CN107527621A - The speech hiding algorithm that dynamic code is grouped based on complete binary tree - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
- G10L19/018—Audio watermarking, i.e. embedding inaudible data in the audio signal
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/065—Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3
- H04L9/0656—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
- G10L2019/0001—Codebooks
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L19/00—Speech or audio signals analysis-synthesis techniques for redundancy reduction, e.g. in vocoders; Coding or decoding of speech or audio signals, using source filter models or psychoacoustic analysis
- G10L2019/0001—Codebooks
- G10L2019/0013—Codebook search algorithms
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Abstract
VoIP (Voice over Internet Protocol) is used as a kind of Internet communication technology, is faced with the great risk of privacy leakage.In order to solve the problems such as privacy leakage in VoIP, speech hiding technology is gradually applied in VoIP.The present invention proposes the speech hiding algorithm that a kind of dynamic code is grouped based on complete binary tree, with reference to iLBC dynamic code book and quantization index modulation (Quantization Index Modulation, QIM) principle, dynamic code book is grouped using complete binary tree.Sender's code book according to corresponding to selecting secret information position carries out the insertion that coding realizes secret information, and subsequent recipient completes the extraction process of secret information according to the attribute of codeword vector.Exploitation and test platform are built in a local network, algorithm performance is have evaluated from hidden capacity, disguise, robustness and processing delay, it was demonstrated that the algorithm is that a kind of capacity is larger, and disguise is higher, robustness is good, processing time is short hidden algorithm.
Description
Technical field
The present invention relates to a kind of new approaches for realizing secret communication --- speech hiding, fundamentally mask secret
The fact that confidential information is present, it is effectively protected privacy of user and information security.
Background technology
VoIP (Voice over Internet Protocol) is used as a kind of Internet communication technology, is faced with privacy and lets out
The great risk of dew.In order to solve the problems such as privacy leakage in VoIP, speech hiding technology is gradually applied in VoIP.
The major domain of Information hiding includes three fundamental research, applied basic research and application technical research aspects, on basis
In terms of theoretical research, Huang et al. completes Information hiding, experimental result table in low rate coding voice flow using Pitch Prediction
Bright, embedded secret information influences smaller on carrier voice quality, and loss value is about 1.2%, and can computational complexity compared with
Ensure preferably anti-steganalysis attacking ability while small；Huang et al. also studied the inactive frame in VoIP voice flows
The hidden algorithm of middle embedded secret information, it was found that the inactive frame of VoIP voice flows is more suitable for doing Information hiding than active frame
Important conclusion.In disguise under the same conditions, data volume embedded in inactive frame is much larger than data embedded in active frame
Amount, reach 101 bits per frame, be a kind of speech hiding algorithm of Large Copacity；Wang et al. proposes to be existed using LSB algorithms
The method that Real-time embedding is done in VoIP voice flows, test result indicates that the processing delay of secret information insertion is maintained at 0.257ms
Left and right, suitable for the real-time speech communicating application such as VoIP；
As increasing people is participated in internet, network bandwidth resources seem precious.2000, Global
IP Sound companies have developed a encoder --- iLBC (the Internet Low Bit Rate suitable for narrowband speech communication
Codec) encoder.The encoder belongs to middle low-rate speech coder, using the teaching of the invention it is possible to provide sane ip voice communication, and support 20ms
With two kinds of frame formats of 30ms, bit rate is respectively 15.20kbit/s and 13.33kbit/s.Cause IP numbers when network environment is bad
It is larger or when there is packet loss according to packet delay, the packet loss masking effect of the encoder (Packet Loss Concealment,
PLC it) can effectively strengthen voice, ensure voice quality.Therefore, the iLBC for possessing outstanding performance is increasingly becoming in VoIP and used
Extensive a encoder.
Xiao et al. devises a kind of brand-new speech hiding algorithm according to the characteristic of low-rate speech coder, complementary adjacent
Summit (Complementary Neighbor Vertices, CNV) algorithm is occupied, the algorithm is first in speech hiding field
The secondary algorithm that code book packet is realized with reference to graph theory relevant knowledge.This grouping algorithm is different from conventional code, and CNV regards each code word
For one in hyperspace isolated point, the relation between each two code word represents that adjacent vertex is respectively by 0 with side and weight
With 1 mark, the process entirely marked is the process of code book packet, is then entered according to secret information value in corresponding code book group
Row search, completes the insertion of secret information.Test result indicates that the algorithm is applied to G.723.1 or in iLBC encoding streams have
Preferably disguised and robustness, obtains the hidden capacity no less than 100bps, is the current higher language of degree of recognition in the world
One of sound Information Hiding Algorithms.
