CN106530368B - A Multi-threshold Progressive Secret Image Sharing and Reconstruction Method in Prime Domain - Google Patents
A Multi-threshold Progressive Secret Image Sharing and Reconstruction Method in Prime Domain Download PDFInfo
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Abstract
本发明给出一种素数域多门限渐进秘密图像分存及重构方法，首先结合随机参与值将密钥分存，将分存密钥和参与值对应的MD5值公布以防止作弊；然后对秘密图像进行8×8频域变换，对分块频域系数进行随机量化和指定码长分配表的2进制表示，按之字形扫描顺序和频带重组形成多个划分频带并通过置乱形成频带备份；其次对频带、频带备份和认证信息在素数域进行多门限分存，并附加1比特认证信息重构分发影子图像。在恢复时首先检测MD5值并结合多门限确定可重建频带，然后利用双重认证重构1次和2次频带备份表并重建对应频带，利用已重建频带重构秘密图像。同现有方法相比，所提方法可充分利用分发影子图像对秘密图像进行渐进分存并提升视觉重建质量。
The invention provides a multi-threshold progressive secret image sharing and reconstruction method in the prime number field. First, the key is stored in combination with the random participation value, and the MD5 value corresponding to the sharing key and the participation value is published to prevent cheating; Perform 8×8 frequency domain transformation on the secret image, randomly quantize the block frequency domain coefficients and specify the binary representation of the code length allocation table, form multiple divided frequency bands according to the zigzag scanning order and frequency band recombination, and form frequency bands by scrambling Backup; secondly, the frequency band, frequency band backup and authentication information are stored in the prime number domain with multiple thresholds, and 1-bit authentication information is added to reconstruct and distribute the shadow image. When restoring, firstly detect the MD5 value and combine multiple thresholds to determine the reconstructable frequency band, then use double authentication to reconstruct the primary and secondary frequency band backup table and reconstruct the corresponding frequency band, and use the reconstructed frequency band to reconstruct the secret image. Compared with the existing methods, the proposed method can make full use of distributed shadow images to progressively share secret images and improve the quality of visual reconstruction.
Description
Technical field
The invention belongs to image information safety and digital image signal process crossing domain, are related to a kind of information point side of depositing
Method, the in particular to progressive secret image sharing of a kind of prime field multi-threshold and reconstructing method.
Background technique
The conventional images information point technology of depositing is derived mainly from the privacy sharing in cryptography, in conjunction with secret sharing scheme, is based on
The image information of (K, N) thresholding point is deposited scheme and is proposed extensively, and the image information based on (K, N) thresholding point of early stage is deposited in scheme
There is no authentication measures, causes the Secret Image authenticity finally reconstructed that can not identify.Scheme is deposited for no authentication measures image point
Existing security risk in use, some documents have also been inquired into the image with certification point and have been deposited.Such as Lin C C, 2004
(Lin C C,Tsai W H.Secret image sharing with steganography and authentication
[J] .The Journal of Systems and Software, 2004,73 (3): 405-414.) in advance by Secret Image
Each pixel be adjusted to [0,251) between, Shamir- (K, N) is then carried out to it and point is deposited, 2 × 2 piecemeal upper right Angle Positions are adjusted
Parity check bit as certification position, but authentication information only has 1 bit parity check position, does not have certain authentication role.To keep away
Exempt from Lin C C, 2004 mention strategy and pre-process to Secret Image Secret Image is caused to be distorted, Yang C N, and 2007
(Yang C N,Chen T S,Yu K H,et al.Improvements of image sharing with
steganography and authentication[J].The Journal of Systems and Software,2007,
80 (7): 1070-1076.) etc. Shamir- (K, N) is extended to GF (28) finite field, and pass through HMAC (Hash-based
Message Authentication Code) still there was only 1 to the authentication method for point depositing information and authenticating, but being proposed
Position is authenticated, malice participant still has very maximum probability to escape inspection, and GF (28) it is related to the addition subtraction multiplication and division of polynomial ring on domain
Operation is related to biggish operation cost.Chang C C, 2008 (Chang C C, Hsieh Y P, Lin C H.Sharing
secrets in stego images with authentication[J].Pattern Recognition,2008,41
(10): 3130-3137.) etc. generating point stored certification position a 4bit using Chinese remainder theorem further to promote certification energy
Power, however mentioned method cannot make full use of authentication capability to repair the pixel of authentification failure, to add repair ability,
Chang C C,2011(Chang C C,Chen Y H,Wang H C.Meaningful secret sharing
technique with authentication and remedy abilities[J].Information Sciences,
2011,181 (14): 3073-3084.) etc. divide the pairing for depositing Secret Image pixel and it using multiple coefficients of Lagrange
Pixel, so that scheme has the repair ability after certain attack, but the authentication information position suggested plans is less, point of secret pixel
It deposits information to store up to two parts and determine the region attacked with minimum vertex-covering rectangle, causes the recovery capability for mentioning strategy inclined
It is low.To improve the repair ability after attack, Wu X T, 2013 (Wu XT, Sun W.Secret image sharing scheme
with authentication and remedy abilities based on cellular automata and
discrete wavelet transform[J].The Journal of Systems and Software,2013,86(4):
Secret Image 1068-1088.) etc. is done into level-one wavelet transform, takes its LL subband to back up 2 parts, to construct secret with original
Close image etc. is big but each pixel bit only has 4 backup images, point deposited using reversible cellular automata Secret Image and
Backup image can be repaired if former secret pixel is attacked by the backup image corresponding position pixel recovered, thus
Obtain better repair ability.But mentioned method is that 28 secret pixels and 24 backup image pixels are amounted to 24
It constructs reversible cellular automata as 8 cellulars at initial 3 moment point deposit, it is real for resulting in the problem that it so not
(3, N) threshold schemes of meaning, 2 secret pictures of Secret Image can be recovered by needing at least three number continuously to divide memory cell
2 backup pixels of element and backup image；Any one pixel in 2 × 4 piecemeals is attacked, that is, cause 2 secret pixels and
Totally 24 information are unavailable for 2 pixels of its backup image, so that this method can not resist any small attacked by noise.
Image given above point deposits scheme point and deposits that scheme is single simultaneously, cannot substantially effectively utilize point being recovered to
Photos and sending messages and sufficiently effective reconstruction is carried out to Secret Image according to the different of significance level, to the progressive recovery matter of Secret Image
It measures extremely limited, in many occasions, often needs according to the difference of participant's quantity and to point stored significance level come gradually
The Secret Image of different visual qualities is recovered into ground.
It is deposited for progressive point, Wang R Z, 2007 (Wang R Z, Shyu S J.Scalable secret image
Sharing [J] .Signal Processing Image Communication, 2007,22 (4): 363-373.) give base
3 kinds progressive point in image block, the grouping of pixel bit and piecemeal grouping mixing is deposited model, as a whole by dividing unit
It carries out (2,2) point and deposits and formed N parts of shadow images, and by recoverable dividing unit quantity in distribution shadow image come to secret
Close image carries out (2, N) and restores.Lin Y Y,2010(Lin Y Y,Wang R Z.Scalable Secret Image
Sharing With Smaller Shadow Images[J].IEEE Signal Processing Letters,2010,17
(3): 316-319. it is (N, 2N-K) that (2,2) point, which further) are deposited expansion, is restored so as to carry out (K, N) to Secret Image.
Yang C N, 2010 (Yang C N, Huang S M.Constructions and properties of k, out of n,
scalable secret image sharing[J].Optics Communications,2010,283(9):1750-
1762.) it combines visual cryptography to give other two kinds and (2, N) point is deposited to the separate-management method expanded and deposited for (K, N) point.In conjunction with
Yang C N, 2010 work, Yang C N, 2011 (Yang C N, Chu Y Y.A general (k, n) scalable
secret image sharing scheme with the smooth scalability[J].Journal of
Systems&Software, 2011,84 (10): 1726-1733.) and Liu Y X, 2014 (Liu Y X, Yang C N, Yeh P
H.Reducing shadow size in smooth scalable secret image sharing[J].Security&
Communication Networks, 2014,7 (12): 2237-2244.) it is further added to smoothness constraint limitation, so that secret
The Quality of recovery of close image is with participant's quantity proportional increase.
Document above Wang R Z, 2007, Lin Y Y, 2010, Yang C N, 2010, Yang C N, 2011 and Liu Y
X, 2014 are restored using the fritter that Secret Image divides as unit is restored, for being grouped based on image block and piecemeal
Mixed mode will be unable to carry out image whole meaning from obscuring to clearly progressive recovery, and pixel bit is grouped
Mode is also only capable of providing the progressive recovery of limited quantity.Lee J S,2015(Lee J S,Chen Y R.Selective
scalable secret image sharing with verification[J].Multimedia Tools&
Applications, 2015:1-11.) binding characteristic figure give based on area-of-interest band certification progressive separate-management method, with
Increasing for shadow image quantity, progressive recovery carried out to interesting image regions, but its essential starting point is with Wang R Z,
2007, Lin Y Y, 2010, Yang C N, 2010, Yang C N, 2011 and Liu Y X, 2014 methods are similar, can not be right
Image carry out whole meaning on from obscuring clearly progressive recovery.
