Method and apparatus for path concealment in networks and graphs

Abstract

A method for data concealment between two parties in a system, including: permitting the system to solicit one or more data from a user; permitting the system to generate a traversed path in a graph by using the one or more data provided by the user to generate the traversed path; performing a sequence of computations; associating square matrices to each connected node of the plurality of nodes of the traversed path in the graph; initiating each of the sequence of computations with a random vector; performing matrix multiplications at each step in the sequence of computations; obtaining a result vector; using the result vector of a matrix and a vector product of each connected node of the plurality of nodes of the traversed path as a vector in a subsequent node in the traversed path; comparing an outcome of the sequence of computations to a value associated with the traversed path of a correct password.

1 . A method for data concealment between two parties in a system, the method comprising:
 permitting the system to solicit one or more data from a user;   permitting the system to generate a traversed path in a graph by using the one or more data provided by the user to generate the traversed path;   performing a sequence of computations, each step in the sequence of computations being dictated by each connected node of a plurality of nodes of the traversed path in the graph;   associating square matrices to each connected node of the plurality of nodes of the traversed path in the graph;   initiating each of the sequence of computations with a random vector;   performing matrix multiplications at each step in the sequence of computations;   obtaining a result vector;   using the result vector of a matrix and a vector product of each connected node of the plurality of nodes of the traversed path as a vector in a subsequent node in the traversed path;   comparing an outcome of the sequence of computations to a value associated with the traversed path of a correct password by using cosine distances between vectors; and   determining whether the user has determined the correct password based on the value associated with the traversed path of the correct password being less than a predetermined threshold value.   
   
   
       2 . The method of  claim 1 , wherein the associated matrices have the form:
   matrix —   i=G   —   {i− 1 } A G{i}  for 2 ≦i≦k− 1;     matrix — 1= A G   — 1; and     matrix —   k=G   —   {k− 1}  A;     where G's are occluding matrices, A is a kernel matrix, i, j, k are index identifiers, (n×n) is the size of the matrix in the matrix multiplications, and matrix — 1 and matrix_k are matrices associated with initial and terminal nodes in the graph, respectively.   
   
   
       3 . The method of  claim 1 , wherein the system is divided into two subsystems, a security handling subsystem being a secure subsystem and an interaction subsystem being an insecure subsystem. 
   
   
       4 . The method of  claim 3 , wherein the secure subsystem generates a symmetric kernel matrix with a dominant eigenvector. 
   
   
       5 . The method of  claim 3 , wherein the secure subsystem retrieves the one or more data and assembles a general verification graph with matrices associated to the nodes. 
   
   
       6 . The method of  claim 5 , wherein the associated matrices have the form:
   matrix —   i=G   —   {i −1 } A G{i}  for 2≦ i≦k− 1;     matrix — 1=A G — 1; and     matrix —   k=G   —   {k− 1} A;   where G's are occluding matrices, A is a kernel matrix, i, j, k are index identifiers, (n×n) is the size of the matrix in the matrix multiplications, and matrix — 1 and matrix_k are matrices associated to initial and terminal nodes in the graph, respectively.   
   
   
       7 . A system for data concealment in a graph, the graph having a plurality of nodes, the system comprising:
 a communications network; and   host system in communication with the network, the host system including software to implement a method comprising:
 permitting a system to solicit one or more data from a user; 
 permitting the system to generate a traversed path in a graph by using the one or more data provided by the user to generate the traversed path; 
 performing a sequence of computations, each step in the sequence of computations being dictated by each connected node of the plurality of nodes of the traversed path in the graph; 
 associating square matrices to each connected node of the plurality of nodes of the traversed path in the graph; 
 initiating each of the sequence of computations with a random vector; 
 performing matrix multiplications at each step in the sequence of computations; 
 obtaining a result vector; 
 using the result vector of a matrix and a vector product of each connected node of the plurality of nodes of the traversed path as a vector in a subsequent node in the traversed path; 
 comparing an outcome of the sequence of computations to a value associated with the traversed path of a correct password by using cosine distances between vectors; and 
 determining whether the user has determined the correct password based on the value associated with the traversed path of the correct password being less than a predetermined threshold value. 
   
   
   
       8 . The system of  claim 7 , wherein the matrix multiplications include the following operations:
   matrix —   i=G   —   {i− 1}  A G{i}  for 2≦ i≦k− 1;     matrix — 1=A G — 1; and     matrix —   k=G   —   {k− 1 } A;     where G's are occluding matrices, A is a kernel matrix, i, j, k are index identifiers, (n×n) is the size of the matrix in the matrix multiplications, and matrix — 1 and matrix_k are matrices associated with initial and terminal nodes in the graph, respectively.   
   
   
       9 . The system of  claim 7 , wherein the system is divided into two subsystems, a security handling subsystem being a secure subsystem and an interaction subsystem being an insecure subsystem. 
   
   
       10 . The system of  claim 9 , wherein the secure subsystem generates a symmetric random vector with a target eigenvalue distribution and obtains a dominant eigenvector. 
   
   
       11 . The system of  claim 10 , wherein the secure subsystem retrieves the one or more data and assembles a general verification network. 
   
   
       12 . A computer program product for path concealment in a graph via a keyphrase verification algorithm, the graph including a plurality of nodes, the computer program product comprising:
 a storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising:
 permitting a system to solicit one or more data from a user; 
 permitting the system to generate a traversed path in a graph by using the one or more data provided by the user to generate the traversed path; 
 performing a sequence of computations, each step in the sequence of computations being dictated by each connected node of the plurality of nodes of the traversed path in the graph; 
 associating square matrices to each connected node of the plurality of nodes of the traversed path in the graph; 
 initiating each of the sequence of computations with a random vector; 
 performing matrix multiplications at each step in the sequence of computations; 
 obtaining a result vector; 
 using the result vector of a matrix and a vector product of each connected node of the plurality of nodes of the traversed path as a vector in a subsequent node in the traversed path; 
 comparing an outcome of the sequence of computations to a value associated with the traversed path of a correct password by using cosine distances between vectors; and 
 determining whether the user has determined the correct password based on a distance between the correct password being below a threshold. 
   
   
   
       13 . The computer program product of  claim 12 , wherein the matrix multiplications include the following operations:
   compute Annotation —   i=G   —   {i− 1}  A G{i}  for 2≦ i≦k− 1;     compute Annotation —   j=Random _( n×n ) j;       compute Annotation — 1=A G — 1; and     compute Annotation a —   k=G   —   {k− 1 } A;     where G is grammar, A is annotation, i, j, k are natural identifiers, and (n×n) is the size of the matrix in the matrix multiplications.   
   
   
       14 . The computer program product of  claim 12 , wherein the system is divided into two subsystems, a security handling subsystem being a secure subsystem and an interaction subsystem being an insecure subsystem. 
   
   
       15 . The computer program product of  claim 14 , wherein the secure subsystem generates a symmetric random vector with a target eigenvalue distribution and obtains a dominant eigenvector. 
   
   
       16 . The computer program product of  claim 14 , wherein the secure subsystem retrieves the one or more data and assembles a general verification network.