Optimized distributed private matrix multiplication

The invention relates to optimized distributed private matrix multiplication. Methods, systems, and computer programs for distributed processing of matrix data structures are disclosed. In one aspect, the method may include obtaining a first matrix data structure (DS); segmenting the obtained matrix DS into a set of M different matrix DS parts; segmenting each of the M different matrix DS portions into a respective set of K matrix DS sub-portions; for each of the respective sets of K matrix DS sub-portions: generating an obfuscation matrix having the same dimension as each of the K matrix DS sub-portions, and generating, by one or more computers, an obfuscation representation of each of the respective sets of K matrix DS sub-portions, the obfuscation representation comprising (i) the K matrix DS sub-portions and (ii) the obfuscation matrix; and transmitting data representing each of the N obfuscated representations of the K matrix DS sub-portions of the respective set of the M matrix DS portions to a differen