For image integrally progressive recovery, Chen S K, 2005 (Chen S K, Lin J C.Fault-tolerant
and progressive transmission of images[J].Pattern Recognition,2005,38(12):
A kind of progressive separate-management method of multi-threshold of bound site flat scanning 2466-2471.) is given, image pixel is divided into and is not weighed
Folded fritter, recombinates by the pixel in fritter by Bit Plane Decomposition and by place bit plane, is put down in place according to recombination pixel
Face significance level difference distributes different dividing and deposits thresholding, Liu W, 2015 (Liu W, Wang A, Chang C C, et al.A
grouped-scalable secret image sharing scheme[J].Multimedia Tools&
Applications, 2015,74 (17): 7095-7109.) give it is a kind of based on Bit Plane Decomposition and Lagrangian difference
Progressive picture separate-management method.But document above Chen S K, 2005 and Liu W, 2015 are in accordance with the bit plane of airspace pixel
Significance level point deposit, extremely limited to the regulating and controlling effect of image vision.
Kong J,2007(Kong J,Zhang Y,Meng X,et al.A Scalable Secret Image
Sharing Method Based on Discrete Wavelet Transform[C]//Bio-Inspired
Computational Intelligence and Applications,International Conference on Life
System Modeling and Simulation,LSMS 2007,Shanghai,China,September 14-17,2007,
Proceedings.2007:736-745. Chen S K) is combined, 2005 work is treated and point deposits image progress piecemeal DWT change
It changes, integer quantisation is carried out to transformed coefficient and bit plane recombinates, come by the significance level of bit plane where recombination DWT coefficient
It distributes different dividing and deposits thresholding to realize that progressive point is deposited, but relative to airspace pixel, the significance level of frequency coefficient is usual and is
Number frequency, i.e. position is closely bound up, merely relies on the bit plane significance level that frequency coefficient divides and regulates and controls to the vision of image
It acts on still extremely limited.
Summary of the invention
It is an object of the invention to overcome prior art defect, a kind of progressive secret image sharing of prime field multi-threshold is provided
And reconstructing method, it makes full use of distribution shadow image to carry out progressive point to Secret Image and deposits and promote optical rehabilitation quality.
To achieve the above object, the invention adopts the following technical scheme:
A kind of progressive secret image sharing method of prime field multi-threshold, comprising the following steps:
Step 1: the parameter of default is deposited by secret holder configuration point, comprising: 320 2 system code length allocation table M=
(mi,j)8×8, system modulus Big prime p, distribution share number N, N ∈ { 1,2 ..., p-1 }, integer Randomized Quantizing thresholding rq > 0 and
0 frequency band of r > point deposits thresholding ki∈ { 2,3 ..., N }, i=0,1 ..., r-1 meets that frequency band is incremented by and frequency band aggregate-value is 64
The factor, by Secret Image S=(si,j)h×wIt is divided into nonoverlapping 8 × 8 fritter Bx,y, x=0,1 ..., m-1, y=0,1 ..., n-
1, wherein m=h/8, n=w/8 and mmod8=0, nmod8=0；
Step 2: N number of random number P is generated by secret holder1,P2,…,PN∈ 0,1 ..., and p-1 } it is used as each shadow figure
As corresponding random participation value and P1mod127,P2mod127,…,PNMod127 two neither etc., by key key ∈ 0,1 ...,
P-1 } it point is saved as N number of point and deposits key subkey1,subkey2,…,subkeyN, and by sub-key (subkeyk,Pk), k=1,
The corresponding MD5 value of 2 ..., N is published to the 3rd side Fang Gongxin to prevent participant from practising fraud, by key key generate length be 64 with
Machine sequence RQx,y=(rqi)64,rqi∈ { 1,2 ..., rq }, is rearranged as Bx,yCorresponding Randomized Quantizing matrix Qx,y,
Wherein x=0,1 ..., m-1, y=0,1 ..., n-1；
Step 3: will each not overlap partition Bx,y=(bi,j)8×8It is transformed to area block FBx,y=(fbi,j)8×8, pass through Qx,y
=(qi,j)8×8By FBx,yIt is quantified as FB 'x,y=(fb 'i,j)8×8And to FB 'x,yMiddle matrix element carry out integer indicate and 2 into
System storage conversion is used as FB "x,y；
Step 4: by all FB "x,yBe converted to 2 system bit bit string IBx,y, by IBx,yBe converted to 1 dimension sequence Ix,y, will
Ix,yWith k0:k1:…:kr-1It is divided into r frequency band for the ration of division, remembers that corresponding frequency band isThenThe element for being included
Number scale is Ni, i=0,1 ..., r-1；
Step 5: all piecemeal same frequency bands are merged, the frequency band BI after being mergedi, to BIiIn element be indexed
Position scramble, as frequency band BIiBackup CIi, wherein i=0,1 ..., r-1；
Step 6: noteBi is generated by key keyi,u,cii,u,cii-1,uCertification
Information
Step 7: by bii,u,cii,uOr bii,u,cii,u,cii-1,uWithCombination is used as integer
A, b, c are then rightLagrange's interpolation, which point deposits to obtain, in prime field point deposits information fi,u
(Sk), k=1,2 ..., N, Sk=Pkmod127；
Step 8: 1 bit random i lumber v is generated by key keyi,u,k∈ { 0,1 } is used as fi,u(Sk) certification position, by fi,u
(Sk) and vi,u,kIt is mapped as fi,′u(Sk) ∈ { 0,1 ..., 255 }, in which: i ∈ { 0,1 ..., r-1 }, k ∈ { 1,2 ..., N }, u ∈
{0,1,…,mn·Ni-1}；
Step 9: note EkFor matrix before the corresponding scramble of k-th of distribution shadow image, Ez,kFor EkZ-th of restructuring matrix
Block, Ez,i,kFor Ez,kI-th of divided band, first reconstruction Ez,i,k, then rebuild Ez,k, finally rebuild Ek, then with key key
And subkeykBy EkScramble is E 'k；
Step 10: by all E 'k, k=1,2 ..., N is as shadow image and N number of sub-key (subkeyk,Pk), k=
1,2 ..., N are distributed to corresponding custodian and take care of, and configure reconfiguration system using the default parameters of system and destroy intermediate ginseng
Number.
Further, 0 frequency band of r > point deposits thresholding k in step 1i∈ 2,3 ..., N }, i=0,1 ..., r-1 meets frequency
The specific constrained procedure for the factor that band is incremented by and frequency band aggregate-value is 64 is formula (1) and formula (2):
N number of point, which is saved as, by key ∈ { 0,1 ..., p-1 } points in step 2 deposits key subkey1,subkey2,…,
subkeyNSpecific method be using key as secret value s, by P1,P2,…,PNRespectively substitute into formula (3) can be obtained N number of point deposit it is close
Key subkey1,subkey2,…,subkeyN:
In formula (3), random numberIt is that random number seed maps to obtain by key；
Key generates the random sequence RQ that length is 64 in step 2x,y=(rqi)64,rqi∈'s { 1,2 ..., rq } is specific
Method is that key is mapped as key by formula (4)x,y, by keyx,yAs random number seed, the random sequence that length is 64 is generated
RQx,y=(rqi)64,rqi∈{1,2,…,rq}
It is rearranged in step 2 as Bx,yCorresponding Randomized Quantizing matrix Qx,ySpecific method be formula (5)
Qx,y=MScanzigzag(Inc(RQx,y),8,8) (5)；
In formula (5), Inc () is sequence increasing function, MScanzigzag() is matrix zigzag scanning function, by sequence scanning
For matrix, the 1st parameter of function is sequence to be scanned, and the 2nd and the 3rd parameter is matrix dimension.