Classical speech hiding algorithm can substantially be divided into three classes：Temporal concealment algorithm, transform domain hidden algorithm and base
In quantization index modulation (Quantization Index Modulation, QIM) hidden algorithm.Temporal concealment algorithm be
Directly secret information is embedded into carrier signal in time domain, the algorithm realizes that simply hidden capacity is big, but during hiding
Directly modification carrier signal will necessarily cause the distortion of carrier signal, increase the difficulty of receiving terminal extraction secret information.Conversion
Domain hidden algorithm is to do Information hiding in the transform domain of carrier information.Carrier information is mapped to transform domain and changed by the algorithm
Some parameter in transform domain reaches the purpose of Information hiding.But voice signal is mapped to transform domain and needs largely to be based on
The computing of signal transacting, the computational complexity height of algorithm is directly results in, the real-time of voice signal is had an impact.Based on amount
Original quantisation code book is grouped by the Information Hiding Algorithms for changing index modulation, is searched for when the different secret information of insertion different
Code book group, contained the code book index of " special " implication.Receiving terminal extracts corresponding concealed letter according to these call numbers
Breath, speech hiding is realized with this.Such as quantization code is originally divided into C1 and C2 two parts, C1 and C2 meet C1 ∪ C2=C andAgreement C1 and C2 represents 0 and 1 in secret information respectively.When embedding information is 0, searched in C1 plain optimal
Quantized value, on the contrary scanned in C2, and receiving terminal judges according to the packet class of call number and extracts the secret of carrier carrying
Information.QIM methods be widely used in it is various using Digital Media as hide carrier Information Hiding Algorithms in, show good
Performance is hidden, but the algorithm universality is poor, can be only applied to the cataloged procedure encoder similar with principle.
The content of the invention
The defects of in the present invention for current widely used code book grouping algorithm, propose a kind of dynamic code based on
The speech hiding algorithm of complete binary tree packet.
Algorithm combination iLBC dynamic code book and quantization index modulation (Quantization Index Modulation,
QIM) principle, dynamic code book is grouped using complete binary tree.Sender's code book according to corresponding to selecting secret information position
The insertion that coding realizes secret information is carried out, subsequent recipient completes the extraction of secret information according to the attribute of codeword vector
Journey.
Binary tree is a finite aggregate comprising n node, is referred to as empty binary tree during n=0, and binary tree is by root during n ＞ 0
Node and two mutually disjoint subtrees collectively constitute.In addition to leafy node, each node at most only two stalks of binary tree
Tree.If the binary tree that a height is h has 2h- 1 (h ＞=0) individual node, then it is such to set referred to as full binary tree.Full y-bend
Node in tree is arranged in order from left to right, from top to bottom, it is specified that the sequence number of root node is 0.Binary tree for height for h,
If the sequence number of each node corresponds with height for the node sequence number of h full binary tree, this tree is referred to as complete two
Fork tree.
Because the construction of complete binary tree is similar to the code book packet in Information hiding, a kind of dynamic code book base is proposed accordingly
In the speech hiding algorithm of complete binary tree packet.It is boundary with the root node 0 of complete binary tree, by codebook vectors according to rule
Then it is stored in the node of binary tree, the packet of dynamic code book is realized according to binary tree subtree principle of mutually disjointing.
Base code book CB can be divided into following two groups in dynamic code book：
CB={ CBl, CBr, 0 }
Wherein, CB in Fig. 3lRepresent the node on the left subtree in complete binary tree, comprising codeword vector have
Cbv0, cbv2, cbv3, cbv6, cbv7 etc., CBrRepresent the node on the right subtree in complete binary tree, comprising code word
Vector has cbv1, cbv4, cbv5 etc..
In order to strengthen the anti-steganalysis ability of algorithm, the arrangement mode of code book is enriched, it is necessary to discharge to codeword vector
It is further improved, by the codeword vector inverted discharge in upper figure, forms the complete binary tree of inverted order.
During embedded secret information, the arrangement mode of codeword vector is determined by control information position.Original state is compiled
Optimal codes index shows randomness caused by code, meets the needs of control information position is to randomness just, therefore select and search
Optimal codes index is control information position caused by rope fixed codebook.Selected codeword vector is worth according to the mould 2 of control information position
The mode of binary tree is generated, if control information position meets index mod 2=0, complete binary tree is generated with positive sequential mode；If
Control information meets index mod 2=1, then complete binary tree is generated in a manner of inverted order.
