude in comparative sequences between candidate's subsequence mode and theme, to determine whether pattern is abnormal electrocardiogram mould Formula, this method need not set abnormal sub-sequence length compared to remaining abnormal subsequence detection algorithm, and combine electrocardiogram (ECG) data neck Domain knowledge, Detection accuracy are very high.The country has also carried out the research of correlation.That studied at first is Xiao of Fudan University in Shanghai Brightness, it is that time series is converted into multiple line segment patterns using line segment as pattern, the general principle of detection, and by based on mould The abnormality degree that formula density defines weighs the intensity of anomaly of pattern, and using the high pattern of intensity of anomaly as abnormal.Zhan Yanyan Propose on the basis of time series linear expression pattern carry out abnormal patterns detection method, the thought of the algorithm be if Pattern is abnormal patterns, then the frequency that the pattern occurs is inevitable very low, so being assigned for the low pattern of the frequency of occurrences higher Exceptional value, and relatively low exceptional value is assigned for the higher pattern of the frequency of occurrences, the high pattern of exceptional value is then abnormal patterns. Du Hongbo proposes using locally linear embedding that come abnormal patterns in detection time sequence its thought is for each in time series Pattern, it is reconstructed by the pattern in neighborhood, compares the otherness between pattern and proterotype after reconstruct, reconstruct misses The bigger subsequence of difference is more probably abnormal patterns.Time series exception subsequence detection method HOTSAX is used for online by Wang Fei Among the abnormality detection of time series data, so as to realize the dynamic increment formula abnormality detection of time series data.Li Guiling is carried The PAA changing patteries for going out time series represent, and utilize cluster result using its cluster result come hunting time sequence variation The search order of sequence is inspired, so as to detection time sequence variation subsequence.
In cloud computing technology growing today, increasing people can select the data of oneself to be put into cloud to deposit up Storage or computing, the efficiency that can make time series abnormality detection with cloud computing technology can greatly improve, but cloud computing Security is troubling always.How data security (including the security of storage and computing at the end of Cloud Server is ensured Security) an and important field of research.Research in the research of existing time series to high in the clouds security is also It is relatively deficient.
The content of the invention
For overcome the deficiencies in the prior art, it is an object of the invention to provide a kind of time sequence based under Secure Row method for detecting abnormality and system.
The purpose of the present invention is achieved through the following technical solutions：A kind of time series abnormality detection based under Secure System, the system include service end and user terminal, wherein, service end at least two servers：Server C and server S； The service end distributed storage the time series for forming a complete data set；Server C is to provide clothes for user terminal The server of business, the multi-party shared of time series, server S are carried out based on BCP encryption systems between server S and server C It is half honest, possesses the master key mk available for decryption, disturbance is all added in the computing that all S are participated in, prevents S from being had Close the relevant information of user；Server S runs BCP initialization programs, and the common parameter of generation is broadcasted, and client receives Public key and private key are generated after to common parameter, each client broadcasts public key, retains private key；Client again by itself when Between sequence data by being stored on the C that uploaded onto the server after public key encryption；When having computing request, server C and service Device S calculates result according to protocol requirement collaboration and returns to requesting client.
On the other hand, a kind of time series method for detecting abnormality based under Secure, methods described are based on the present invention Abnormality detection system, specifically comprise the following steps：
Step 1, server C and server S initialization BCP encryption systems；
Step 2, server C are supplied to server S after the time series being stored thereon is encrypted；
Step 3, server S carry out the abnormality detection of time series under security protocol.
Compared with prior art, the present invention has advantages below and technique effect：The invention enables examined extremely under folk prescription Survey produced problem is all resolved well in multi-party, and the security protocol of the invention designed solves in many ways again under Privacy concern.Therefore, the time series abnormality detection proposed by the present invention based under Secure is that have very big practicality Value.
Brief description of the drawings
Fig. 1 is electrocardiogram (ECG) data for the same patient for belonging to A and B Liang Jia hospitals；
Fig. 2 is the present invention based on the time series abnormality detection system schematic diagram under Secure；
Fig. 3 is performance of three kinds of safe computings in data length N=1024；
Fig. 4 is performance of three kinds of safe computings under different data lengths.
Specific embodiment
The present invention is described in further detail below by embodiment combination accompanying drawing, but the embodiment party of the present invention Formula not limited to this.
