Called variously the 1956 War, the Sinai Campaign, Operation Kadesh (after the IDF codename), and the 100 hours war (the length of time it took the Israeli’s to win).
Egypt, Syria and Jordan were planning a joint war on Israeli, however, events took a different turn. Egypt had nationalised the Suez Canal – thus offending the British and French – and subsequently closed the Straits of Tiran to Israeli shipping, hence blocking Israeli access to the Red Sea. On top of this growing attacks by Egyptian infiltrators forced the Israeli’s to take preemptive steps. Israel secretly planned simultaneous operations with the British and French, the latter two to open the Suez Canal, and the former to attack Sinai.
Operation Kadesh was wholly fought between Israel and Egypt. The entire campaign lasted 100 hours from when Israel invaded Egyptian held Sinai on 29 Oct 1956 until 1 Nov when the IDF forces had stopped 10 miles short of the Suez Canal (as agreed with the British and French). The war officially ended on 7 Nov when the UN imposed a ceasefire.
Shimon Peres described it as “one of the most brilliant [operations] of all time” however, the historian Van Creveld (1998) points out that its scale – two Divisions over 5 days – perhaps does not warrant this enthusiasm.
References
Van Creveld, M. (1998). The Sword and the Olive: A critical history of the Israeli Defense Force. New York: Public Affairs.