Patent ID: 8843762

Claim:
A homomorphic cryptographic system, comprising: (a) a memory configured to store computer-executable instructions; (b) at least one hardware processor configured to execute said computer-executable instructions that when executed cause the processor to: (1) perform matrix multiplications in an encrypted domain using a multiplication protocol based on homomorphic computation and secret sharing, wherein data remains encrypted at all times within the encrypted domain by: (i) generating a set of random values; and (ii) obtaining an encrypted product of encrypted matrices using said set of random values and homomorphic operations; (2) solve systems of linear equations in the encrypted domain using at least one secure iterative protocol configured for operating with matrices containing no restrictions on the coefficients being real or complex by: (i) generating shares of a diagonal matrix through homomorphic operations; (ii) calculating an encrypted modified matrix and an encrypted modified vector using secure multiplication; and (iii) performing iterations using homomorphic operations; wherein said homomorphic cryptographic system performs iterative computations, signal processing, and data analysis on encrypted data in untrusted environments without the need to decrypt said encrypted data.