Further, in step 3 by the not overlap partition B of each divisionx,y=(bi,j)8×8It is transformed to area block FBx,y=
(fbi,j)8×8Specific method be formula (6):
FBx,y=D2DCT (Bx,y) (6)
In formula (6), function D2DCT () is 2 dimension discrete cosine transforms, shown in calculating formula such as formula (7):
In step 3 by FBx,yRandomized Quantizing is FB 'x,y=(fb 'i,j)8×8Specific method be formula (8):
fb′i,j=fbi,j/qi,j, i, j=0,1 ..., 7 (8)
In step 3 to FB 'x,yMiddle element, which carries out integer, to be indicated to be converted to FB " with 2 system storagesx,ySpecific method
For formula (9):
In formula (9),WithCorrespond to code length allocation table M=(mi,j)8×8Element mi,jThe maximum that can be indicated
Value and minimum value, corresponding distribution principle are determined by formula (10):
In step 4 by all FB 'x′,yBe converted to 2 system bit bit string IBx,ySpecific method be formula (11):
IBx,y=BScanzigzag(FB″x,y) (11)
In formula (11), function BScanzigzag() is bit bit string zigzag scanning function, and the function of execution is will to input square
The element of battle array is attached by its 2 system storage form with zigzag scanning sequency；
By IB in step 4x,yBe converted to 1 dimension sequence Ix,ySpecific method be formula (12):
Ix,y=BCut (IBx,y,5) (12)
In formula (12), function BCut () is bit bit string segmentation function, wherein the 1st parameter corresponds to bit bit string, the 2nd
A parameter is the segmentation unit of bit bit string, and the function that formula (12) executes is by BCut (IBx,y, 5) and by bit bit string IBx,yWith
5 bit bit strings are that separate units are converted to 1 dimension sequence Ix,y；
First prime number N that each divided band is included in step 4i, i=0,1 ..., r-1 can be determined by formula (13):
Further, the specific method in step 5 merged all piecemeal same frequency bands is formula (14):
In formula (14), " | | " it is sequence connector, i.e., by the frequency band of all piecemealsIt links together and constitutes sequence conduct
Frequency band BI after mergingi, BIiIt in total include mnN in sequenceiA element；
To BI in step 5iIn element be indexed position scramble specific method be key is mapped as by formula (15)
keyi, by keyiAs random number seed, for BIiMiddle element is indexed position scramble:
Bi is generated by key in step 6i,u,cii,u,cii-1,uAuthentication information it is specific
Method is to combine bi by formula (16)i,u,cii,u,cii-1,uKey key is mapped as keyi,u, by keyi,uIt is produced as random number seed
Raw kiA random number carries out mapping as to bi by formula (17)i,u,cii,u,cii-1,uAuthentication information
In formula (16), as i=0, a upper frequency band CI is not present at this timei-1；As u >=size (CIi-1) when, indicate CIi-1
Middle element, which has stored, to be finished, and backup element ci is not presenti-1,u, size (CIi-1) indicate CIi-1Number of elements；
Further, by bi in step 7i,u,cii,uOr bii,u,cii,u,cii-1,uWithGroup
Cooperation is integer a, and the specific method of b, c are formula (18):
It is right in step 7The specific method that Lagrange's interpolation point is deposited in prime field
For formula (19):
In formula (19), gp=127, if k0When=2, storage bi is only needed at this time0,u,ci0,u, while being also only capable of generation 2 and recognizing
Demonstrate,prove informationTherefore directly a and b point deposit；
1 bit random i lumber v is generated by key key in step 8i,u,k∈ { 0,1 } is used as fi,u(Sk) certification position it is specific
Method is to generate random number seed key by formula (20)i,u,k, by keyi,u,kGenerate 1 bit authentication information vi,u,k:
keyi,u,k=(fi,u(Sk)×key+fi,u(Sk)+key+i+u+i×u)modp (20)
Step 8 is by fi,u(Sk) and vi,u,kIt is mapped as fi,′u(Sk) ∈ { 0,1 ..., 255 } specific method be formula (21):
f′i,u(Sk)=27×vi,u,k+fi,u(Sk) (21)；
E is rebuild in step 9z,i,kSpecific method be first by formula (22) rebuild Ez,i,k, right back-pushed-type (23) reconstruction Ez,k, most
Back-pushed-type (24) rebuilds Ek:
Ez,k=MScanzigzag(Ez,0,k||Ez,1,k||...||Ez,r-1,k,8,8) (23)
Ek=MSet (Ek,z/n,zmodn,Ez,k), z=0,1 ..., mn-1 (24)
In formula (24), function MSet () is that function is arranged in matrix-block, and the 1st parameter is to place the matrix of matrix fritter, the
2,3 parameters correspond to matrix-block coordinate, and the 4th parameter corresponds to the matrix fritter to be placed；
With key key and subkeykBy EkScramble is E 'kSpecific method be formula (25)
A kind of progressive Secret Image reconstructing method of prime field multi-threshold, comprising the following steps:
Step 1: remember the reconstruct default parameters of configuration, comprising: 320 2 system code length allocation tables are M=(mi,j)8×8, divide and deposit
Modulus p, distribution share number are N, and N ∈ { 1,2 ..., p-1 }, integer Randomized Quantizing thresholding rq > 0 and 0 frequency band of r > point deposit door
It is limited to ki∈ { 2,3 ..., N }, i=0,1 ..., r-1, it is assumed that have vinit(vinit≥k0) a participant participates in restoring, remember k-th
Participant provide sub-key and shadow image be respectivelyWithIt calculatesCorresponding MD5 value compares its MD5 value stored with the 3rd side Fang Gongxin to come
Sub-key legitimacy is verified, statistics sub-key authenticates the participant's quantity v passed throughsubkey；
Step 2: if vsubkey≥k0, then master key key is reconstructed, the random sequence RQ that length is 64 is generated by keyx,y=
(rqi)64,rqi∈ { 1,2 ..., rq }, is rearranged as Bx,yCorresponding Randomized Quantizing matrix Qx,y, wherein x=0,
1 ..., m-1, y=0,1 ..., n-1, if otherwise vsubkey< k0, then failure is reconstructed；
Step 3: by vsubkeyDetermination can maximum reconstructed t, t ∈ { 0,1 ..., r-1 } a frequency band, by the key of recovery andIt is mapped asThe participant that k-th of sub-key certification is passed through is containing close shadow
ImageInverted is disorderlyIt rebuildsUpper z-th of reconstruction sub-blockByIt rebuilds all frequency bands in z-th of piecemeal and divides setK-th of son is close
All piecemeal same frequency bands of participant that key certification passes through merge to obtainWherein i=0,
1 ..., r-1, k=1,2 ..., vsubkey, NiThe first prime number for including by each divided band；
Step 4: byReconstruct 1 time and 2 backup tablesRebuild Secret Image frequency bandWith
And 1 time and 2 backup tables and reconstruction Secret Image frequency band are authenticated
Step 5: according toIt willWithIt is fused to finally back up
Step 6: rightIn each bii,uIf aci,u=1 does not modify its value then, otherwise using final
Ci in backupi,uReplace bii,u, wherein i=0,1 ..., t, u=0,1 ..., mnNi-1；
Step 7: by Secret Image frequency bandRebuild Secret Image S=(si,j)h×w。
Further, the specific method for reconstructing master key key in step 2 is formula (26):
In formula (26),I-th, the i=1,2 that pass through are authenticated for sub-key ..., vsubkeyA participation
The sub-key that person provides,ForMould p multiplicative inverse；
The random sequence RQ that length is 64 is generated by key key in step 2x,y=(rqi)64,rqi∈{1,2,…,rq}
Specific method be by formula (4) key to be mapped as keyx,y, by keyx,yAs random number seed, generate length be 64 it is random
Sequence RQx,y=(rqi)64,rqi∈{1,2,…,rq}；
It is rearranged in step 2 as Bx,yRandomized Quantizing matrix Qx,ySpecific method be formula (5):
Qx,y=MScanzigzag(Inc(RQx,y),8,8) (5)；
In step 3 by vsubkeyDetermination can maximum reconstructed t, the method for a frequency band of t ∈ { 0,1 ..., r-1 } is formula
(31):
In step 3 by key andIt is mapped asMethod be formula (27):
It rebuilds in step 3Upper z-th of sub-blockMethod be formula (28):
In formula (28), function MGet () is that matrix fritter obtains function, and the 1st parameter of function is the square where matrix fritter
Battle array, the 2nd and the 3rd parameter correspond to the coordinate of matrix-block, and the 4th and the 5th parameter correspond to matrix-block dimension, wherein x=
0,1 ..., m-1, y=0,1 ..., n-1；
In step 3 byIt rebuildsSpecific method be formula (29):
In formula (29), function SScanzigzag() is sequence zigzag scanning function, and the function of execution is to be by matrix-scanning
1 dimension sequence；
Merge in step 3 and obtainsSpecific method be formula (30):
First prime number N that each divided band is included in step 3iIt is determined by formula (13):
Further, in step 4 by1 time and 2 times backup of reconstruct
TableRebuild Secret Image frequency bandAnd 1 time, 2 backup tables and reconstruction Secret Image frequency band are authenticatedMethod particularly includes:
4.1st step: initialization AndIt is rightIn each divide memory cellIt obtains point depositing information by formula (32) and formula (33)With 1 bit authentication informationIt will by formula (34)
Key andIt is mapped as random number seedByRegenerate 1 bit authentication informationIfThen pass through the 1st re-authentication, on the contrary then authentification failure；
4.2nd step: current point the depositing information and be by the 1st re-authentication of noteWherein vfirst
To deposit information content by current point of the 1st re-authentication, if vfirst< ki, then ac is seti,u=0 indicates authentification failure, if otherwise
vfirst≥kiIt is aThen reduction obtains by the following step
4.2.1 step: initialization number of attempt try=0；
4.2.2 step: from vfirstIn enumerate kiA point is deposited information conductWhereinTable
Show the current k for participating in restoringiA point of k-th deposited in information, sets try=try+1；
4.2.2 step: byIt is calculated by formula (35)
In formula (35),Indicate the k for participating in restoringiA point of j-th deposited in information is corresponding random containing close shadow image
Participation value,It corresponds toMultiplicative inverse under mould gp, wherein gp is equal to 127；
4.2.3 step: when i=0 or when, obtain otherwise restoring by formula (36) and formula (37) by formula (36) reduction and obtain
4.2.4 step: key is mapped as random number seed key by formula (38)i,uGenerate kiA random number
And it is mapped to obtain the 2nd re-authentication information by formula (39)By its withComparison, ifThen pass through the 2nd re-authentication and ac is seti,u=1,
If otherwiseThen turn 4.2.2 step, ifDo not pass through the 2nd re-authentication then and ac is seti,u=0, whereinFor
From vfirstIn enumerate kiA point of stored number of combinations；
4.3rd step: output And
Further, basis in step 5It willWithIt is fused to finally back upMethod particularly includes:
5.1st step: initializationWork as i=0, when 1 ..., t-1, is merged by formula (40), work as i=t
When, it is not present at this timeTherefore it directly enables
5.2nd step: key is mapped as key by formula (15)i, with keyiFor random number seed, by dividing key in deposit systemiIt is right
The disorder method answered willInverted is random, to finally be backed up
Further, by Secret Image frequency band in step 7Rebuild Secret Image S=(si,j)h×wTool
Body method are as follows:
7.1st step: willWith NiA element is divided into segment by formula (41) for unit
Sequence B Iz,i, i=0,1 ..., r-1, right back-pushed-type (42) reconstruction IBz, wherein z=0,1 ..., mn-1；
IBz=BIz,0||BIz,1||...||BIz,r-1 (42)
7.2nd step: by all IBz, z=0,1 ..., mn-1 is converted to FB " by formula (43)x,y=(fb "i,j)8×8, by formula
(45) FB ' is obtainedx,y=(fb 'i,j)8×8, FB is obtained by formula (46)x,y=(fbi,j)8×8；
In formula (43), function SBin () is 2 system bit string transfer function of sequence, and the 1st parameter of SBin () is to be transformed
One-dimensional sequence, the 2nd parameter are 2 system digits of sequential element conversion, function BMScanzigzag() is by bit bit string by it
Font scanning sequency and code length allocation table are converted to the matrix fritter big with code length allocation table etc., BMScanzigzag() the 1st ginseng
Number is bit bit string, and corresponding the 2nd parameter is code length allocation table, and the 3rd parameter corresponds to marker bit, for marking reconstruction small
The coordinate position of non-reconstruction band in block, formula (43) is middle to rebuild fritter FB "x,yIn the position mark and element fb " lateri,jAll
It is set to
fbi,j=fbi′,j×qi,j, i, j=0,1 ..., 7 (46)
In formula (45) and formula (46),Corresponding to code length allocation table is M=(mi,j)8×8Corresponding position element institute can table
The minimum value shown；qi,jCorrespond to quantization table Qx,yIn element；
7.3rd step: by formula (47) to FBx,yIt carries out inverse dct transform and obtains Bx,y=(bi,j)8×8If after frequency-domain transform, as
Plain value is overflowed, then takes 255 when pixel is greater than 255, take 0 when pixel is less than 0；
7.4th step: by all piecemeal Bx,y, x=0,1 ..., m-1, y=0,1 ..., n-1 rebuild secret figure by formula (48)
As S=(si,j)h×w；
S=MSet (S, z/n, zmodn, Bx,y), z=0,1 ..., mn-1 (48).
