Secure Scalar Product Calculation Using Homomorphic Encryption
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Solution Overview
Problem
Existing secure multi-party computation techniques for calculating scalar products are slow, complex, and unsuitable for time-sensitive applications due to high computational and communication overhead, particularly when dealing with private data.
Innovation Solution
A method for two computers to concurrently calculate the scalar product of vectors without revealing their respective vectors to each other using additive homomorphic encryption, specifically the Paillier cryptosystem, allowing secure and efficient comparison and interaction based on the scalar product without transmitting square magnitudes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If secure multi-party computation techniques are used to calculate scalar products, then data privacy is preserved, but computation time and communication overhead increase significantly
Solution Approach 1:
The patent extracts only the necessary components for scalar product calculation from the full vectors. By using masked vectors that contain only the portions needed for computation and removing unnecessary data elements, the system achieves both privacy preservation and reduced computation time. The extraction principle is applied by transmitting only relevant vector components rather than complete vectors.
Solution Approach 2:
The patent performs preliminary masking and encryption of vectors before transmission. By pre-processing the vectors to apply masks and encryption schemes beforehand, the system reduces the computational burden during the actual scalar product calculation, thereby decreasing overall computation time while maintaining privacy guarantees.
2Reliability
If secure multi-party computation techniques are used to calculate scalar products, then data privacy is preserved, but communication overhead increases due to large numbers of messages
Solution Approach 1:
The patent extracts and transmits only the essential masked vector components needed for scalar product calculation, rather than transmitting complete vectors or multiple intermediate values. This extraction approach significantly reduces the quantity of data communicated between parties while preserving the ability to compute the scalar product securely.
Solution Approach 2:
The patent implements a streamlined communication protocol that performs only the necessary communication steps required for secure scalar product calculation, omitting redundant message exchanges. By applying partial action—doing just enough communication to achieve the security goal without excessive messaging—the system reduces communication overhead.
3Reliability
If conventional secure computation protocols are used, then privacy is maintained, but the protocols become complex and unsuitable for time-sensitive applications
Solution Approach 1:
The patent extracts and implements only the core essential steps required for secure scalar product calculation, removing complex auxiliary protocols and procedures from conventional approaches. This focused extraction simplifies the overall protocol structure while maintaining the fundamental privacy preservation capabilities.
Solution Approach 2:
The patent changes key parameters of the computation protocol by using masked vectors with specific mathematical properties and optimized encryption schemes. These parameter changes simplify the protocol operations and reduce complexity compared to conventional approaches, making the system suitable for time-sensitive applications while preserving privacy.
Data Source
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AI summary
A method and system for performing a calculation of a privacy preserving scalar product are provided. A first party and a second party (e.g., a first computer and a second computer) possessing a first vector and a second vector respectively, can concurrently determine the scalar product of the two vectors, without revealing either vector to the other party. Each vector can be masked and then encrypted using a public key of an asymmetric key pair. Using homomorphic encryption operations, the scalar product of the vectors can be determined while the vectors are still encrypted. Each party can compare the scalar product, or a value derived from the scalar product against a predetermined threshold. As an example, two parties can perform the scalar product to compare two biometric templates expressed as vectors without revealing the biometric templates to one another, preserving the privacy of persons corresponding to those biometrics.