It is to concentrate all to think time series data in the prior art, and the algorithm taken also all is to think current number It is complete according to collection.And in actual applications, what data distribution was often disperseed, such as the electrocardiogram (ECG) data of patient, may be at certain One regional tri- hospital of A, B, C all preserves the electrocardiogram (ECG) data of some patient.Therefore when the electrocardiogram (ECG) data for analyzing the patient When, it is necessary to A, B, C Data Integration of tri- are formed into a complete data set together, in complete data and upper progress Data mining.
As shown in Figure 1, time series A and time series B is the heart for the same patient for being belonging respectively to A and B Liang Jia hospitals Electrograph (ECG) data.B hospitals want to note abnormalities on time series B now, if B hospitals only consider time series B feelings Condition, then be the sequence for having maximum abnormality degree according to the abnormal definition subsequence x1 of time series, x1 can be judged for abnormal sub- sequence Row, data that can be later x1 in actually time series B be all it is abnormal, on the contrary x1 as normal data abnormal Seem among data " abnormal ".But when considering time series A, because the data in A are all normal, and x1 patterns All much like, with reference to finding that x2 possesses the abnormality degree of maximum afterwards, therefore, algorithm judges that x2 is abnormal subsequence.So introduce After multi-party participation, can solve the insurmountable problem under folk prescription.
But simultaneously it will be noted that the data resource important as one, often has valency very much for owner It is worth, especially the information of patient in hospital, is a kind of typical height private data.A, B, C tri- data are needed to do number According to excavation, but any one in A, B, C be it is not desirable that other two private datas for knowing oneself, at such a Under part, still expect from complete data and concentrate the result that draws of analysis, therefore this is related to multi-party computations Problem.
In the case that the present invention expands to the abnormal definition of time series suitable for multi-party participate in, safety detection is devised Algorithm detection time sequence variation, the secure cryptographic algorithm taken allow the data of input in different public key encryptions, and can be right The data of different public key encryptions carry out computing.In addition, algorithm proposed by the present invention either in multinuclear and can all divide parallel Can parallel processing in cloth system.
Reference documents below of the present invention：
Non-patent literature 1：Bresson E, Catalano D, Pointcheval D.A Simple Public-Key Cryptosystem with a Double Trapdoor Decryption Mechanism and Its Applications [C] //Advances in Cryptology-ASIACRYPT 2003, International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, November 30-December 4,2003, Proceedings.DBLP, 2003:37-54.
Non-patent literature 2：Peter A, Tews E, Katzenbeisser S.Efficiently Outsourcing Multiparty Computation Under Multiple Keys[J].IEEE Transactions on Information Forensics＆Security, 2013,8 (12):2046-2058.
Non-patent literature 3：Liu X, Deng R H, Choo K K R, et al.An Efficient Privacy- Preserving Outsourced Calculation Toolkit With Multiple Keys[J].IEEE Transactions on Information Forensics＆Security, 2016,11 (11):2401-2414.
The AES that the present invention uses is the BCP encryption systems (referring to non-patent literature 1-3) based on homomorphic cryptography, together State encryption just refers to that AES has isomorphism.Data Jing Guo homomorphic cryptography are handled to obtain an output, by this One output is decrypted, and its result is the same with handling the output result that the initial data of unencryption obtains with Same Way. It is formulated as：
Dsk([m1]pk·[m2]pk)=m1+m2
Wherein, pk represents public key, and sk represents private key, [m1]pkRepresent m1Encrypted with pk, Dsk([m1]pk) represent to be decrypted with sk.
And BCP encryption systems are a kind of special homomorphic encryption algorithms, BCP have one it is critically important the characteristics of be exactly that it has two Set decryption service.In description above, decryption is private key sk, but also has a kind of ginseng for being referred to as master key in BCP Number can decrypt encryption data, and master key is represented with mk.
The system model of the present invention as shown in Figure 2, first, two servers is used in server end：Server C kimonos Be engaged in device S, and wherein server S is half honest, possesses the master key mk that can be decrypted.Mean that server S can be according to agreement Regulation performs each step, but may attempt to analyze by the average information obtained in protocol implementation and infer it The correlated inputs output information of his participant.Therefore, in the computing that all S are participated in, disturbance will be added, prevents S from being had Close the relevant information of user.