The present invention is analyzed compared with technological merit:
1. traditional images divide scheme of depositing single, substantially effectively cannot sufficiently be had using distribution information to Secret Image
The reconstruction of effect, it is extremely limited to Secret Image Quality of recovery.Tradition is based on image block, the grouping of pixel bit and piecemeal point
The group mixing progressive separate-management method of class is restored using the fritter that Secret Image divides as unit is restored, for being based on image
Piecemeal and piecemeal grouping mixed mode will be unable to carry out image whole meaning from obscuring to clearly progressive recovery, and for
It is also only capable of providing the progressive recovery of limited quantity under pixel bit group mode；And combine airspace pixel bit plane significance level
Whole progressive separate-management method is extremely limited to image vision regulating and controlling effect, and merely relies on the simple bit plane of frequency coefficient and divide
It is still extremely limited to image vision regulating and controlling effect.With above method difference, the present invention carries out piecemeal frequency to Secret Image first
Domain transformation carries out Randomized Quantizing to each piecemeal frequency coefficient, recombinates to form multiple divisions by zigzag scanning sequency and frequency band
Frequency band deposits so as to avoid simple dependence frequency coefficient simple bit plane division institute's band different frequency bands using dividing for different thresholdings
The poor efficiency of next image vision regulation not only effectively can carry out whole progressive point to image and deposit, but also pass through to divide and draw when depositing
Enter frequency band backup, when recovery by multi-threshold determination can reconstruction band, can also effectively be mentioned in conjunction with 1 time and 2 subband backup tables
The progressive Quality of recovery of high shadow image.
2. traditional dividing is deposited in scheme, the participation value of secret holder's setting is usually defaulted as 1,2 ..., and N, there are larger
Security risk introduces random participation value in the present invention so that even if key key compared with being rebuild under low threshold, due to point
The random participation value for issuing each participant, which can not be predicted may be not present, point deposits key subkey1,subkey2,…,subkeyNIt lets out
The risk of dew, while can not also deduce that other users distribute shadow share.To provide enough safeties, all places in the present invention
Generating random number in reason link all enhances safety, such as the corresponding Randomized Quantizing battle array of Secret Image piecemeal frequency-domain transform
Qx,yIt is bound with block position (x, y) and key key；bii,u,cii,u,cii-1,uAuthentication information generate key and bii,u,cii,u,
cii- 1, u and key binding；fi,u(Sk) certification position and fi,u(Sk) and key binding；The shadow image scramble share of each user
Scramble key not only point to deposit key with user related, also bound with key key, so that each user can not deduce point of oneself
Share is sent out, can not also be practised fraud to the sub-key that oneself is administered in combination with the sub-key MD5 value of the 3rd side storage.
3. mentioned method can be substantially effectively using the polynomial multiple coefficients of prime field Lagrange come to current secret
Information, current backup information, the backup information (if upper frequency band presence) of a upper frequency band and corresponding authentication information point deposit,
Image repair ability is also enhanced while improving and authenticating accuracy.
4. the present invention has mechanism and multiple to guarantee the accuracy restored: 1) being tested by the MD5 value of the 3rd side Fang Gongxin storage
Demonstrate,prove sub-key legitimacy；2) by participant's quantity determine can maximum reconstructed frequency band；3) 1 time and 2 frequencies are reconstructed by double authentication
Then band backup table rebuilds final backup, so that the accuracy of recovery can be improved.
Detailed description of the invention
Fig. 1 is point to deposit flow chart；
Fig. 2 is reconstruct flow chart；
Fig. 3 is Secret Image, 24 gray level image Lena that resolution ratio is 512 × 512；
Fig. 4 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Fig. 5 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Fig. 6 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Fig. 7 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Fig. 8 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Fig. 9 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Figure 10 is embodiment, and resolution ratio is that 24 of 512 × 512 contain close shadow image；
Figure 11 is embodiment, the Secret Image recovered by Fig. 4~Fig. 6, PSNR 27.31dB；
Figure 12 is embodiment, the Secret Image recovered by Fig. 4~Fig. 7, PSNR 29.98dB；
Figure 13 is embodiment, the Secret Image recovered by Fig. 4~Fig. 8, PSNR 34.05dB；
Figure 14 is embodiment, the Secret Image recovered by Fig. 4~Fig. 9, PSNR 37.02dB；
Figure 15 is embodiment, the Secret Image recovered by Fig. 4~Figure 10, PSNR 43.36dB；
Figure 16 is attack pattern 1；
Figure 17 is attack pattern 2；
Figure 18 is the result images that Fig. 9 is attacked by Figure 16；
Figure 19 is the result images that Figure 10 is attacked by Figure 17；
Figure 20 is the Secret Image recovered by Fig. 4~Fig. 8, Figure 18 and Figure 19, PSNR 36.03dB.
Specific embodiment
Below using JAVA jdk1.8.0_65 as case implementation environment, embodiment of the present invention is carried out in conjunction with attached drawing detailed
Illustrate, but be not limited to the implementation case, wherein Fig. 1 is point to deposit flow chart, and Fig. 2 is reconstruct flow chart.Below with specific example
Point process of depositing is illustrated:
Step 1: 320 code length allocation table M for dividing deposit system to default by secret holder configuration choose Big prime p=
1000000007 are used as system default modulus, and quantum key distribution quota N=7, integer Randomized Quantizing thresholding rq=12, r is arranged
It is k that=6 points, which are deposited thresholding,0=3≤k1=4≤k2=5≤k3=6≤k4=7≤k5=7 and k0+k1+…+k5=32, meet formula
(1) and the constraint condition of formula (2) Secret Image S=(s, is readi,j)8×8, it is divided into nonoverlapping 8 × 8 fritter Bx,y, x=
0, y=0, then B0,0=S, at this time only one block, in which:
Step 2: N number of random number P is generated by secret holder1,P2,…,PN∈ 0,1 ..., and p-1 } it is used as each shadow figure
As random participation value and P1mod127,P2mod127,…,PNMod127 two neither etc., using key key as secret value s, by P1,
P2,…,PNSubstitution formula (3) can be obtained N number of point and deposit key subkey respectively1,subkey2,…,subkeyN, and by sub-key
(subkeyk,Pk), the corresponding MD5 value of k=1,2 ..., N is published to the 3rd side Fang Gongxin to prevent participant from practising fraud, and incites somebody to action by formula (4)
Key is mapped as keyx,y, by keyx,yAs random number seed, the random sequence RQ that length is 64 is generatedx,y=(rqi)64,rqi∈
{ 1,2 ..., rq } regard it as B by formula (5) arrangementx,yCorresponding Randomized Quantizing matrix Qx,y, wherein x=0,1 ..., m-1, y=
0,1,…,n-1；
Such as: generate N=7 random number P1=14, P2=50, P3=53, P4=15, P5=22, P6=1, P7=26 make
For participation value at random, P can be verified1mod127,P2mod127,…,PNNeither etc., key key=131819 is made by mod127 two
For secret value s, by P1=14, P2=50, P3=53, P4=15, P5=22, P6=1, P7=26 substitute into formula (3) respectively can be obtained:
subkey1=42367649, subkey2=504447269, subkey3=565929662, subkey4=48330104,
subkey5=101064233, subkey6=595802, subkey7=139838477, by sub-key (subkeyk,Pk), k=
The corresponding MD5 value of 1,2 ..., N is published to the 3rd side Fang Gongxin, such as (subkey1,P1) corresponding MD5 value is 0xef8afaa75
b6eafc24ab0ea73288988de；X=0, y=0 are taken, key=131819 is mapped as key by formula (4)0,0=363, it will
key0,0=363 are used as random number seed, generate the random sequence RQ that length is 640,0=3,12,2,2,2,12,3,12,10,
5,1,8,1,6,8,4,12,1,6 ..., 8,2,5,10,2, Isosorbide-5-Nitrae, 2,6,10 }, it is regard as B by formula (5) arrangement0,0Random quantity
Change matrix
Step 3: will each not overlap partition Bx,y=(bi,j)8×8Area block FB is transformed to by formula (6)x,y=(fbi,j)8×8,
By FBx,yFB ' is quantified as by formula (8)x,y=(fbi′,j)8×8, by formula (9) to FB 'x,yMiddle element carries out integer expression and according to M
=(mi,j)8×8Carry out the 2 systems storage of corresponding digit；With b0,0=160, b0,1For=162, fb can be obtained by formula (6)0,0=
1279.625 and fb0,1=9.035376, to fb0,0,fb0,1Fb ' can be obtained by formula (8)0,0=fb0,0/q0,0=1279.625 Hes
fb′0,1=fb0,1/q0,1=9.035376, by formula (9) to fb '0,0=1279.625, fb '0,1=9.035376 carry out integer
It indicates and according to m0,0=11 and m0,1=10 is availableWith
Step 4: note integer indicates and the FB ' of 2 systems storagex,yFor FB 'x′,y, by all FB 'x′,yTurn by formula (11)
It is changed to 2 system bit bit string IBx,y, by IBx,y1 dimension sequence I is converted to by formula (12)x,y, by Ix,yBy k0:k1:…:kr-1It is divided into
Corresponding frequency band is denoted as by r frequency bandFirst prime number N that each divided band is includediIt can be determined by formula (13), wherein i
=0,1 ..., r-1；
With x=0, for y=0,
It can be obtained by formula (11): IB0,0=101000000001000001000100000010 ...
