Yong Zhang1,2,*, Bian Yang3, and Xia-Mu Niu1,2,3 1 Shenzhen Graduate School at Harbin Institute of Technology
Shenzhen 518055, P.R. China xiamu.niu@isec.hitsz.edu.cn
2 Shenzhen Innovation International
Shenzhen 518057, P.R. China
zhangyong076@gmail.com, xiamu.niu@hit.edu.cn
3 School of Computer Science and Technology at Harbin Institute of Technology
Harbin 150001, P.R.China
bian@ict.hit.edu.cn, xiamu.niu@hit.edu.cn
Received 5 May 2006; Revised 12 June 2006 ; Accepted 15 June 2006
Abstract. A reversible watermarking scheme for relational databases is proposed in this paper to achieve lossless and exact authentication of relational databases via expansion on data error histogram. This reversi-ble watermarking scheme possesses the ability of perfect restoration of the original attribute data from the un-tampered watermarked relational databases, thus guaranteeing a “clear and exact” un-tampered-or-not authenti-cation without worry about causing any permanent distortion to the database. In this scenario, only the secret key owner possesses the capability to exactly restore the database’s original state. Simulations demonstrate the scheme’s security and feasibility for low-correlated data in typical databases.
Keywords: reversible watermark, digital watermarking, relational databases
1 Introduction
Security is of increasing concern with databases for database’s high added values and extensive installation in modern information systems. In addition to encryption, watermarking techniques is practically proven as another possible solution to enhance databases’ content security especially for copyright protection [1-6] and data tam-pering detection [7]. Unlike encryption or hash description, typical watermarking techniques modify original data as a modulation of the watermark information, and inevitably cause permanent distortion to the original data, and therefore cannot meet the integrity requirement of the data in some applications. This underlying defect can be relieved by reversible watermarking techniques [8-22] by their reversibility in both robust watermarking [8,9] and fragile watermarking [10-18]. The direct beneficiary from this reversibility is those applications requiring zero permanent distortions such as medical imaging, military imaging, forensics of documents and art work au-thentication. On the other hand, the perfect restoring ability realizes watermarking based lossless authentication which accounts for the major part of earlier algorithms [8-11]. In recent years, researches on reversible water-marking center on increasing embedding capacity to meet requirements of large volume data embedding [12-18]. In the meanwhile, its applications reach to non-raster image fields [20-22]. However so far, almost all the re-versible watermarking schemes exploit high correlation among neighboring data samples, and therefore face difficulty in the application of relational databases which usually contains only low-correlated, or even in the extreme case, completely random generated data.
Some schemes were proposed [1-6] to watermark relational databases for copyright protection, which are based on the facts that the relational data have enough redundancy and can tolerate some unnoticeable degrada-tion in data precision caused by watermark embedding. The targets of the papers [1-6] are to verify the copyright of the relational data and the ownership of the owner, and the fragile watermarking scheme algorithm proposed in [7] is to detect and localize the tampered area of relational data,which however, inevitably introduces permanent distortion to the cover data.
Above relevant works all assume that minor distortions caused to some attribute data can be tolerated to some specified precision grade. However some applications in which relational data are involved cannot tolerate any permanent distortions and data’s integrity needs to be authenticated. To meet this requirement, we propose a reversible watermarking technique for lossless authentication of relational databases. Considering the typical case of randomly generated data sequence with even distribution as the host data, the scheme takes advantage of the uneven distribution of the error of two even-distributed variables and gains embedding capacity from reversible histogram expansion [15,17,18]. The rest of the paper is organized as follows: section 2 analyzes the distribution of errors between randomly generated even-distributed data as a simulation of practical numerical attributes in a database; section 3 presents the proposed scheme of reversible watermarking for relational databases; section 4 presents analysis and simulations, and section 5 concludes the paper.
