It's tempting to say that Israeli doctrine is derived from the original draft of Maneuver War, ie. Germany (circa 1915). The Imperial German Army had many Jewish officers (most were 'reservists' due to the anti-semitic attitudes that existed under the Kaiser). German-Jews (WWI vets) emigrating to Palestine during the inter-War years could have brought military training manuals along with them and used these as the basis for training some of the Israeli militias in the '20's & '30's. Only problem with this theory is that nobody can name a significant Israeli military figure from that period who "fits that description", nor can you really point to any doctrinal writings that fit the German 'template'.
That leaves the Soviet-model of the '30's. Before Stalin's purge of the Soviet Military, the Soviets were leaders in Maneuver Doctrine. Therefore, I 'lean' toward the Soviet template. But I gotta tell ya, some of the armor and CAS tactics sure 'look' like the German Blitzkrieg.
Well as I said, there is no "single direct" doctrine taken from one specific nation. In general, the methods are Soviet-German-British. Sometimes the methods were adopted not because of the origin of the commanders and soldiers, but due to their proven success in battle (WW-I, WW-II, etc.)
The tactic of "Blitzkrieg" was probably taken from Germany.
Two of the main IDF tactics are to transfer the battle deep into enemy territory and to achieve the targets of the war quickly- this due to few reasons: The IDF can't fight a full scale war for more than 6 months- as its based on reservs, and during a long war the economy will be ruined.
Another reason is based on the fact that Israel has a small territory, and therefore it can't afford a war on it's land.
Perhaps this tactic is most famous due to it's role at the legendary Six-Day War, that was by all means a war against all odds, and seen one of the quickest and most astonishing victories in the modern history.