10101010101010101010101010101, by IB0,01 dimension sequence I is converted to by formula (12)0,0=BCut (IB0,0, 5)=
{(10100)2(00000)2(01000)2(00100)2
(01000)2(00010)2(11000)2(00000)2(01111)2…(10101)2(01010)2(10101)2
(01010)2(10101)2, by I0,0Take ratio cut partition as 6 frequency bands of 3:4:5:6:7:7, for ease of description, here with 10 into
Number processed is illustrated, such asN is determined by formula (13)0=6, N1=8 ..., N5=14；
Step 5: the same frequency band of all piecemeals is merged by formula (14), the frequency band BI after being mergedi, by master key
Key is mapped as key by formula (15)i, by keyiAs random number seed, for BIiMiddle element is indexed position scramble, will
BI after scrambleiAs BIiBackup CIi, wherein i=0,1 ..., r-1；
By taking i=0 as an example, due to only one piecemeal of image S, soBy formula
(15) key=131819 can be mapped as key0=363, by key0=363 are used as random number seed, for BI0Middle element position
Scramble can obtain BI0Backup CI0={ 8,0,20,8,4,2 }；
Step 6: noteBi is combined by formula (16)i,u,cii,u,cii-1,uBy key
Key is mapped as keyi,u, by keyi,uK is generated as random number seediA random numberIt is reflected by formula (17)
It penetrates as to bii,u,cii,u,cii-1,uAuthentication information
With i=0, for u=0, since a upper band information is not present as i=0, so being combined by formula (16)
bi0,0=20, ci0,0Key key=131819 can be mapped as key by=80,0=3822911, by key0,0=
3822911 are used as random number seed to can produce k0=3 random numbersBi can be obtained by formula (17)0,0=
20,ci0,0=8 authentication information
Step 7: by bii,u,cii,uOr bii,u,cii,u,cii-1,uWithIt is carried out by formula (18)
Combination is used as a, and b, c are simultaneously right using formula (19)Glug is bright in the prime field that modulus is 127
Day interpolation point, which deposits to obtain, point deposits information fi,u(Sk), k=1,2 ..., N, Sk=Pkmod127；
With i=0, for u=0, by bi0,0=20, ci0,0=8 HesIt presses
Formula (18) is combined as a=20, b=8, c=9 and right using formula (19)It is in modulus
127 prime field point is deposited and can be obtained: f0,0(14)=118, f0,0(50)=60, f0,0(53)=71, f0,0(15)=6, f0,0(22)=
107,f0,0(1)=37, f0,0(26)=89；
Step 8: in conjunction with fi,u(Sk) by formula (20) key key is mapped as keyi,u,kAnd generate 1 bit random i lumber vi,u,k∈
{ 0,1 } as to fi,u(Sk) certification position, by fi,u(Sk) and vi,u,kF is mapped as by formula (21)i,′u(Sk) ∈ 0,1 ...,
255 }, in which: i ∈ { 0,1 ..., r-1 }, k ∈ { 1,2 ..., N }, u ∈ { 0,1 ..., mnNi-1}；
With i=0, for u=0, k=1, in conjunction with f0,0(S1Key key=131819 is mapped as by)=118 by formula (20)
key0,0,1=15686579 and 1 bit random i lumber v of generation0,0,1=(1)2As f0,0(S1The certification position of)=118, by f0,0(S1)
=118 and v0,0,1=(1)2F can be mapped as by formula (21)0′,0(S1)=246, wherein { 0,1 ..., 5 } i ∈, u ∈ 0,1 ...,
64·64·Ni-1},k∈{1,2,…,7}；
Step 9: note EkFor matrix before the corresponding scramble of k-th of distribution shadow image, Ez,kFor EkZ-th of restructuring matrix
Block, Ez,i,kFor Ez,kI-th of divided band, then can by formula (22) rebuild Ez,i,k, E is rebuild by formula (23)z,k, by formula (24) weight
Build Ek, by key and subkeykIt is mapped as by formula (25)Then withIt is random number seed by EkScramble is E
′k；Such as: with z=0, for i=0, k=1, E is rebuild by formula (22)0,0,1=f '0,0,1||f′0,1,1||...||f′0,5,1=
{ 246,239,47,145,246,61 } obtain E by formula (23)0,1, E is obtained by formula (24)1=MSet (E1,z/64,zmod64,Ez,1)=
E0,1, by key=131819 and subkey1=42367649 are mapped as by formula (25)Then pass throughBy E1Scramble is E1', in which:
Step 10: by all E 'k, k=1,2 ..., 7 are used as shadow image and N=7 sub-key (subkeyk,Pk),k
=1,2 ..., 7, which are distributed to corresponding custodian, takes care of, and configures reconfiguration system using the default parameters of system and destroys centre
Parameter.
Restructuring procedure is illustrated with specific example below:
Step 1: the code length allocation table of reconfiguration system configuration is chosenModulus p=
1000000007, distribution share number N=7, Randomized Quantizing thresholding rq=12, r=6 frequency band point deposit thresholding k0=3, k1=4, k2
=5, k3=6, k4=7, k5=7, it is assumed that have vinit=7 (vinit≥k0) a participant participates in restoring, remember that k-th of participant provides
Sub-key and containing close shadow image beWithIt calculatesCorresponding MD5 value compares its MD5 value stored with the 3rd side Fang Gongxin to test
Sub-key legitimacy is demonstrate,proved, statistics sub-key authenticates the participant's quantity passed through, it is assumed here that the MD5 value of all participants is all just
Really, i.e. vsubkey=7；
Step 2: if vsubkey≥k0, then master key key is reconstructed by formula (26), key is mapped as key by formula (4)x,y, will
keyx,yAs random number seed, the random sequence RQ that length is 64 is generatedx,y=(rqi)64,rqi∈ { 1,2 ..., rq }, by it
Secret Image fritter B is used as by formula (5) arrangementx,yCorresponding quantization matrix Qx,y, wherein x=0,1 ..., m-1, y=0,1 ...,
N-1, if otherwise vsubkey< k0, then failure is reconstructed；
With x=0, y=0, vsubkeyFor=7, vsubkey=7 >=k0, it can be obtained by formula (26): key=131819, by formula
(4) key=131819 is mapped as key0,0=363, thus produce the random sequence RQ that length is 640,0=3,12,2,2,
2,12,3,12,10,5,1,8,1,6,8,4,12,1,6,9,5,10,8,6,3,2,11,6,8,12,2,11,7,3,5,7,2,6,
4,2,6,10,6,3,2,10,7,4,7,7,1,6,7,10,8,2,5,10,2, Isosorbide-5-Nitrae, 2,6,10 }, arrange by formula (5) as secret
Image fritterQuantization matrixIf otherwise vsubkey< k0, then
Reconstruct failure；
Step 3: by the key of recovery andIt is mapped as by formula (27)
Then withFor random number seed, contain close shadow image for what the participant that k-th of sub-key certification passes through providedInverted is disorderlyIt is rebuild by formula (28)Upper z-th of reconstruction sub-blockIt presses
Formula (29) is rebuildAll points of participant that k-th of sub-key certification is passed through
Block same frequency band is merged by (30) to be obtainedWherein i=0,1 ..., r-1, k=1,2 ...,
vsubkey, NiIt is first prime number that each divided band is included, is determined by formula (13), by vsubkeyMaximum reconstructed is determined by formula (31)
T, a frequency band of t ∈ { 0,1 ..., r-1 }；
With i=0, for k=1, z=0, by key=131819 andIt is mapped by formula (27)
ForThen withFor random number seed, by the sub- key authentication in kth=1
By participant provide contain close shadow image:
It reverts toDue toOnly one piecemeal, so rebuildingUpper z
=0 reconstruction sub-blockIt can be rebuild by formula (29):Due toOnly
One piecemeal, soWherein i=0,1 ..., 5, k=1,
2 ..., 7, it can determine N by formula (13)0=6, N1=8 ..., N5=14, by vsubkey=7 can maximum reconstructed by formula (31) determination
The t=5 frequency band, i.e., all frequency bands are all rebuild；
Step 4: byReconstruct 1 backup table2 backup tablesRebuild Secret Image frequency bandAnd 1 time and 2 backup tables and reconstruction Secret Image frequency band are authenticatedIts method particularly includes:
4.1st step: initialization AndIt is rightIn each divide memory cellIt obtains point depositing information by formula (32) and formula (33)With 1 bit authentication informationIt will by formula (34)
Key key andIt is mapped as random number seedByRegenerate 1 bit authentication informationIfThen pass through the 1st re-authentication, on the contrary then authentification failure；
Such as: initialization AndIt is right for u=0, k=1 with i=0In divide memory cellIt is obtained by formula (32) and formula (33)WithBy formula (34) by key=131819 andIt is mapped asByRegenerate 1 bit authentication informationBy
InThen pass through the 1st re-authentication；
4.2nd step: current point the depositing information and be by the 1st re-authentication of noteWherein vfirst
To deposit information content by current point of the 1st re-authentication, if vfirst< ki, then ac is seti,u=0 indicates authentification failure, if otherwise
vfirst≥kiIt is aThen reduction obtains by the following step
With i=0, for u=0, current point the depositing information and be by the 1st re-authentication of noteIts
Middle vfirstTo deposit information content by current point of the 1st re-authentication, it is assumed that there are vfirst=7 >=k0It is aReduction obtains a, b, c by the following step:
4.2.1 step: initialization number of attempt try=0；
4.2.2 step: from vfirstIn enumerate kiA point is deposited information conductWhereinTable
Show the current k for participating in restoringiA point of k-th deposited in information, sets try=try+1；
Such as: from vfirstK is enumerated in=70=3 points are deposited information conductWherein