Collaboration calculating processes of the server C and S for addition is summarized as follows：
Due to homomorphism plus algorithm require two ciphertexts must be in the case of same public key encryption could computing, i.e.,：
([m1]pk·[m2]pk)=[m1+m2]pk
If two ciphertexts are different public key encryptions, then then can not direct computing, [m1]pk1·[m2]pk2Can not be direct Computing.But the public key of each side is all different in multi-party calculate, therefore the computing for being related to multi-party lower ciphertext just needs to take Business device C and server S collaboration computing.The public key of client each first is that all participants are both known about, therefore server C will The two ciphertexts all add disturbance, pass through calculating：
[m1]pk1·[r1]pk1=[m1+r1]pk1
[m2]pk2·[r2]pk2=[m2+r2]pk2
By [m1+r1]pk1[m2+r2]pk2Server S is all sent to, S has master key to decrypt the two ciphertexts, obtained The two clear datas are added again after plaintext, obtain m1+r1+m2+r2, by m1+r1+m2+r2With the public key encryption of some client After be sent to server C, server C knows disturbance r1, and r2In the present embodiment, step S2 specifically includes following steps1+m2]pk.At this moment by this Ciphertext data are sent to client, and client decrypts to obtain plaintext result using the private key of oneself.
The system of the present invention is mainly the exception of detection time sequence, and uses the phase that most computings is exactly time series Like the calculating of property, the similarity measurement of use is Euclidean distance, and the definition of Euclidean distance is subsequence A=(a1, a2..., an) and subsequence B=(b1, b2..., bn) between Euclidean distanceEuclidean distance Computing mainly used addition and multiplication, extracting operation can omit because extracting operation simply have impact on the final of result Value, do not change relative size, i.e., most greatly counted before evolution also certain maximum after evolutions.In addition in the process of abnormality detection In, the comparison of abnormality degree is also used, the maximum subsequence of abnormality degree is abnormal subsequence, and the definition of abnormality degree is subsequence To the distance of its arest neighbors, therefore it is related to the computing compared.So to sum up consider, the time sequence under Secure of the invention The computing that row abnormality detection relates generally to has addition, multiplication and comparison operation.
Addition, multiplication and comparison operation required for for more than, the present invention devise three kinds of agreements and go to realize in safety Addition (SAP), multiplication (SMP) and comparison operation (SMIN) are realized under multi-party.
SAP：Give two ciphertexts encrypted under different public keysServer C wants to know the two In the present embodiment, step S2 specifically includes following stepsProd.pk.Prod.pk is the product of all public keys, can equally in BCP To be gone to decrypt the ciphertext encrypted under Prod.pk with mk.
1st, two random number r are selected firsta,Server C is calculated：
2nd, X and Y are sent to server S, S is decrypted with master key mk, then calculates Z=x+ra+y+rb, Z is encrypted to [Z]Prod.pkRe-send to server C
3rd, server C have received [Z]Prod.pk, calculate R=ra+rb, R is encrypted to [R]Prod.pkCalculate again
[Z]Prod.pk·[R]Prod.pk N-1=[Z-R]Prod.pk=[x+y] Prod.pk
So SAP algorithms just complete, and whole process meets being required of being previously discussed as, therefore can be assumed that and be Safety.(in BCP AESs, [m]pk N-1=[- m]pk, detailed proof procedure is referring to reference to non-patent literature 1,2.)
SMP：Give two ciphertexts encrypted under different public keysServer C wants to know the two Several products, the target of SMP algorithms are exactly to obtain [x*y]Prod.pk。
1st, two random number r are selected firsta,Server C is calculated：
2nd, X and Y are sent to server S, S is decrypted with master key mk, then calculates Z=(x+ra)*(y+rb), Z is encrypted Into [Z]Prod.pkRe-send to server C；
3rd, server C have received [Z]Prod.pk, calculate
[Z-rb·x-ra·y-ra·rb]Prod.pk=[xy]Prod.pk。
Before SMIN is introduced, a leading agreement is first introduced --- safety is less than agreement SLT, i.e., given two in difference The ciphertext encrypted under public keySLT agreements are exactly it is expected to obtain [u*]Prod.pk, wherein u*Be expression x and y it Between magnitude relationship.