Transmitting terminal does recursive traversal according to embedded secret information value on complete binary tree after constructing complete binary tree,
When embedded secret information is 0, recursive search is done on the left subtree of complete binary tree, searching meets optimal match search condition
Codeword vector and optimal index；Conversely, when embedded secret information is 1, recurrence time is done on the right subtree of complete binary tree
Go through, find the codeword vector and optimal index for meeting optimal match search condition.By optimal index and other ginsengs after the completion of search
Number is according to fixed format packed and is sent on network, realizes hiding for voice messaging.
Receiving terminal parses after the iLBC packets comprising secret information are received to it, extracts associated encoding parameter,
Reconstruct original state simultaneously judges the make of complete binary tree according to fixed codebook optimal index value, then builds in code book
Deposit, corresponding complete binary tree is built according to code book internal memory.Finally according to corresponding to dynamic code book index codebook vectors in y-bend
Present position judges secret information position in tree, extracts the secret information of transmitting terminal insertion, the extraction of secret information is realized with this.
Because sender does not stop encoder immediately after the completion of secret information insertion, and it is complete to be to wait for all carrier voice codings
Into rear stopping encoder, therefore, randomness will be shown by being not embedded into the call number of the carrier of secret information, and recipient can not root
Whether go out according to position judgment of the call number in binary tree with the presence of secret information, so the extraction algorithm is a kind of non-Blind extracting
Algorithm.
Brief description of the drawings
Fig. 1 is the generating process of base code book in dynamic code book.
Fig. 2 is complete binary tree structure chart.
Fig. 3 is grouped for dynamic code book positive sequence.
Fig. 4 is grouped for dynamic code book inverted order.
Fig. 5 is secret information telescopiny.
Fig. 6 is secret information extraction process.
Fig. 7 is that LAN tests topological diagram.
Fig. 8 is that ping orders test network is connective.
Fig. 9 is hidden voice communications module.
Figure 10 is JNI implementation processs.
Figure 11 is VoIP talk clients.
Figure 12 is the request dialog box of customer end B ejection.
Figure 13 is that customer end B ejects reminder dialog frame.
Figure 14 is the secret information of customer end A display extraction.
Figure 15 is that the hidden algorithm that dynamic code is grouped based on complete binary tree is embedded in comparison of wave shape before and after secret information.
Figure 16 is dynamic code this grouping algorithm ABX false determination ratios based on complete binary tree.
Figure 17 is that PESQ values contrast under the speech hiding algorithm 30ms frame formats based on this packet of dynamic code.
Figure 18 is that PESQ values contrast under the speech hiding algorithm 30ms frame formats based on this packet of dynamic code.
Embodiment
1. building development platform on the local computer first, test environment is built in a local network, and ROUTER is in Fig. 7
The common a TP-Link routers of in the market, model is TL-WR886N.Terminal USER A and USER B are two PC, parameter
It is as follows, processor：Intel(R)Core(TM)i3-4370 [email protected] 3.80GHz；Internal memory：4GB；Sound card：Realtek
High Definition Audio；System：The professional version Service Pack 1 of Windows 7.Network configuration uses after completing
The connectedness of ping order test networks.
2. and then software realizes speech hiding module, and speech hiding algorithm is realized from C language.Due to realizing
The limitation of environment, the agreement in the VoIP voice communications of this software masking more than transport layer, since transport layer realizes that voice leads to
Believe module.
3. realizing voice communications module using Java network programmings, pass through JNI (Java Native Interface) technology
Realize calling of the voice communications module to iLBC encoder integrated speech Information Hiding Algorithms modules.Create and complete to carry this place
The javac instruments compiling Java files provided after the source program of method using JDK, produce .class files, then using javah works
The header file of tool generation nation method, it is newly-built to be incorporated into VC++ by the header file AudioCodec.h of generation
In Win32Dynamic-Link Library (DLL) engineering, the method stated in header file, speech hiding module are realized
With iLBC coding modules, DLL engineerings are then compiled, generate local .dll files.Finally it is introduced into Java engineerings
Realize interacting for Java and C language.
4. the voice call starting stage, IP address is respectively that 10.5.47.119 and 10.5.47.183 two LANs are mutual
Join PC (hereinafter referred to as customer end A and customer end B) each self-starting VoIP talk clients, now shown in buddy list column
It is current it is online can conversation object.It is assumed that initiating call request from customer end A to customer end B, customer end A chooses conversation object
IP address after click on " initiate call " button, start voice call watcher thread, now, customer end B can eject request call
Dialog box.