2 Distribution of Error of Two Even-Distributed Variables
Considering the low correlation between neighboring data of a typical database, we assume an extreme case – randomly generated real values – as the host media for reversible watermarking. Since so far most of reversible watermarking algorithms are based on high correlation among neighboring pixels, these algorithms are hard to embed a large capacity of watermark bits in the low-correlated or independent values in a typical database. In this paper, we investigate the distribution of error between two even-distributed variables and consider the possibility of reversibly watermarking these errors and their corresponding original data. Now we analyze the distribution of the error between two even-distributed variables as follows:
Assume X and Y are two independent variables with even distribution over [a,b] (a,b
∈
R and a<b), and the probability density function of error Z=X-Y is( ) ( ) 2 2 , 0 , 0 ( ) 0 , Z z a b a b z b a b a z z b a f z b a others − + − ≤ < − − − ≤ < − = − . (1)
with the distribution shown in Fig.1.
From figure 1 it is obvious that the errors take on an uneven distribution centering near zero, reminding us of the histogram expansion technique [15] to exploit the uneven distribution for a reversible watermark embedding.
Fig. 1. PDF of error of two even-distributed variables a and b
3 The Proposed Scheme
Other than the case of histogram expansion used for images in the greyscale range [0,255], the real values have an uneven distribution over a variable range of [a-b,b-a]. To simplify the implementation of histogram expansion in this real value case, we extract just part of each original real value (called partial real value in the follows) instead of the whole one, and then retrieve the digits resident in the main value order of each error generated from two neighboring original real values to form the final histogram. Details are presented as follows.
3.1 Partial Error Generation
Let DNiD(N-1)iD(N-2)i…DMi*D(M-1)i…D2iD1i (1≤≤≤≤i ≤≤≤≤ L，N
≥≥≥≥
M>0，L is the length of original real value sequence,N is the total digit number of a real value, and L,N,M are all positive integers) be an original real value sequence. We can choose Dji as the initial digit to obtain a partial value DjiD(j-1）iD(j-2）i…DMi* D(M-1)i…D2iD1i for partial
error calculation:
di = djid(j-1)id(j-2)i…dMi* d(M-1)i…d2id1i =Dj(i+1)D(j-1)(i+1)D(j-2)(i+1)…DM(i+1)*D (M-1)(i+1)…D2(i+1)D1(i+1) – DjiD(j-1)iD(j-2)i…DMi*D(M-1)i…D2iD1i .
(2)
where 1≤ j ≤N and ‘*’ is a decimal point. Note that here practical applications’ requirement in precision can be adjusted with j when performing the histogram expansion on all partial errors: the smaller is j, the smaller will be the watermarking distortion and in this way the watermark embedding distortion can be well controlled.
The capacity in the proposed scheme is gained from the partial errors between two neighbouring original par-tial values. Assume an arbitrary pair of neighbouring original parpar-tial values xi, xi+1(xi<xi+1), the errors can be
cal-culated as
di = xi+1– xi . (3)
Now find those errors with nonzero initial digits (dji≠0) and extract them to form a histogram. It is easy to see
that dji are resident in the main value order of each error, i.e., errors with nonzero digits in the jth value order
account for definitely major part of all errors (around 80% in experiments). In this way the variable range of [a-b,b-a] can be simplified to a fixed integer scale range from 1 to 9 which forms the final histogram bins, i.e., dji =
1,2,…,9. The histogram expansion technique can be then employed on these nonzero initial digits for reversibly embedding and leave those digits lower than j (from d(j-1）i to d1i) unchanged. Let di’ be the watermarked version
of di, the difference between the two is limited to the initial digits dji, and therefore di’ can be expressed as
di’ = dji’d(j-1）id(j-2）i…dMi*d(M-1)i…d2id1i . (4)
where dji’ is the watermarked version of dji, and ‘*’ is a decimal point.
Now we consider using the inverse integer Haar wavelet tranform to derive watermarked database values x'i
and x'i+1 from the watermark information carrier dji’. Removing the decimal point from xi+1, xi and d’ by
multipli-cation with 10M-1 to obtain integers xIi, xIi+1 and dI’. Define the median value of xIi and xIi+1as
xIm=
(xIi+xIi+1)/2
. (5)Let d’ be the watermarked version of d, the watermarked integers can be obtained by the inverse integer Haar wavelet:
xI'i = xIm–
dI'/2
. (6)xI'i+1 = xIm+
(dI'+1)/2
. (7)and after division by 10M-1 we can obtain the watermarked database partial values x'i and x'i+1.