Indicate the current k for participating in restoring0A point of k-th deposited in information, sets try=try+1；
4.2.2 step: byIt is calculated by formula (35)
Such as: byA=20, b=8, c=9 are calculated by formula (35)；
4.2.3 step: as i=0 orWhen, it is obtained by formula (36) reductionOtherwise it is obtained by formula (36) and formula (37) reductionSuch as: due to i=0, can restore to obtain by formula (36):
4.2.4 step: key is mapped as random number seed key by formula (38)i,uGenerate kiA random number
And it is mapped to obtain the 2nd re-authentication information by formula (39)By its withComparison, ifThen
By the 2nd re-authentication and ac is seti,u=1, if otherwiseThen turn 4.2.2 step, ifDo not recognize again by the 2nd then
It demonstrate,proves and ac is seti,u=0,For from vfirstIn enumerate kiA point of stored number of combinations；
Such as: key=131819 is mapped as random number seed key by formula (38)0,0=3822911 generate k0=3 with
Machine numberAnd it is mapped to obtain the 2nd re-authentication information by formula (39)By its withComparison, due toThen pass through the 2nd re-authentication and ac is set0,0=1, it is on the contrary
IfThen turn 4.2.2 step, ifDo not pass through the 2nd re-authentication then and ac is set0,0=0；
4.3rd step: output And
By taking i=0 as an example, output And
Step 5: according toIt willWithIt is fused to finally back upIts method particularly includes:
5.1st step: initializationWork as i=0, when 1 ..., t-1, is merged by formula (40), work as i=t
When, it is not present at this timeTherefore it directly enables
With i=0, for u=0, initializationDue to ac0,0=1, ac1,0=1 can by formula (40) fusion
It obtainsAs i=5, it is not present at this timeTherefore it directly enables
5.2nd step: key is mapped as key by formula (15)i, with keyiFor random number seed, by dividing key in deposit systemiIt is right
The disorder method answered willInverted is random, to finally be backed up
By taking i=0 as an example, key=131819 is mapped as key by formula (15)0=363, with key0=363 be random several
Son, by dividing key in deposit system0=363 corresponding disorder methods willInverted is random, from
And it is finally backed up
Step 6: rightIn each bii,uIf aci,u=1 does not modify its value then, otherwise using final
Ci in backupi,uReplace bii,u, wherein i=0,1 ..., t, u=0,1 ..., mnNi-1；
It is right for u=0 with i=0In bi0,0, due to ac0,0=1 does not modify its value then, otherwise
Use ci0,0Replace bi0,0；
Step 7: by Secret Image frequency bandRebuild Secret Image S=(si,j)h×w, method particularly includes:
7.1st step: willWith NiA element is divided into segment by formula (41) for unit
Sequence B Iz,i, i=0,1 ..., r-1, right back-pushed-type (42) reconstruction IBz, wherein z=0,1 ..., mn-1；
It, will for z=0 with i=0With N0=6 elements are that unit presses formula
(41) it is divided into segment sequence B I0,0={ 20,0,8,4,8,2 }, right back-pushed-type (42) are rebuild:
IB0=20,0,8,4,8,2,24,0,15,22,31,25,31,23,28,31,20,0,15,19,27,0,23,
29,30,16,7,20,1,31,0,16,3,25,30,31,15,7,27,29,28,30,30,30,30,30,30,31,0,29,
27,23,14,29,27,13,22,27,10,21,10,21,10,21}；
7.2nd step: by all IBz, z=0,1 ..., mn-1 is converted to FB ' by formula (43)x′,y=(fbi′,′j)8×8, press
Formula (45) obtains FB 'x,y=(fbi′,j)8×8, FB is obtained by formula (46)x,y=(fbi,j)8×8；Such as: due to z=0, so IB0It presses
Formula (43) is converted to FB '0′,0, FB ' is converted to by formula (45)0,0, FB is converted to by formula (46)0,0, in which:
7.3rd step: by formula (47) to FBx,yIt carries out inverse dct transform and obtains Bx,y=(bi,j)8×8If after frequency-domain transform, as
Plain value is overflowed, then takes 255 when pixel is greater than 255, take 0 when pixel is less than 0；
7.4th step: by all piecemeal Bx,y, x=0,1 ..., m-1, y=0,1 ..., n-1 rebuild secret figure by formula (48)
As S=(si,j)h×wAt this time due to only one piecemeal, so rebuilding Secret Image S=(s by formula (48)i,j)8×8=B0,0。
Fig. 4~Figure 10 is embodiment, using Fig. 3 as Secret Image, by Fig. 1 point deposit that process obtains containing close shadow image；Figure
11 be embodiment, recovers Secret Image by Fig. 4~Fig. 6 by Fig. 2 reconstruct process, the PSNR relative to Fig. 3 is 27.31dB；Figure
12 be embodiment, Secret Image is recovered from Fig. 4~Fig. 7 by Fig. 2 reconstruct process, the PSNR relative to Fig. 3 is 29.98dB；
Figure 13 is embodiment, reconstructs process, the Secret Image recovered from Fig. 4~Fig. 8 by Fig. 2, the PSNR relative to Fig. 3 is
34.05dB；Figure 14 is embodiment, reconstructs process, the Secret Image recovered from Fig. 4~Fig. 9, the PSNR relative to Fig. 3 by Fig. 2
For 37.02dB；Figure 15 is embodiment, reconstructs process, the Secret Image recovered from Fig. 4~Figure 10, relative to Fig. 3's by Fig. 2
PSNR is 43.36dB；Figure 18 is the image after Fig. 9 is attacked by Figure 16, and Figure 19 is the image after Figure 10 is attacked by Figure 17, figure
20 be that process, the Secret Image recovered from Fig. 4~Fig. 8, Figure 18 and Figure 19 are reconstructed by Fig. 2, and the PSNR relative to Fig. 3 is
36.03dB。
Claims (10)
1. a kind of progressive secret image sharing method of prime field multi-threshold, it is characterised in that the following steps are included:
Step 1: default parameters is deposited by secret holder configuration point, comprising: 320 2 system code length allocation table M=(mi,j)8×8, it is
System modulus Big prime p, distribution share number N, N ∈ { 1,2 ..., p-1 }, integer Randomized Quantizing thresholding rq > 0 and 0 frequency band of r >
Divide and deposits thresholding ki∈ { 2,3 ..., N }, i=0,1 ..., r-1 meet the factor that frequency band is incremented by and frequency band aggregate-value is 64, will be secret
Image S=(si,j)h×wIt is divided into nonoverlapping 8 × 8 fritter Bx,y, x=0,1 ..., m-1, y=0,1 ..., n-1, wherein h, w are
Positive integer, m=h/8, n=w/8 and mmod8=0, nmod8=0；
Step 2: N number of random number P is generated by secret holder1,P2,…,PN∈ 0,1 ..., and p-1 } it is used as each shadow image pair
The random participation value and P answered1mod127,P2mod127,…,PNMod127 two neither etc., by key key ∈ { 0,1 ..., p-1 }
Point being saved as N number of point deposits key subkey1,subkey2,…,subkeyN, and by sub-key (subkeyk,Pk), k=1,2 ..., N
Corresponding MD5 value is published to the 3rd side Fang Gongxin to prevent participant from practising fraud, and generates the random sequence that length is 64 by key key
RQx,y=(rqi)64,rqi∈ { 1,2 ..., rq }, is rearranged as Bx,yCorresponding Randomized Quantizing matrix Qx,y, wherein x
=0,1 ..., m-1, y=0,1 ..., n-1；Rq is integer Randomized Quantizing thresholding；
Step 3: will each not overlap partition Bx,y=(bi,j)8×8It is transformed to area block FBx,y=(fbi,j)8×8, pass through Qx,y=
(qi,j)8×8By FBx,yIt is quantified as FB 'x,y=(fb 'i,j)8×8And to FB 'x,yMiddle matrix element, which carries out integer, to be indicated and 2 systems
Storage conversion is used as FB "x,y；
Step 4: by all FB "x,yBe converted to 2 system bit bit string IBx,y, by IBx,yBe converted to 1 dimension sequence Ix,y, by Ix,yWith
k0:k1:…:kr-1It is divided into r frequency band for the ration of division, remembers that corresponding frequency band isThenThe element number scale for being included is
Ni, i=0,1 ..., r-1；
Step 5: all piecemeal same frequency bands are merged, the frequency band BI after being mergedi, to BIiIn element be indexed position
Scramble, as frequency band BIiBackup CIi, wherein i=0,1 ..., r-1；
Step 6: noteBi is generated by key keyi,u,cii,u,cii-1,uAuthentication informationWherein, u=0,1 ..., mnNi-1；mn·NiFor BIiLength；
Step 7: by bii,u,cii,uOr bii,u,cii,u,cii-1,uWithCombination is used as integer a, b,
C is then rightLagrange's interpolation, which point deposits to obtain, in prime field point deposits information fi,u(Sk),k
=1,2 ..., N, Sk=Pkmod127；
Step 8: 1 bit random i lumber v is generated by key keyi,u,k∈ { 0,1 } is used as fi,u(Sk) certification position, by fi,u(Sk) and
vi,u,kIt is mapped as f 'i,u(Sk) ∈ { 0,1 ..., 255 }, in which: i ∈ { 0,1 ..., r-1 }, k ∈ { 1,2 ..., N }, u ∈ 0,
1,…,mn·Ni-1}；
Step 9: note EkFor matrix before the corresponding scramble of k-th of distribution shadow image, Ez,kFor EkZ-th of restructuring matrix block,
Ez,i,kFor Ez,kI-th of divided band, first reconstruction Ez,i,k, then rebuild Ez,k, finally rebuild Ek, then with key key and
subkeykBy EkScramble is E 'k；
Step 10: by all E 'k, k=1,2 ..., N is as shadow image and N number of sub-key (subkeyk,Pk), k=1,
2 ..., N are distributed to corresponding custodian and take care of, and configure reconfiguration system using the default parameters of system and destroy intermediate ginseng
Number.
