Method of comparing private data without revealing the data

1. A method for identity verification, the method comprising steps of:

receiving, by a client computer from an interface gateway, a device identifier (DID) and a noise-added biometric sample (S 1 +N) where S 1 is a biometric sample of an individual, N is noise, and the device identifier (DID) identifies a device that transmitted the noise-added biometric sample (S 1 +N) to the interface gateway;

retrieving from a database, by the client computer, an encryption key laden with noise-added biometric sample (K 1 +S 2 +N), where S 2 is a stored biometric sample corresponding to S 1 , K 1 is a first key, the retrieving being based on the device identifier (DID), wherein the client computer does not know the first key (K 1 ) or the noise (N), and S 1 and S 2 are non-identical;

computing, by the client computer, a second key (K 2 ) by solving K 2 =(K 1 +S 2 +N)−(S 1 +N);

determining whether or not the second key (K 2 ) is similar within a threshold to a stored value of the first key (K 1 ) located on a server computer without revealing the stored value of the first key (K 1 ) by computing, using the client computer and the server computer, a non-zero bisector vector (x) in the equation (A 1 +A 2 )x=λ d1 V d1 +λ d2 V d2 , where A 1 and A 2 are private matrixes corresponding to K 1 and K 2 , respectively, λ d1 and λ d2 are respective eigenvalues and V d1 and V d2 are corresponding unity normalized eigenvectors, the computing occurring by exchanging encrypted matrix A 1 ; encrypted vector λ d1 V d1 ; encrypted matrix A 2 ; and encrypted vector λ d2 V d2 respectively, without the client computer or the server computer revealing d 1 , λ d1 , V d1 , d 2, λ d2 or V d2 ;

if the determining within the threshold is satisfied, the second key (K 2 ) and the stored value of the first key (K 1 ) are deemed sufficiently similar;

if the determining within the threshold is unsatisfied, the second key (K 2 ) and the stored value of the first key (K 1 ) are deemed dissimilar;

transmitting from the server computer to the client computer, if the threshold is satisfied, helper data that permits the client computer to reconstruct a secret key (K′) identical to the first key (K 1 ) by combining the helper data with the private matrix A 1 ;

transmitting, to the interface gateway, the secret key (K′).

2. The method as recited in claim 1 , wherein K 1 is not known by the client computer or the individual.

3. The method as recited in claim 2 , wherein the device is a mobile cellular telephone or tablet computer.

4. The method as recited in claim 2 , wherein the biometric sample of the individual is a voice biometric sample.

5. The method as recited in claim 2 , wherein the biometric sample of the individual is a picture of a face.

6. The method as recited in claim 2 , wherein the biometric sample of the individual is a fingerprint.

7. A non-transient program storage device readable by machine, tangibly embodying a program of instructions executable by machine to perform a method for identity verification, the method comprising steps of:

receiving, by a client computer from an interface gateway, a device identifier (DID) and a noise-added biometric sample (S 1 +N) where S 1 is a biometric sample of an individual, N is noise, and the device identifier (DID) identifies a device that transmitted the noise-added biometric sample (S 1 +N) to the interface gateway;

retrieving from a database, by the client computer, an encryption key laden with noise-added biometric sample (K 1 +S 2 +N), where S 2 is a stored biometric sample corresponding to S 1 , K 1 is a first key, the retrieving being based on the device identifier (DID), wherein the client computer does not know the first key (K 1 ) or the noise (N), and S 1 and S 2 are non-identical;

computing, by the client computer, a second key (K 2 ) by solving K 2 =(K 1 +S 2 +N)−(S 1 +N);

determining whether or not the second key (K 2 ) is similar within a threshold to a stored value of the first key (K 1 ) located on a server computer without revealing the stored value of the first key (K 1 ) by computing, using the client computer and the server computer, a non-zero bisector vector (x) in the equation (A 1 +A 2 )x=λ d1 V d1 +λ d2 V d2 , where A 1 and A 2 are private matrixes corresponding to K 1 and K 2 , respectively, λ d1 and λ d2 are respective eigenvalues and V d1 and V d2 are corresponding unity normalized eigenvectors, the computing occurring by exchanging encrypted matrix A 1 ; encrypted vector λ d1 V d1 ; encrypted matrix A 2 ; and encrypted vector λ d2 V d2 respectively, without the client computer or the server computer revealing d 1 , λ d1 , V d1 , d 2, λ d2 or V d2 ;

if the determining within the threshold is satisfied, the second key (K 2 ) and the stored value of the first key (K 1 ) are deemed sufficiently similar;

if the determining within the threshold is unsatisfied, the second key (K 2 ) and the stored value of the first key (K 1 ) are deemed dissimilar;

transmitting from the server computer to the client computer, if the threshold is satisfied, helper data that permits the client computer to reconstruct a secret key (K′) identical to the first key (K 1 ) by combining the helper data with the private matrix A 1 ;

transmitting, to the interface gateway, the secret key (K′).

8. The program storage device as recited in claim 7 , wherein K 1 is not known by the client computer or the individual.

9. The program storage device as recited in claim 8 , wherein the device is a mobile cellular telephone or tablet computer.

10. The program storage device as recited in claim 8 , wherein the biometric sample of the individual is a voice biometric sample.

11. The program storage device as recited in claim 8 , wherein the biometric sample of the individual is a picture of a face.

12. The program storage device as recited in claim 8 , wherein the biometric sample of the individual is a fingerprint.