It is obvious the original partial value pair xi, xi+1 and their watermarked version x'i and x'i+1 form a lossless
transform by integer Haar wavelet. Based on this lossless transform, the watermark information can be losslessly embedded into the partial values of the cover data.
3.2 Expansion on Partial Error Histogram
The values contained in the database attributes for embedding are assumed to be even-distributed numerical data with specified data precision (controlled by selection of j for the initial digit Dji) and our scheme embeds
water-mark on the errors’ initial digits dji, whose distribution looks almost same as the uneven distribution in Fig.1.
This is because the nonzero ones account for a major part of all dji and therefore watermarking on nonzero dji is
equivalent to watermarking most of original partial values in the database.
The reversible watermark embedding process is illustrated in Fig.2 and described as follows:
Step 1: Set j of the initial digit Dji according to the precision requirements of practical applications and extract
all nonzero errors’ initial digits dji to form a histogram H(dji) with bins from 1 to 9 representing dji = 1,2,…,9;
Step2: Use the histogram expansion techniques to reversibly watermark the selected nonzero errors’ initial digits dji: find a bin P out of 1~8 with peak absolute amplitude (usually when dji=1 in this case) and right shift by
1 unit all amplitudes in bin range
≥
P, i.e., to add 1 to all dji with absolute value≥
P. Now the original bin P hasbeen emptied and watermark bits can be modulated into P and P+1 as illustrated in Fig.2 (detailed description in [15,17,18]). Note that in this case, only the initial digits dji have been modified and other digits unchanged. The
Fig. 2. Histogram expansion based reversible watermarking on the initial digits dji
total capacity provided by histogram expansion is h1= h’1+ h’2 bits which is the total number of those errors with
dji =1 in the case of Fig.2;
Step 3: Record the overhead information to distinguish the original digits dji =9 from those newly generated
from the original dji =8. Obviously, it needs a binary sequence with a length of h’9= h8+ h9 in the case of Fig.2
(“0” to tag those original ones and “1” the newly generated ones);
Step 4: Embed the watermark bits together with the overhead bits into the errors by histogram expansion de-scribed in Step3. Perform the inverse Haar wavelet transform and obtain the watermarked database attribute. It is easy to see the final capacity of this reversible watermarking scheme is around (h1– h8 – h9) bits.
The watermark extraction is an inverse process of the above embedding process.
3.3 Over- / Underflow Prevention
Note that when an initial digit Dji of the original partial value xi equals 1 or 9, the inverse integer Haar wavelet
over the watermarked errors may cause the resultant partial value x'i and x'i+1 to over-and underflow, i.e., drive x'i
or x'i+1
≥
10j-M+1 or≤
10j-M and thus fail to guarantee the perfect restoration of the watermark any more. In view ofthe fixed watermarking distortion of one unit on the initial digit dji, the maximum absolute distortion caused by
watermarking is 10 j-M and the maximum absolute distortion caused to x'i and x'i+1 is less than 0.5×10 j-M+10 –M+1.
Thus we limit the watermarking range of partial value xi and xi+1 to [0.5×10 j-M
+10 –M+1,10 – 0.5×10 j-M –10 –M+1] and distinguish the original partial values from the over-and-underflowed ones in (0, 0.5×10 j-M+10 –M+1) and (10 – 0.5×10 j-M –10 –M+1,10) using overhead bits. Obviously, with the decrease of j, this overhead with length around 2× (L–1)×10j–N–1bits (where L is the length of the original real value sequence and N is the total number of digits of an original real value) will also decrease to a very small number. Now we can give the final capacity estimation provided by our reversible watermarking scheme:
Capacity = h1 – h8 – h9 –2×(L –1)×10j-N-1 . (8)
3.4 Relational Database Authentication
Fig.3 presents the framework for reversible relational database embedding and authentication, where K1 is a
cryp-tographic key used to sort the original real values by a preset rule and to select the appropriate real values for watermarking, and K2 is a cryptographic key used to do watermark embedding and extraction. K1 and K2 are
secret keys owned by the authorized person to authenticate the database. Note that there are two parts of over-head bits: (h8+h9) bits of discrimination information for original real values with initial digits of 8 and 9, and 2×
(L –1)×10j-N-1 bits of discrimination information for original real values prone to over- and underflow and those watermarked ones. MD5 or SHA functions can be employed to hash the original state of some specified parts or the whole database for authentication.
