Method and system for privacy-preserving linear optimization

A computing apparatus for using a privacy preserving linear optimization technique to perform computations on encrypted data while ensuring that original data remains confidential and secure from unauthorized access, the computing apparatus comprising:

• a processor;
• a memory;
• and
• a communication interface coupled to each of the processor and the memory,
• wherein the processor is configured to:
• establish, via a network, a joint optimization session with a plurality of entities, wherein the each of the plurality of entities are external entities with respect to one another and resides on a differing network;
• receive, via the communication interface from each respective entity from among the plurality of entities, a respective input that includes first encrypted data, wherein encryption performed on the first encrypted data is performed by each of the respective entity among the plurality of entities for limiting exposure of underlying data of the first encrypted data to other entities among the plurality of entities;
• construct, using the respective input from each respective entity among the plurality of entities, a first table that includes first information that relates to a first predetermined objective function, second information that relates to a first predetermined boundary value, and third information that relates to a predetermined polynomial function that is applicable to each respective input;
• perform a plurality of iterations for each respective input, wherein each of the plurality of iterations include:
• determining a pivot column of the first table based on the received respective inputs;
• determining a pivot row of the first table based on the received respective inputs and the pivot column;
• updating the pivot row by performing a first predetermined operation that is based on the first predetermined polynomial function and the first predetermined boundary value;
• and
• updating each respective column of the first table by performing a second predetermined operation that is based on the first predetermined polynomial function, the first predetermined boundary value, and the updated pivot row;
• determine, based on performing the plurality of iterations for each respective input, a first value that maximizes the predetermined polynomial function while satisfying a constraint that a result of applying the first predetermined objective function to the first value is less than or equal to the first predetermined boundary value, wherein underlying data of the first value remain unexposed to the plurality of entities for reducing gross exposure to the plurality of entities.

A non-transitory computer readable storage medium storing instructions for using a privacy preserving linear optimization technique to perform computations on encrypted data while ensuring that original data remains confidential and secure from unauthorized access, the storage medium comprising executable code which, when executed by a processor, causes the processor to:

• establish, via a network, a joint optimization session with a plurality of entities, wherein the each of the plurality of entities are external entities with respect to one another and resides on a differing network;
• receive, from each respective entity from among the plurality of entities, a respective input that includes first encrypted data, wherein encryption performed on the first encrypted data is performed by each of the respective entity among the plurality of entities for limiting exposure of underlying data of the first encrypted data to other entities among the plurality of entities;
• construct, using the respective input from each respective entity among the plurality of entities, a first table that includes first information that relates to a first predetermined objective function, second information that relates to a first predetermined boundary value, and third information that relates to a predetermined polynomial function that is applicable to each respective input;
• perform a plurality of iterations for each respective input, wherein each of the plurality of iterations include:
• determining a pivot column of the first table based on the received respective inputs;
• determining a pivot row of the first table based on the received respective inputs and the pivot column;
• updating the pivot row by performing a first predetermined operation that is based on the first predetermined polynomial function and the first predetermined boundary value;
• and
• updating each respective column of the first table by performing a second predetermined operation that is based on the first predetermined polynomial function, the first predetermined boundary value, and the updated pivot row;
• determine, based on performing the plurality of iterations for each respective input, a first value that maximizes the predetermined polynomial function while satisfying a constraint that a result of applying the first predetermined objective function to the first value is less than or equal to the first predetermined boundary value, wherein underlying data of the first value remain unexposed to the plurality of entities for reducing gross exposure to the plurality of entities.