2. a kind of progressive secret image sharing method of prime field multi-threshold as described in claim 1, it is characterised in that: the 1st
0 frequency band of r > point deposits thresholding k in stepi∈ { 2,3 ..., N }, i=0,1 ..., r-1 meets that frequency band is incremented by and frequency band aggregate-value is
The specific constrained procedure of 64 factor is formula (1) and formula (2):
N number of point, which is saved as, by key ∈ { 0,1 ..., p-1 } points in step 2 deposits key subkey1,subkey2,…,subkeyN's
Specific method is using key as secret value s, by P1,P2,…,PNIt can be obtained N number of point respectively as k substitution formula (3) and deposit key
subkey1,subkey2,…,subkeyN:
In formula (3), random numberIt is that random number seed maps to obtain by key；
Key generates the random sequence RQ that length is 64 in step 2x,y=(rqi)64,rqiThe specific method of ∈ { 1,2 ..., rq }
For key is mapped as key by formula (4)x,y, by keyx,yAs random number seed, the random sequence RQ that length is 64 is generatedx,y=
(rqi)64,rqi∈{1,2,…,rq}
It is rearranged in step 2 as Bx,yCorresponding Randomized Quantizing matrix Qx,ySpecific method be formula (5)
Qx,y=MScanzigzag(Inc(RQx,y),8,8) (5)；
In formula (5), Inc () is sequence increasing function, MScanzigzag() is matrix zigzag scanning function, is square by sequence scanning
Battle array, the 1st parameter of function are sequence to be scanned, and the 2nd and the 3rd parameter is matrix dimension.
3. a kind of progressive secret image sharing method of prime field multi-threshold as described in claim 1, it is characterised in that: the 3rd
By the not overlap partition B of each division in stepx,y=(bi,j)8×8It is transformed to area block FBx,y=(fbs,t)8×8Specific method be
Formula (6):
FBx,y=D2DCT (Bx,y) (6)
In formula (6), function D2DCT () is 2 dimension discrete cosine transforms, shown in calculating formula such as formula (7):
In step 3 by FBx,yRandomized Quantizing is FB 'x,y=(fb 'i,j)8×8Specific method be formula (8):
fb′i,j=fbi,j/qi,j, i, j=0,1 ..., 7 (8)
Wherein, qi,jIt is Randomized Quantizing matrix Qx,yElement in the position i-th, j；
In step 3 to FB 'x,yMiddle element, which carries out integer, to be indicated to be converted to FB " with 2 system storagesx,ySpecific method be formula
(9):
In formula (9),WithCorrespond to code length allocation table M=(mi,j)8×8Element mi,jCan indicate minimum value and
Maximum value, corresponding distribution principle are determined by formula (10):
In step 4 by all FB "x,yBe converted to 2 system bit bit string IBx,ySpecific method be formula (11):
IBx,y=BScanzigzag(FB″x,y) (11)
In formula (11), function BScanzigzag() is bit bit string zigzag scanning function, and the function of execution is by input matrix
Element is attached by its 2 system storage form with zigzag scanning sequency；
By IB in step 4x,yBe converted to 1 dimension sequence Ix,ySpecific method be formula (12):
Ix,y=BCut (IBx,y,5) (12)
In formula (12), function BCut () is bit bit string segmentation function, wherein the 1st parameter corresponds to bit bit string, the 2nd ginseng
Number is the segmentation unit of bit bit string, and the function that formula (12) executes is by BCut (IBx,y, 5) and by bit bit string IBx,yWith 5
Bit bit string is that separate units are converted to 1 dimension sequence Ix,y；
First prime number N that each divided band is included in step 4i, i=0,1 ..., r-1 can be determined by formula (13):
4. a kind of progressive secret image sharing method of prime field multi-threshold as described in claim 1, it is characterised in that: the 5th
The specific method for merging all piecemeal same frequency bands in step is formula (14):
In formula (14), " | | " it is sequence connector, i.e., by the frequency band of all piecemealsIt links together and constitutes sequence as merging
Frequency band BI afterwardsi, BIiIt in total include mnN in sequenceiA element；
To BI in step 5iIn element to be indexed the specific method of position scramble be that key is mapped as key by formula (15)i, will
keyiAs random number seed, for BIiMiddle element is indexed position scramble:
Bi is generated by key in step 6i,u,cii,u,cii-1,uAuthentication informationSpecific method
To combine bi by formula (16)i,u,cii,u,cii-1,uKey key is mapped as keyi,u, by keyi,uK is generated as random number seedi
A random numberMapping is carried out as to bi by formula (17)i,u,cii,u,cii-1,uAuthentication information
In formula (16), as i=0, a upper frequency band CI is not present at this timei-1；As u >=size (CIi-1) when, indicate CIi-1Middle member
Element, which has stored, to be finished, and backup element ci is not presenti-1,u, size (CIi-1) indicate CIi-1Number of elements；
5. a kind of progressive secret image sharing method of prime field multi-threshold as described in claim 1, it is characterised in that: the 7th
By bi in stepi,u,cii,uOr bii,u,cii,u,cii-1,uWithCombination is used as integer a, and b's, c is specific
Method is formula (18):
It is right in step 7The specific method that Lagrange's interpolation point is deposited in prime field is formula
(19):
In formula (19), gp=127, k0∈ { 2,3 ..., N }, if k0When=2, storage bi is only needed at this time0,u,ci0,u, while being also only capable of
Generate 2 authentication informationsTherefore directly a and b point deposit；
1 bit random i lumber v is generated by key key in step 8i,u,k∈ { 0,1 } is used as fi,u(Sk) certification position specific method
To generate random number seed key by formula (20)i,u,k, by keyi,u,kGenerate 1 bit authentication information vi,u,k:
keyi,u,k=(fi,u(Sk)×key+fi,u(Sk)+key+i+u+i×u)modp (20)
Step 8 is by fi,u(Sk) and vi,u,kIt is mapped as f 'i,u(Sk) ∈ { 0,1 ..., 255 } specific method be formula (21):
f′i,u(Sk)=27×vi,u,k+fi,u(Sk) (21)；
E is rebuild in step 9z,i,kSpecific method be first by formula (22) rebuild Ez,i,k, right back-pushed-type (23) reconstruction Ez,k, finally press
Formula (24) rebuilds Ek:
Ez,k=MScanzigzag(Ez,0,k||Ez,1,k||…||Ez,r-1,k,8,8) (23)
In formula (23), MScanzigzag() be matrix zigzag scanning function, the 1st parameter of function be sequence to be scanned, the 2nd
It is matrix dimension with the 3rd parameter；Ek=MSet (Ek,z/n,zmodn,Ez,k), z=0,1 ..., mn-1 (24)
In formula (24), function MSet () is that function is arranged in matrix-block, and the 1st parameter is to place the matrix of matrix fritter, the 2nd, 3
Parameter corresponds to matrix-block coordinate, and the 4th parameter corresponds to the matrix fritter to be placed；
Step 9 is with key key and subkeykBy EkScramble is E 'kSpecific method be by formula (25) generate random keyThen byBy EkScramble is E 'k:
6. a kind of progressive Secret Image reconstructing method of prime field multi-threshold, it is characterised in that the following steps are included:
Step 1: remember the reconstruct default parameters of configuration, comprising: 320 2 system code length allocation tables are M=(mi,j)8×8, divide and deposit modulus
P, distribution share number are N, and N ∈ { 1,2 ..., p-1 }, integer Randomized Quantizing thresholding rq > 0 and 0 frequency band of r > point deposit thresholding and be
ki∈ { 2,3 ..., N }, i=0,1 ..., r-1, it is assumed that have vinit(vinit≥k0) a participant participates in restoring, remember k-th of participation
Person provide sub-key and shadow image be respectivelyWithIt calculatesCorresponding MD5 value compares its MD5 value stored with the 3rd side Fang Gongxin to come
Sub-key legitimacy is verified, statistics sub-key authenticates the participant's quantity v passed throughsubkey；
Step 2: if vsubkey≥k0, then master key key is reconstructed, the random sequence RQ that length is 64 is generated by keyx,y=(rqi)64,
rqi∈ { 1,2 ..., rq }, is rearranged as Bx,yCorresponding Randomized Quantizing matrix Qx,y, wherein x=0,1 ..., m-1, y
=0,1 ..., n-1, if otherwise vsubkey< k0, then failure is reconstructed；
Step 3: by vsubkeyDetermination can maximum reconstructed t, t ∈ { 0,1 ..., r-1 } a frequency band, by the key of recovery andIt is mapped asThe participant that k-th of sub-key certification is passed through is containing close shadow
ImageInverted is disorderlyIt rebuildsUpper z-th of reconstruction sub-blockByIt rebuilds all frequency bands in z-th of piecemeal and divides setK-th of son is close
All piecemeal same frequency bands of participant that key certification passes through merge to obtainWherein i=0,
1 ..., r-1, k=1,2 ..., vsubkey, NiThe first prime number for including by each divided band；ForR frequency band of division；mn·NiForLength；