H( dji)
d
Histogram expansion range h 1 H’(dj i) d h '1 h '2 h1= h’1+ h’2
dij histogram expansion and
watermark embedding
wm = “0” wm = “1”
Fig. 3. (a) Histogram expansion based reversible watermarking on the initial digits dji,
Fig. 3. (b) Watermarking framework: authentication
4 Algorithm Analysis and Simulations
Typically, authentication for database authentication usually needs 128 bits or higher in length, so the numerical data’s length in the relational databases should be long enough to provide capacity for overhead bits plus the authentication bits. We generate a relational database containing several 10,001-sized attributes with different data formats, and we embed the authentication information into a attribute of 14-digit numeric data in floating-point format with even distribution over the value range [0,10000), so L＝10000，N=14，M=11. The data are random generated by the function rand() from Matlab. In our simulations, the j of the errors’ initial digit dji is set
to be 13 and therefore the absolute watermarking distortion can be limited to 0.5×102. It is obvious that decreas-ing j can reduce the watermarkdecreas-ing distortion to almost zero, but the capacity will not be affected if the data are rigidly even-distributed. Table 1 presents a simulation result of the distribution of error di generated from the
original real values in the attribute whose watermarking range is limited in (50,9950) so as to avoid over- and underflows. In Table 1, the 9 columns denotes the 9 digits from 1 to 9, the 4 rows denotes 4 value orders on which absolute errors are distributed, and the figures in the main body show the quantity of absolute errors dis-tributed in a certain value order with a certain initial digit. By Eq.(8) we can estimate the final capacity of the tested example shown in Table 1 as 516 bits, which is very close to the actual capacity of 503 bits in our simula-tion. This capacity should be large enough for authentication of part or even the whole of the database.
Table 1. Absolute errors distribution with original real values’ watermarking range of (50,9950).
d13i 1 2 3 4 5 6 7 8 9 100 1 2 0 2 1 3 2 1 0 101 6 14 13 11 15 6 13 10 8 102 103 96 85 110 89 81 98 104 79 103 898 719 657 551 416 343 228 138 43 Histogram Expansion Embedding Hash
Function Authentication bits Database Partial real
values Attribute selection & sorting Overhead bits Waterarked real values K2 Inverse Sorting Watemarked database K1 Inverse Sorting Authentication bits A Watemarked real values Watermark retrieval Overhead bits Restored Attribute Hash Function Authentication bits B A = B ? K2 K1 Watemarked database Attribute selection & sorting K1 Restored partial real values
From the scheme description in section 3 and the results in table 1, we can see that if RDB is not tampered, the watermark can be extracted, and the original RDB can be restored perfectly. Once RDB is tampered, the ex-tracted watermark will not match the hash value calculated from the restored RDB, thus authenticating RDB as tampered.
5 Conclusions
The reversible watermarking scheme for relational databases proposed in this paper provides an exact and loss-less method to authenticate the relational databases, especially suitable for sensitive data requiring no permanent distortions. The scheme takes advantage of the uneven distribution of errors between neighboring randomly gen-erated values in the same attribute to realize reversibly watermarking, and show ability to limit the watermarking distortion to requirement of practical applications by taking partial real values to calculate errors using initial digit specification. Beside database, this scheme shows great advantage in reversible watermarking for other low-correlated data like encrypted data, images heavily polluted by noises, and noise data itself. Our future work focuses on finer temper localization schemes for relational databases, and more compact descriptions of overhead information.
6 Acknowledgement
This work was supported by the National Natural Science Foundation of China (Project Number: 60372052), the Science Foundation of Guangdong Province (Project Number: 05109511), the Foundation for the Author of National Excellent Doctoral Dissertation of China(Project Number: FANEDD-200238),the Multidiscipline Sci-entific Research Foundation of Harbin Institute of Technology (Project Number: HIT.MD-2002.11), the Scien-tific Research Foundation of Harbin Institute of Technology(Project Number: HIT.2003.52), the Foundation for the Excellent Youth of Heilongjiang Province, and the Program for New Century Excellent Talents in University.
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