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A system of tamperproof electronic black boxes is proposed to implement a technique which prevents the launching of nuclear missiles for a ``first strike,'' but which allows them to be launched for a retaliatory ``second strike.'' The proposed black box technology is very similar to one developed during the past ten years to provide security in retail electronic banking systems. After more than 30 years of senseless competition, with the ever-present risk of catastrophic destruction by accident or miscalculation, both the U.S. and Soviet Union appear desirous of ending the nuclear arms race. Neither side has any current intention of launching a deliberate ``first strike'' against the other. Nevertheless each side believes it must maintain its retaliatory capability, and only this ``balance of terror'' holds the other side in check. Thus a mutually agreeable method for arms control has so far been impossible to find. Unless a solution to this impasse is soon found, a major escalation of the arms race is highly probable. This will be a technological race, as each side attempts to build an impenetrable missile defense system, as exemplified by the currently planned ``SDI'' (Strategic Defense Initiative), and the other side attempts to build more sophisticated missiles that can counter these defenses. This paper suggests a new type of technology, one that is intended to make effective arms control possible, and thus end the stalemate.