CRYPTOGRAPHIC SYSTEM FOR PERFORMING SECURE COMPUTATIONS AND SIGNAL PROCESSING DIRECTLY ON ENCRYPTED DATA IN UNTRUSTED ENVIRONMENTS

Disclosed embodiments include a cryptographic system implemented in at least one digital computer with one or more processors or hardware such as FPGAs for performing secure computations, analysis, and signal processing directly on encrypted data in untrusted environments. According to a basic embodiment, the proposed cryptographic system comprises: (a) at least one secure protocol for performing matrix multiplications in the encrypted domain, and (b) at least one secure protocol for solving systems of linear equations in the encrypted domain. According to a particular embodiment, the system comprises a plurality of privacy-preserving protocols for solving systems of linear equations (SLE) directly based on homomorphic computation and secret sharing. More specifically, according to a particular embodiment, the system uses a protocol whereby systems of linear equations are solved securely by direct Gaussian elimination using a secure protocol without imposing any restrictions on the matrix coefficients.