1st, server C first is calculated
One piece of coin of server C throwings, if positive, calculate (l here is an intermediate variable)
If reverse side, calculate
2nd, server C selects a random number r,WhereinRepresent u binary length. Calculate [l1]Prod.pk=([l]Prod.pk)r, by [l1]Prod.pkIt is sent to server S；
3rd, server S decryption [l1]Prod.pkObtain l1, make u*=1 works asOtherwise u*Then=0. will u*It is encrypted to [u*]Prod.pkIt is sent to server C；
4th, server C receives [u*]Prod.pkIf the coin of just throwing is face-up, do not handle, otherwise count Calculate
[u*]Prod.pk=[1]Prod.pk·([u*]Prod.pk)N-1=[1-u*]Prod.pk
If the 5th, u*=0, x >=y is represented, if u*=1, represent x ＜ y.
SMIN：Give two ciphertexts encrypted under different public keysSMIN agreements are exactly to obtain [min (x, y)]Prod.pk·
1st, server C and server S calculate below equation jointly：
Once the 2nd, obtain [u*]Prod.pk, server C calculating
First, the present invention tests the efficiency of three kinds of security protocols, as shown in Figure 2, in the BCP AESs of use, N Size be 1024 bits, all time, which employs the method that 1,000 computings are averaged, in accompanying drawing 2 prevents other reasonses Influence result.
The performance of 1 three kinds of safe computings of table
In BCP AESs, N length is critically important, public key, private key, the generation of master key and plaintext length all There is close association with N.The scene when length that N is only considered in table 1 is 1024 bit, what has after changing N value The situation of sampleAs shown in Figure 3, it is same for each data, all it is 1000 average values for asking it of computing.
From accompanying drawing 3 as can be seen that being continuously increased with N length, algorithm expense has obvious growth, this is just meaned That N is bigger, it is necessary to which the time of computing is more.
What the length of the plaintext employed in experiment above was just as, in BCP AESs, the requirement to plaintext isThe change of so plaintext size can influence the efficiency of BCP AESs
From accompanying drawing 4 as can be seen that with the change of length of the plaintext, the time spent by each agreement is almost unchanged, and this is just Illustrate the size of plaintext does not influence for BCP AESs.This is also to explain, because in BCP AESs In, no matter plaintext size it is much, as long as in plain text meetBCP AESs all can by be encrypted to N in plain text this is big It is small, so in the computing based on ciphertext, as long as N keeps constant, no matter plaintext size it is much, the spent time be difference not More.
The invention enables under folk prescription abnormality detection produced problem be all resolved well in multi-party, Er Qieben Invent the privacy concern security protocol designed solves in many ways again under.Therefore, it is proposed by the present invention based under Secure Time series abnormality detection has great practical value.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to is assert The specific implementation of the present invention is confined to these explanations.For general technical staff of the technical field of the invention, On the premise of not departing from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention's Protection domain.

Claims (7)

  1. 310013 Hangzhou, Zhejiang province city Xihu District Yuhang Tang Lu 866 And client, wherein, service end at least two servers：Server C and server S；The service end distributed storage Form the time series of a complete data set；Server C is the server that service is provided for client, server S and clothes The multi-party shared of time series is carried out based on BCP encryption systems between business device C, server S is half honest, possesses and can be used for solving Close master key mk, disturbance is all added in the computing that all S are participated in, prevent S from obtaining the relevant information of relevant user；Server C and server S initialization BCP encryption systems；The common parameter of generation is broadcasted by server S；Client receives public Public key and private key are generated after parameter, each client broadcasts public key, retains private key；Client is again by the time series of itself Data on the C that uploaded onto the server after private key encryption by storing；When having computing request, server C and during server S pair Between sequence carry out collaboration and calculate the results of unusual sequences, and result is returned into requesting client, client utilizes the private of oneself Key is decrypted to obtain plaintext result.
  2. 2. system according to claim 1, it is characterised in that：The BCP encryption systems are based on homomorphic cryptography：To by same The data of state encryption are handled to obtain an output, and this output is decrypted, and its result with Same Way with being handled not The output result that the initial data of encryption obtains is the same.
  3. 3. system according to claim 1, it is characterised in that：The abnormality detection of the time series is entered using Euclidean distance Row similarity measurements, the computing related generally to have addition, multiplication and comparison operation.
