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