Server-Assisted Secure Two-Party Matrix Inversion

The patent segments the secure matrix inversion computation into multiple independent phases: matrix multiplication phase, inversion phase, and result aggregation phase. Each phase is executed separately with dedicated protocols, allowing optimization of each segment while maintaining overall security. The computation is divided among multiple servers that work in parallel, reducing the burden on any single server and improving overall efficiency.

The patent introduces random matrices as intermediary elements that facilitate secure computation without requiring direct homomorphic encryption operations. These random matrices act as mediators that allow servers to perform computations on encrypted data through standard linear algebra operations, significantly reducing computational overhead compared to direct homomorphic encryption.

The patent divides the cloud computing infrastructure into multiple independent servers that each hold only a portion of the computational task and data. No single server has access to the complete private data or can complete the entire computation alone, preventing collusion attacks from compromising security. The segmentation is achieved through distributed matrix operations where each server processes specific matrix blocks.

Different servers are assigned different local qualities or roles in the computation process. Some servers perform multiplication operations, others perform inversion operations, and each operates on locally stored data portions. This local specialization ensures that even if one server is compromised, the damage is limited to its specific computational domain.

The patent changes the parameter space by working in the rational number field Q rather than finite fields modulo large primes. This allows the use of standard floating-point arithmetic with maintained precision while achieving security through protocol design rather than cryptographic encoding. The security is derived from the computational difficulty of the underlying mathematical problems in the rational field.

The patent replaces the cryptographic mechanical system (large prime number encryption) with a protocol-based security mechanism. Instead of relying on the mathematical properties of large primes for security, the system uses carefully designed interaction protocols among multiple servers that collectively provide security guarantees without requiring large prime encodings.

The patent extracts and removes the need for complex oblivious transfer protocols by using a different security model based on semi-honest auxiliary servers. The security is achieved by designing the computation protocol to inherently protect privacy through the structure of matrix operations and the distribution of computational tasks, rather than layering oblivious transfer on top of the computation.

The patent uses random matrix copies as placeholders and intermediate representations that allow computation to proceed without requiring direct access to sensitive data. These copied matrices serve as substitutes that maintain the mathematical structure needed for computation while containing no sensitive information, eliminating the need for complex privacy-preserving communication protocols.