  4. 4. system according to claim 3, it is characterised in that：The add operation uses Secure addition agreement SAP Realize, be specially：Give two ciphertexts encrypted under different public keysServer C want to know this two Number and [x+y]Prod.pk, Prod.pk is the product of all public keys, can be gone to decrypt under Prod.pk with mk equally in BCP The ciphertext of encryption,
    (1) two random number r are selected firsta,Server C is calculated：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>X</mi> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>Y</mi> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
    (2) X and Y are sent to server S, S is decrypted with master key mk, then calculates Z=x+ra+y+rb, Z is encrypted to [Z]Prod.pkRe-send to server C；
    (3) server C have received [Z]Prod.pk, calculate R=ra+rb, R is encrypted to [R]Prod.pkCalculate again
    [Z]Prod.pk·[R]Prod.pk N-1=[Z-R]Prod.pk=[x+y]Prod.pk。
  5. 5. system according to claim 3, it is characterised in that：The multiplying uses Secure multiplication agreement SMP Realize, be specially：Give two ciphertexts encrypted under different public keysServer C want to know this two The product [x*y] of numberProd.pk,
    (1) two random number r are selected firsta,Server C is calculated：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>X</mi> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>a</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <mi>Y</mi> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>b</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
    (2) X and Y are sent to server S, S is decrypted with master key mk, then calculates Z=(x+ra)*(y+rb), Z is encrypted to [Z]Prod.pkRe-send to server C；
    (3) server C have received [Z]Prod.pk, calculate
    [Z-rb·x-ra·y-ra·rb]Prod.pk=[xy]Prod.pk。
  6. 6. system according to claim 3, it is characterised in that：The comparison operation compares agreement SMIN using Secure Realize, be specially：Give two ciphertexts encrypted under different public keysServer C want to know this two The size [min (x, y)] of numberProd.pk,
    (1) server C and server S calculate below equation jointly：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>A</mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> <mo>,</mo> </mrow> </msub> <msub> <mrow> <mo>&amp;lsqb;</mo> <mn>0</mn> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>A</mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mn>0</mn> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> <mo>,</mo> </mrow> </msub> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>L</mi> <mi>T</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>X</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>M</mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>Y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>M</mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
    (2) once obtaining [u*]Prod.pk, server C calculating
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msubsup> <mrow> <mo>&amp;lsqb;</mo> <mi>Y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>&amp;CenterDot;</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>X</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mi>y</mi> <mo>+</mo> <msup> <mi>u</mi> <mo>*</mo> </msup> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>,</mo> </mrow>
    Wherein, safety is less than i.e. given two ciphertexts encrypted under different public keys of agreement SLTIt is expected to obtain Obtain [u*]Prod.pk, u*It is to express the magnitude relationship between x and y,
    (1) server C first is calculated
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>x</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;CenterDot;</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>1</mn> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> </mrow>
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <mn>2</mn> <mi>y</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> </mrow>
    One piece of coin of server C throwings, if positive, calculate
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>l</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>A</mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>,</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> </mrow>
    If reverse side, calculate
    <mrow> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>l</mi> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>Pr</mi> <mi>o</mi> <mi>d</mi> <mo>.</mo> <mi>p</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>S</mi> <mi>A</mi> <mi>P</mi> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>b</mi> </msub> </mrow> </msub> <mo>,</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msub> <mi>pk</mi> <mi>a</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    (2) server C selects a random number r,WhereinRepresent u binary length.Calculate [l1]Prod.pk=([l]Prod.pk)r, by [l1]Prod.pkIt is sent to server S；
    (3) server S decryption [l1]Prod.pkObtain l1, u*=1 works asOtherwise u*=0. then by u*Encryption Into [u*]Prod.pkIt is sent to server C；
    (4) server C receives [u*]Prod.pkIf the coin of just throwing is face-up, do not handle, otherwise calculate
    [u*]Prod.pk=[1]Prod.pk·([u*]Prod.pk)N-1=[1-u*]Prod.pk
    (5) if u*=0, x >=y is represented, if u*=1, represent x<y.
  7. 7. a kind of time series method for detecting abnormality based under Secure, methods described is based on being appointed according to claim 1-6 Detecting system described in one, it is characterised in that methods described specifically comprises the following steps：
    The common parameter of generation is broadcasted by step 1, server C and server S initialization BCP encryption systems, server S；
    Step 2, client generate public key and private key after receiving common parameter, and each client broadcasts public key, retain private Key；Client on the C that uploaded onto the server after public key encryption again by the time series data of itself by storing；
    Step 3, when having computing request, server C and server S carry out collaboration fortune according to protocol requirement to time series The result of unusual sequences is calculated, and result is returned into requesting client, client is decrypted to obtain and tied in plain text using the private key of oneself Fruit.
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