Polynomial representation of nn for communication-less smpc and method of performing statistical information-theoretical secure (sits) distributed communication-less smpc (dclsmpc) of a distributed unknown finite state machine (dufsm)

A method for performing Statistical Information-Theoretical Secure (SITS) Distributed Communication-Less Secure Multiparty Computation (DCLSMPC) of a Distributed Unknown Finite State Machine (DUFSM), comprising:

• a) passing secret shares of the input(s) and output(s) to/from the computing parties, with no communication between said computing parties throughout the computation;
• b) providing a polynomial representation or a Look-Up Table (LUT) representation of the transition table of said DUFSM, for arithmetic circuits evaluation, joined with a CRT secret sharing scheme and FHE, to computationally mitigate information leakage from individual CRT shares;
• c) implementing said DUFSM by secret sharing of said the transition table or the coefficients of said polynomial over a finite ring, to imply communication-less SMPC of said DUFSM, said polynomial encoding the information of all the transitions from a state x and input y to the next state z;
• d) describing said polynomial by an arithmetic circuit that can be evaluated distributively by the SMPC participants, while allowing each participant to evaluate said arithmetic circuit using CRT-SITS secret sharing scheme where the shares are encrypted using FHE.

A system for performing effective secure multi-party computation by participating parties being one or more computerized devices for executing said multi-party computation, with no communication between the parties, using at least one trained Deep Neural Network (DNN), comprising one or more computerized devices that contain one or more processors being adapted to:

• a) approximate said at least one trained DNN by polynomial functions representing a single or multiple layers of said DNN by:
• a.1) representing each neuron unit of said DNN by a polynomial being a weighted sum of vector multiplication of weights with an n-dimensional input;
• a.2) representing the output of each neuron unit by applying an activation function to said weighted sum;
• b) generate additive secret shares for every polynomial coefficient;
• c) distribute said secret shares among said participating parties;
• d) send the input x to said participating parties, for execution;
• e) after execution, receive the output of polynomial activation function of each participating party;
• and
• f) output the final result as the sum of the received output.