Step 4: byReconstruct 1 time and 2 backup tablesRebuild Secret Image frequency bandAnd 1 time and 2 backup tables and reconstruction Secret Image frequency band are authenticated
Step 5: according toIt willWithIt is fused to finally back up
Step 6: rightIn each bii,uIf aci,u=1 does not modify its value then, otherwise using final backup
In cii,uReplace bii,u, wherein i=0,1 ..., t, u=0,1 ..., mnNi-1；mn·NiFor BIiLength；
Step 7: by Secret Image frequency bandRebuild Secret Image S=(si,j)h×w。
7. a kind of progressive Secret Image reconstructing method of prime field multi-threshold as claimed in claim 6, it is characterised in that: the 2nd
The specific method that master key key is reconstructed in step is formula (26):
In formula (26),I-th, the i=1,2 that pass through are authenticated for sub-key ..., vsubkeyA participant mentions
The sub-key of confession,ForMould p multiplicative inverse；For vsubkeyA sub-key is recognized
Card passes through the random participation value of i-th of participant in participant,For vsubkeyA sub- key authentication passes through in participant
J-th of participant participation value at random；
The random sequence RQ that length is 64 is generated by key key in step 2x,y=(rqi)64,rqiThe tool of ∈ { 1,2 ..., rq }
Body method is that key is mapped as key by formula (4)x,y, by keyx,yAs random number seed, the random sequence that length is 64 is generated
RQx,y=(rqi)64,rqi∈{1,2,…,rq}；
It is rearranged in step 2 as Bx,yRandomized Quantizing matrix Qx,ySpecific method be formula (5):
Qx,y=MScanzigzag(Inc(RQx,y),8,8) (5)；
In formula (5), MScanzigzag() is matrix zigzag scanning function, is matrix by sequence scanning, and the 1st parameter of function is
Sequence to be scanned, the 2nd and the 3rd parameter are matrix dimension；
In step 3 by vsubkeyDetermination can maximum reconstructed t, the method for a frequency band of t ∈ { 0,1 ..., r-1 } is formula (31):
In step 3 by key andIt is mapped asMethod be formula (27):
It rebuilds in step 3Upper z-th of sub-blockMethod be formula (28):
In formula (28), function MGet () is that matrix fritter obtains function, and the 1st parameter of function is the matrix where matrix fritter,
2nd and the 3rd parameter corresponds to the coordinate of matrix-block, and the 4th and the 5th parameter correspond to matrix-block dimension, wherein x=0,
1 ..., m-1, y=0,1 ..., n-1；
In step 3 byIt rebuildsSpecific method be formula (29):
In formula (29), function SScanzigzag() is sequence zigzag scanning function, and it is 1 dimension that the function of execution, which is by matrix-scanning,
Sequence；
Merge in step 3 and obtainsSpecific method be formula (30):
First prime number N that each divided band is included in step 3iIt is determined by formula (13):
8. a kind of progressive Secret Image reconstructing method of prime field multi-threshold as claimed in claim 6, it is characterised in that: the 4th
In step byReconstruct 1 time and 2 backup tablesmn·NiForLength；Rebuild Secret Image frequency bandAnd 1 time, 2 backup tables and reconstruction Secret Image frequency band are authenticatedMethod particularly includes:
4.1st step: initialization AndIt is rightIn each divide memory cellIt obtains point depositing information by formula (32) and formula (33)With 1 bit authentication informationIt will by formula (34)
Key andIt is mapped as random number seedByRegenerate 1 bit authentication informationIfThen pass through the 1st re-authentication, on the contrary then authentification failure；
4.2nd step: current point the depositing information and be by the 1st re-authentication of noteWherein vfirstTo pass through
Current point of 1st re-authentication deposits information content, if vfirst< ki, then ac is seti,uOtherwise=0 indicates authentification failure, if vfirst≥ki
It is aThen reduction obtains by the following step
4.2.1 step: initialization number of attempt try=0；
4.2.2 step: from vfirstIn enumerate kiA point is deposited information conductWhereinExpression is worked as
The preceding k for participating in restoringiA point of k-th deposited in information, sets try=try+1；
4.2.2 step: byIt is calculated by formula (35)
In formula (35),Indicate the k for participating in restoringiA point of j-th deposited in information corresponding random participation containing close shadow image
Value,It corresponds toMultiplicative inverse under mould gp, wherein gp is equal to 127；It is random participation valueThe later result of mould 127；L=1 ... ki；J=1 ... ki；
4.2.3 step: as i=0 orWhen, it is obtained by formula (36) and formula (37) reductionOtherwise it is obtained by formula (36) and formula (37) reduction
4.2.4 step: key is mapped as random number seed key by formula (38)i,uGenerate kiA random numberAnd it presses
Formula (39) is mapped to obtain the 2nd re-authentication informationBy its withComparison, ifThen pass through the 2nd re-authentication and ac is seti,u=1,
If otherwiseThen turn 4.2.2 step, ifDo not pass through the 2nd re-authentication then and ac is seti,u=0, whereinFor
From vfirstIn enumerate kiA point of stored number of combinations；
4.3rd step: output And
9. a kind of progressive Secret Image reconstructing method of prime field multi-threshold as claimed in claim 6, it is characterised in that: the 5th
Basis in stepIt willWithIt is fused to finally back upMethod particularly includes:
5.1st step: initializationWork as i=0, when 1 ..., t-1, is merged by formula (40), as i=t, this
When be not presentTherefore it directly enables
5.2nd step: key is mapped as key by formula (15)i, with keyiFor random number seed, by dividing key in deposit systemiIt is corresponding
Disorder method willInverted is random, to finally be backed up
10. a kind of progressive Secret Image reconstructing method of prime field multi-threshold as claimed in claim 6, it is characterised in that: the 7th
By Secret Image frequency band in stepRebuild Secret Image S=(si,j)h×wMethod particularly includes:
7.1st step: willWith NiA element is divided into segment sequence by formula (41) for unit
BIz,i, i=0,1 ..., r-1, right back-pushed-type (42) reconstruction IBz, wherein z=0,1 ..., mn-1；
IBz=BIz,0||BIz,1||…||BIz,r-1 (42)
Wherein, formula (41) is used to for i-th of frequency band being located at whole N of z-th of piecemealiA element is as division segment sequence B Iz,i；
Formula (42) is for merging the r whole frequency bands of z-th of piecemeal as sequence IBz；
7.2nd step: by all IBz, z=0,1 ..., mn-1 is converted to FB " by formula (43)x,y=(fb "i,j)8×8, by formula (45)
Obtain FB 'x,y=(fb 'i,j)8×8, FB is obtained by formula (46)x,y=(fbi,j)8×8；
In formula (43), function SBin () is 2 system bit string transfer function of sequence, and the 1st parameter of SBin () is to be transformed one-dimensional
Sequence, the 2nd parameter are 2 system digits of sequential element conversion, function BMScanzigzag() is by bit bit string by a zigzag
Scanning sequency and code length allocation table are converted to the matrix fritter big with code length allocation table etc., BMScanzigzag(), the 1st parameter was
Bit bit string, corresponding the 2nd parameter is code length allocation table, and the 3rd parameter corresponds to marker bit, is rebuild in fritter for marking
The coordinate position of non-reconstruction band, formula (43) is middle to rebuild fritter FB "x,yIn the corresponding element in the position mark and its member later
Plain fb "i,jAll it is set to
fbi,j=fb 'i,j×qi,j, i, j=0,1 ..., 7 (46)
In formula (45) and formula (46),Corresponding to code length allocation table is M=(mi,j)8×8What corresponding position element can indicate
Minimum value；qi,jCorrespond to quantization table Qx,yIn element；
7.3rd step: by formula (47) to FBx,yIt carries out inverse dct transform and obtains Bx,y=(bs,t)8×8If after frequency-domain transform, pixel value
It overflows, then takes 255 when pixel is greater than 255, take 0 when pixel is less than 0；
7.4th step: by all piecemeal Bx,y, x=0,1 ..., m-1, y=0,1 ..., n-1 rebuild Secret Image S=by formula (48)
(si,j)h×w；
S=MSet (S, z/n, zmodn, Bx,y), z=0,1 ..., mn-1 (48)
In formula (48), function MSet () is that function is arranged in matrix-block, and the 1st parameter is to place the matrix of matrix fritter, the 2nd, 3
Parameter corresponds to matrix-block coordinate, and the 4th parameter corresponds to the matrix fritter to be placed；
H, w are positive integer.
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