5. customer end B is agreed to carry out voice communication, both sides will start voice call thread and enter the voice call stage.Logical
During words, customer end B inputs to be prepared in advance into secret information text box (uses one section of process two to enter in this experiment
The text message of inhibition and generation, length 900bit) secret information, click on " embedded secret information " button, this section of secret information is just
It has been sequentially embedded in carrier voice.After secret information is embedded in, customer end B ejection reminder dialog frame prompting user is concealed
Information insertion is completed.Hereafter, customer end A and customer end B carry out normal speech communication.
6. when customer end A have received the voice flow with secret information of customer end B transmission, customer end A is receiving
Also start identifiers in voice flow is detected while voice messaging, start secret information when monitoring start identifiers
Extraction thread starts to extract secret information, terminates secret information extraction thread when monitoring end identifiers.The secret extracted
Presentation of information is in " extracting secret information " text box.
7. last, client any one party terminates voice communication, closes client.
8. speech hiding algorithm that pair dynamic code is grouped based on complete binary tree and with its thought similar in two kinds
The hidden capacity of algorithm is contrasted, and as shown in table 1, algorithm one is that dynamic code is hidden based on what complete binary tree was grouped in table
Algorithm, algorithm two be dynamic code based on the hidden algorithm of parity packet, algorithm three is CNV algorithms.
The hidden capacity of table 1 contrasts
As can be seen from Table 1, algorithm one is identical with the hidden capacity of algorithm two, and reason is that two algorithms have used identical
Hide thought and Hidden field --- Information hiding is carried out using the thought of code book packet in dynamic code book, and both belonged to
The larger hidden algorithm of capacity, embedded speed are higher.Algorithm three uses fixed codebook grouping algorithm, and capacity is slightly smaller, but also reaches
200bps is arrived.Comprehensive analysis, set forth herein the speech hiding algorithm that is grouped based on complete binary tree of dynamic code be
A kind of larger hidden algorithm of capacity, meets the needs of real-time covert communications of VoIP are to hidden capacity.
9. the disguise of pair hidden algorithm proposed is analyzed, one group of voice signal is randomly selected from experimental data,
The time domain beamformer and spectrogram before and after carrier voice signal insertion secret information are drawn respectively, and it is hidden to assess to introduce PESQ values
Hide the disguise of algorithm.Embedded secret information is assessed to change caused by voice signal auditory perception, is believed using ABX tested speech
Number similarity.
10. verify dynamic code based on the speech hiding algorithm that complete binary tree is grouped when by noise jamming it is hidden
The stability of secret information.From randn () functional simulation random noise in MATLAB, carry out plus make an uproar to attack to carrying code stream
Hit, then secret information under attack is extracted with extraction algorithm.
11. influence of the speech hiding algorithm that test dynamic code is grouped based on complete binary tree to real-time Communication for Power,
Only the insertion to secret information and extraction process time delay are analyzed, and the disturbing factor of delay may be caused by excluding other.
Claims (2)
1. based on widely used iLBC (Internet Low Bit in VoIP (Voice over Internet Protocol)
Rate Codec) encoder research, propose the speech hiding algorithm that be grouped based on complete binary tree of dynamic code, its spy
Sign is：
Through the following steps that realize：
(1) dynamic code book in iLBC codings is generated；
(2) complete binary tree is built；
(3) embedded secret information；
(4) secret information is extracted.
