1. A method of securely executing an input stream of symbols, by non-interactive, multi-party computation, comprising: distributing, by a dealer, said input stream among a plurality of parties of servers or computation cloud components, which do not communicate among themselves throughout execution, wherein said dealer having a secret initial state, and distributing shares of said secret state between said plurality of parties; providing a finite-state automaton defined by a series of cascaded equations, to execute said input stream by a hardware processor, said automaton being a cascade product of component automata of different types and shared by said plurality of parties; at any execution stage, concealing said input stream and current state of the original automaton from any coalition of participants being smaller than a given threshold, wherein the threshold is a minimum number of participants required to reveal automaton states; upon receiving a signal from said dealer, said plurality of parties terminate their execution and submit their individual internal state to said dealer; and computing, by the dealer, the current state that defines the computation result.