Abstract: 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 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 and iteratively without imposing any restrictions on the matrix coefficients.

Abstract: Disclosed embodiments include a method and an apparatus for digital content transmission that comprise: (a) partitioning the digital content into a plurality of sequential segments; (b) selecting a plurality of transmission time instants for each of the sequential segments as a function of their order; (c) generating a plurality of linear combinations of the plurality of sequential segments during the plurality of transmission time instants resulting in a plurality of linearly combined coded segments; and (c) transmitting the plurality of linearly combined coded segments from a server to a plurality of clients. In particular embodiments, the method and apparatus further comprise performing error correction based on an implicit error correction (IEC) method that employs the redundancy present in the linearly combined coded segments to perform error correction at the client side without extra bandwidth cost.

Abstract: Disclosed embodiments include a method and an apparatus for digital content transmission that comprise: (a) partitioning the digital content into a plurality of sequential segments; (b) selecting a plurality of transmission time instants for each of the sequential segments as a function of their order; (c) generating a plurality of linear combinations of the plurality of sequential segments during the plurality of transmission time instants resulting in a plurality of linearly combined coded segments; and (c) transmitting the plurality of linearly combined coded segments from a server to a plurality of clients. In particular embodiments, the method and apparatus further comprise performing error correction based on an implicit error correction (IEC) method that employs the redundancy present in the linearly combined coded segments to perform error correction at the client side without extra bandwidth cost.