Obfuscation and protection of data rights
First Claim
1. A computer implemented method for data obfuscation and right-protection, the method comprising:
- accessing, by a computer, an initial matrix Xi, the initial matrix Xirepresenting an initial data set; and
obtaining, by a computer, from the initial matrix Xi, a final matrix Xf, wherein obtaining the final matrix Xf further comprises;
projecting the initial matrix Xi in a space having a lower dimension than the initial matrix Xi;
obtaining a projected matrix XProj by the following operation;
XProj=P(Xi);
obfuscating the projected matrix XProj to obtain a private matrix XPriv, the private matrix XPriv obtained by the following operation;
XPriv=XProj+E=P(Xi)+E, the noise matrix E is added to the projected matrix XProj, to embed noise; and
multiplying the private matrix XPriv by the matrix F, the final matrix Xf obtained by the operations Xf=(P(Xi)+E)F is right-protected,wherein the final matrix Xf is obtained by performing one of the following operations;
Xf=(P(Xi)+E)F;
Xf=P(Xi)F+E; and
Xf=P(XiF)+E;
wherein the final matrix Xf further includes one or more of;
a secret, the secret based on a random vector;
a multiplicative noise value, having a lower magnitude than the obfuscated embedded noise;
the matrix F, wherein a leading term is identity by a matrix I, the matrix I including one or more higher-order terms of the perturbation series of the matrix F, the secret, the multiplicative noise value, and a right-protected matrix, the right-protected matrix being multiplied by the matrix F;
a perturbation matrix, the perturbation matrix being a matrix only using a perturbation series of the identity matrix I;
a matrix FI, the matrix FI can be represented by an equation FI=I+I1, wherein a matrix I1 embeds the secret and multiplicative noise;
a matrix I1w, the matrix I1w further comprising pW, wherein W being a diagonal matrix containing a watermark w on its diagonal and p is a predetermine scalar value such that pW that has a lower magnitude than the added noise matrix E, the watermark w being a random vector with independent and identically distributed {−
1,1} entries at positions indexed by a value S, the value S being an index set based on a fraction of the largest columns;
a matrix Fw, the matrix Fw represented by the equation Fw=I+I2, wherein the matrix I2 comprises p1W1, W1 being a diagonal matrix containing a watermark w1 on its diagonal, w1 being a second random vector and p1 is a scalar inversely proportional to theta value, the theta value being a lower magnitude than an added Gaussian noise value, the added Gaussian noise value being embedded through the noise matrix E; and
a magnitude value of the secret, the magnitude value of the secret being multiplicative noise such that the preserve pairwise distances in the private matrix XPriv is preserved to a predetermined degree,wherein P(.) is a projection operator that projects an input initial matrix in a space having a lower dimension than the input matrix, E represents a noise matrix, and F represents a matrix as a perturbation series;
storing ell2 norms ∥
xi∥
2 of columns of the private matrix XPriv=[x1, . . . , xn];
generating a set of final data corresponding to the final matrix Xf available to one or more third-parties; and
performing datamining on the generated set of final data based on the final matrix Xf.
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Accused Products
Abstract
Embodiments of the present invention disclose a method, computer program product, and system for data obfuscation and right-protection. An initial matrix Xi, represents the initial data set of the application and final matrix Xf is obtained from Xi. The final matrix Xf is obtained by performing one of the following operations Xf=(P(Xi)+E)F; Xf=P(Xi)F+E; and Xf=P(XiF)+E. Where P(.) is a projection operator that projects an input initial matrix in a space having a lower dimension than the input matrix, E represents a noise matrix, and F represents a matrix as a perturbation series. The matrix F is represented as a perturbation series, whose leading term is the identity matrix I, one or more higher-order terms of the perturbation series embedding a secret, multiplicative noise, so as for a matrix multiplied by the matrix F is right-protected.