2. the speech hiding algorithm that dynamic code according to claim 1 is grouped based on complete binary tree, its feature
It is：
Wherein：Step (1) is that the coded data for completing original state coding is decoded, according to the LPC (Linear decoded
Predictive Coding) pumping signal filling code book internal memory, length is 85 or 147, code book internal memory when often encoding next subframe
In data all in dynamic change, thus generate the dynamic code book in iLBC codings；
Step (2) builds complete binary tree, using the linear and Linked Storage Structure of binary tree, with the root node of complete binary tree
0 is boundary, and codebook vectors are stored in the node of binary tree according to rule, according to binary tree subtree mutually disjoint principle realize it is dynamic
The packet of state code book；In order to strengthen the anti-steganalysis ability of algorithm, the arrangement mode of code book is enriched, codeword vector can be fallen
Discharge is put, therefore dynamic code book can be divided into positive sequence packet and inverted order packet；
Step (3) is determined the arrangement mode of codeword vector by control information position, selectes search during embedded secret information
Optimal codes index is control information position caused by fixed codebook, is worth selected codeword vector life according to the mould 2 of control information position
Into the mode of binary tree, the insertion of secret information specifically needs following nine processes；
1. secret information is encrypted：To plaintext secret information S={ b1, b2..., bnDo the encryption process, obtain ciphertext E={ e1,
e2..., en, to strengthen the security of covert communications；
2. carrier framing：According to iLBC coding standards, input signal is divided into 20ms frames or 30ms frames, and following steps are with 30ms frames
Exemplified by, it is assumed that input signal has N frames, F={ fi| i=0......N }, fiRepresent the i-th frame；
3. selection original state simultaneously encodes, residual signals are normalized；
4. build dynamic code book：The i-th frame f in voice flow FiRemoving outside original state has 5 subframes, i.e. fi={ fi 1, fi 2, fi 3,
fi 4, fi 5, according to code book internal memory, form dynamic code book CBi={ CBi 1, CBi 2, CBi 3, CBi 4, CBi 5, wherein CBiRepresent i-th
The dynamic code book of speech frame, CBi KRepresent the dynamic code book of k-th subframe in i-th of speech frame；
5. complete binary tree T is constructed according to control information position：If control information position meets index mod 2=0, with positive sequence
Mode constructs complete binary tree, if control information position meets index mod 2=1, binary tree is constructed in a manner of inverted order；It is dynamic
State code book CBi KIt is changed into CBi K={ CBi K, L, CBi K, R, 0 } and=T, wherein CBi K, LRepresent left subtree T in complete binary tree T1On it is dynamic
State code book, CBi K, RRepresent right subtree T in complete binary tree T2On dynamic code book；
6. secret information is embedded in：According to the secret information E={ e after encryption1, e2..., enIn eiValue selection corresponding to code
Originally scan for：
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If secret information ei=0, then the code book group CB formed in the left subtree of binary treei K, LMiddle search Optimum Matching code book arrow
Amount, if ei=1, then the code book group CB formed in the right subtree of binary treei K, RMiddle search Optimum Matching codebook vectors；Corresponding
Code book in, do Optimum Matching with target vector and codebook vectors, find optimal index number and optimum gain and quantified, it is complete
Into after the information insertion of present sub-frame, target vector is updated, while one is moved after secret information, is updated to ei+1；
7. second level codebook search, repeat step 4., step 5. with step 6.；
8. third level codebook search, repeat step 4., step 5. with step 6.；
9. if secret information insertion finishes, remaining carrier carries out standard iLBC codings, and otherwise, return to step is 3.；
Step (4) is that receiving terminal parses after the iLBC packets comprising secret information are received to it, extracts correlative coding
Parameter, reconstruct original state and the make of complete binary tree is judged according to fixed codebook optimal index value, then build code
This internal memory, corresponding complete binary tree is built according to code book internal memory, finally the codebook vectors according to corresponding to dynamic code book index exist
Present position judges secret information position in binary tree, extracts the secret information of transmitting terminal insertion, secret information is realized with this
Extraction, the insertion of secret information specifically need following ten processes；
1. receiving terminal parses to the iLBC packets received, relevant parameter is obtained；
2. judging whether sender has secret information insertion, and determine to be embedded in the digit of secret information, if secret information is embedding
Enter, go to step 3., otherwise, go to step 10.；
3. reconstruct original state；
4. building code book internal memory according to original state, control information position is judged according to the fixed codebook indices of acquisition；
5. dynamic code book CB is built according to the code book internal memory in 4.i={ CBi 1, CBi 2, CBi 3, CBi 4, CBi 5, wherein CBiRepresent the
The dynamic code book of i speech frame, CBi KRepresent the dynamic code book of k-th subframe in i-th of speech frame；
6. binary tree is constructed according to control information position：If control information position meets indexmod2=0, then with positive sequential mode
Complete binary tree T ' is constructed, if control information position meets index mod 2=1, then construct complete y-bend in a manner of inverted order
Set T '；
7. secret information is extracted according to code book index：The position judgment secret information of codebook vectors according to corresponding to code book index
Position, if BWi K∈CBi K, L, then ei=0, otherwise ei=1；
8. the secret information extracted is integrated, the secret information E={ e encrypted1, e2..., en}；
9. the E 8. obtained using secret key pair step is decrypted, integrate again, obtain plaintext S={ b1, b2..., bn}；
10. extraction finishes, algorithm terminates.
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