CRYPTOGRAPHIC SYSTEM FOR PERFORMING SECURE ITERATIVE MATRIX INVERSIONS AND SOLVING SYSTEMS OF LINEAR EQUATIONS

Fundacion Centro Tecnoloxico de Telecomunicacions de Galicia (Gradiant)
posted on 02/02/2012

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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 iterative 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 iterative protocol for performing matrix inversions and solving systems of equations based on an iterative secure protocol substantially equivalent to a Newton secure protocol. 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 secure iterative protocol whereby systems of linear equations and matrix inversions are solved securely and iteratively without imposing any restrictions on the matrix coefficients based on an iterative protocol substantially equivalent to a Newton secure protocol.