9 Citations
13 Claims
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1. A computer implemented method for data obfuscation and right-protection, the method comprising:
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accessing, by a computer, an initial matrix Xi, the initial matrix Xirepresenting an initial data set; and obtaining, by a computer, from the initial matrix Xi, a final matrix Xf, wherein obtaining the final matrix Xf further comprises; projecting the initial matrix Xi in a space having a lower dimension than the initial matrix Xi; obtaining a projected matrix XProj by the following operation;
XProj=P(Xi);
obfuscating the projected matrix XProj to obtain a private matrix XPriv, the private matrix XPriv obtained by the following operation;
XPriv=XProj+E=P(Xi)+E, the noise matrix E is added to the projected matrix XProj, to embed noise; andmultiplying the private matrix XPriv by the matrix F, the final matrix Xf obtained by the operations Xf=(P(Xi)+E)F is right-protected, wherein the final matrix Xf is obtained by performing one of the following operations;
Xf=(P(Xi)+E)F;
Xf=P(Xi)F+E; and
Xf=P(XiF)+E;
wherein the final matrix Xf further includes one or more of; a secret, the secret based on a random vector; a multiplicative noise value, having a lower magnitude than the obfuscated embedded noise; the matrix F, wherein a leading term is identity by a matrix I, the matrix I including one or more higher-order terms of the perturbation series of the matrix F, the secret, the multiplicative noise value, and a right-protected matrix, the right-protected matrix being multiplied by the matrix F; a perturbation matrix, the perturbation matrix being a matrix only using a perturbation series of the identity matrix I; a matrix FI, the matrix FI can be represented by an equation FI=I+I1, wherein a matrix I1 embeds the secret and multiplicative noise; a matrix I1w, the matrix I1w further comprising pW, wherein W being a diagonal matrix containing a watermark w on its diagonal and p is a predetermine scalar value such that pW that has a lower magnitude than the added noise matrix E, the watermark w being a random vector with independent and identically distributed {−
1,1} entries at positions indexed by a value S, the value S being an index set based on a fraction of the largest columns;a matrix Fw, the matrix Fw represented by the equation Fw=I+I2, wherein the matrix I2 comprises p1W1, W1 being a diagonal matrix containing a watermark w1 on its diagonal, w1 being a second random vector and p1 is a scalar inversely proportional to theta value, the theta value being a lower magnitude than an added Gaussian noise value, the added Gaussian noise value being embedded through the noise matrix E; and a magnitude value of the secret, the magnitude value of the secret being multiplicative noise such that the preserve pairwise distances in the private matrix XPriv is preserved to a predetermined degree, wherein P(.) is a projection operator that projects an input initial matrix in a space having a lower dimension than the input matrix, E represents a noise matrix, and F represents a matrix as a perturbation series; storing ell2 norms ∥
xi∥
2 of columns of the private matrix XPriv=[x1, . . . , xn];generating a set of final data corresponding to the final matrix Xf available to one or more third-parties; and performing datamining on the generated set of final data based on the final matrix Xf. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A computer program product for data obfuscation and right-protection, the computer program product comprising:
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a computer-readable storage media and program instructions stored on the computer-readable storage media, the program instructions, executable by a device, comprising; instructions to access, by a computer, an initial matrix Xi, the initial matrix Xi representing an initial data set; and instructions to obtain, by a computer, from the initial matrix Xi, a final matrix Xf, wherein instructions to obtain the final matrix Xf further comprises; instructions to project the initial matrix Xi in a space having a lower dimension than the initial matrix Xi; instructions to obtain a projected matrix XProj by the following operation;
XProj=P(Xi);instructions to obfuscate the projected matrix XProj to obtain a private matrix XPriv, the private matrix XPriv obtained by the following operation;
XPriv=XProj+E=P(Xi) +E, the noise matrix E is added to the projected matrix XProj, to embed noise; andinstructions to multiply the private matrix XPriv by the matrix F, the final matrix Xf obtained by the operations Xf =(P(Xi)+E)F is right-protected; wherein the final matrix Xf is obtained by performing one of the following operations;
Xf=(P(Xi)+E)F;
Xf=P(Xi)F+E; and
Xf=P(XiF)+E,wherein the final matrix Xf further includes one or more of; a secret, the secret based on a random vector; a multiplicative noise value, having a lower magnitude than the obfuscated embedded noise; the matrix F, wherein a leading term is identity by a matrix I, the matrix I including one or more higher-order terms of the perturbation series of the matrix F, the secret, the multiplicative noise value, and a right-protected matrix, the right-protected matrix being multiplied by the matrix F; a perturbation matrix, the perturbation matrix being a matrix only using a perturbation series of the identity matrix I; a matrix FI, the matrix FI can be represented by an equation FI=I+I1, wherein a matrix I1 embeds the secret and multiplicative noise; a matrix I1w, the matrix I1w further comprising pW, wherein W being a diagonal matrix containing a watermark w on its diagonal and p is a predetermine scalar value such that pW that has a lower magnitude than the added noise matrix E, the watermark w being a random vector with independent and identically distributed {−
