Mr. Lichtenfeld set off for the British Mandate of Palestine in 1940, and he began training the Zionist forces in skills like stick fighting and bayonet tactics.

After the state of Israel was established in 1948, he became the Israeli military’s close-quarters combat chief. The system has since evolved into a vital component of Israeli combat training. Elite forces endure many hours of intense coaching. There is no competitive Krav Maga circuit, because the idea is to break all the rules, not play by them, although the army did institute an annual Krav Maga contest a few years ago.

The chief producer of the documentary, Paul Szyarto, an American fitness guru and co-founder of VMMA, a chain of mixed martial arts training centers, accompanied Mr. Kahn to Israel and interviewed Mr. Gidon for the movie.

The best defense, said Mr. Gidon — who drove a tank in the 1967 and 1973 Israeli wars — is to avoid getting into a confrontation in the first place and, if possible, to run. “But if there’s no choice and there’s a knife to your throat, you’ve got to know how to face it,” he said. “Even with eye gouging, you have to know how. You have to bring your thumb all the way in.”

For Mr. Szyarto, Krav Maga encapsulates the essence of Israeliness: resourcefulness, versatility and a mind-set of doing whatever it takes to win. Mr. Gidon said he agreed, at least in the military context, but also preached humility. “There is no such person as a fearless person,” he said. “The point is to deal with the fear.”

Mr. Gidon, who worked in the diamond industry after being released from military service, said he first met Mr. Lichtenfeld in 1969 and began training with him. As evidence of how far their relationship went back, Mr. Gidon related that Mr. Lichtenfeld attended his wedding in 1974.