1,1} entries at positions indexed by a value S, the value S being an index set based on a fraction of the largest columns;a matrix Fw, the matrix Fw represented by the equation Fw=I+I2, wherein the matrix I2 comprises p1W1, W1 being a diagonal matrix containing a watermark w1 on its diagonal, w1 being a second random vector and p1 is a scalar inversely proportional to theta value, the theta value being a lower magnitude than an added Gaussian noise value, the added Gaussian noise value being embedded through the noise matrix E; and a magnitude value of the secret, the magnitude value of the secret being multiplicative noise such that the preserve pairwise distances in the private matrix XPriv is preserved to a predetermined degree, wherein P(.) is a projection operator that projects an input initial matrix in a space having a lower dimension than the input matrix, E represents a noise matrix, and F represents a matrix as a perturbation series; instructions to store ell2 norms ∥
xi∥
2 of columns of the private matrix XPriv=[x1, . . . , xn];
instruction to generate a set of final data corresponding to the final matrix Xf available to one or more third-parties; and instructions to perform datamining on the generated set of final data based on the final matrix Xf. - View Dependent Claims (9, 10)
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11. A computer system for data obfuscation and right-protection, the computer system comprising:
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one or more computer processors; one or more computer-readable storage media; program instructions stored on the computer-readable storage media for execution by at least one of the one or more processors, the program instructions comprising; instructions to instructions to access, by a computer, an initial matrix Xi, the initial matrix Xi representing an initial data set; and instructions to obtain, by a computer, from the initial matrix Xi, a final matrix Xf, wherein instructions to obtain the final matrix Xf further comprises; instructions to project the initial matrix Xi in a space having a lower dimension than the initial matrix Xi; instructions to obtain a projected matrix XProj by the following operation;
XProj=P(Xi);instructions to obfuscate the projected matrix XProj to obtain a private matrix XPriv, the private matrix XPriv obtained by the following operation;
XPriv=XProj+E=P(Xi)+E, the noise matrix E is added to the projected matrix XProj, to embed noise; andinstructions to multiply the private matrix XPriv by the matrix F, the final matrix Xf obtained by the operations Xf=(P(Xi)+E)F is right-protected; wherein the final matrix Xf is obtained by performing one of the following operations;
Xf=(P(Xi)+E)F;
Xf=P(Xi)F+E; and
Xf=P(XiF)+E,wherein the final matrix Xf further includes one or more of; a secret, the secret based on a random vector; a multiplicative noise value, having a lower magnitude than the obfuscated embedded noise; the matrix F, wherein a leading term is identity by a matrix I, the matrix I including one or more higher-order terms of the perturbation series of the matrix F, the secret, the multiplicative noise value, and a right-protected matrix, the right-protected matrix being multiplied by the matrix F; a perturbation matrix, the perturbation matrix being a matrix only using a perturbation series of the identity matrix I; a matrix FI, the matrix FI can be represented by an equation FI=I+I1, wherein a matrix I1 embeds the secret and multiplicative noise; a matrix I1w, the matrix I1w further comprising pW, wherein W being a diagonal matrix containing a watermark w on its diagonal and p is a predetermine scalar value such that pW that has a lower magnitude than the added noise matrix E, the watermark w being a random vector with independent and identically distributed {−
1,1} entries at positions indexed by a value S, the value S being an index set based on a fraction of the largest columns;a matrix Fw, the matrix Fw represented by the equation Fw=I+I2, wherein the matrix I2 comprises p1W1, W1 being a diagonal matrix containing a watermark w1 on its diagonal, w1 being a second random vector and p1 is a scalar inversely proportional to theta value, the theta value being a lower magnitude than an added Gaussian noise value, the added Gaussian noise value being embedded through the noise matrix E; and a magnitude value of the secret, the magnitude value of the secret being multiplicative noise such that the preserve pairwise distances in the private matrix XPriv is preserved to a predetermined degree, wherein P(.) is a projection operator that projects an input initial matrix in a space having a lower dimension than the input matrix, E represents a noise matrix, and F represents a matrix as a perturbation series; instructions to store ell2 norms ∥
xi∥
2 of columns of the private matrix XPriv=[x1,. . . ,xn];instruction to generate a set of final data corresponding to the final matrix Xf available to one or more third-parties; and instructions to perform datamining on the generated set of final data based on the final matrix Xf. - View Dependent Claims (12, 13)
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Specification