Groucho Marx famously quipped: "Those are my principles, and if you don't like them … well, I have others." The International Quartet (the US, the UN, Russia and the EU) has long applied three principles Hamas must adopt to take part in negotiations. It must renounce violence, recognise Israel and abide by previous agreements between Israel and the Palestinians. At no point has Hamas satisfied these conditions – or indicated any intention to do so.

Those who advocate talking to Hamas are urging a Groucho-Marxist policy in a complex, unstable region. If Hamas is too extreme to accept these principles, they argue, we must tailor our principles to match Hamas's extremism.

The Hamas charter advocates the destruction of the state of Israel, the genocidal slaughter of Jews and the imposition of an Islamic state governed by sharia law. When an organisation's constitution venerates your murder, it is difficult to know how negotiations should begin – perhaps with a discussion of the flowers for one's funeral.

This week marks the fifth anniversary of Israel's disengagement from Gaza. We withdrew every Israeli soldier and citizen, gambling on the formula of land for peace. Instead of peace and progress we received missiles and misery. Hamas made Gaza a terrorist enclave, launching thousands of missiles at Israeli civilians.

In 2006 it kidnapped Gilad Shalit, holding him in isolation for four years without a single visit from the Red Cross. In a bloody coup in 2007 Hamas attacked its own people, chasing Fatah out of Gaza and hurling its Palestinian brothers from the rooftops. It imposed an Islamic penal code along with the routine torture and execution of political opponents. Simultaneously it relentlessly attacked Israelis and, with Iranian support, stockpiled weapons that today can hit Tel Aviv.

After years of missiles, the bombardment became unbearable. We targeted the terrorist infrastructure through Operation Cast Lead. Israel has tried to stop the flood of weapons through a naval blockade. When Hamas supporters attempt to break the blockade, as occurred with the Turkish IHH flotilla, Israel's defensive measures must be understood in context. Hamas recently fired a Grad missile at Ashkelon and dispatched a terror cell from Gaza into Sinai that fired missiles at Eilat in Israel, and Aqaba in Jordan: Hamas threatens not only Israel but also Egypt and Jordan.

Some in the west fondly refer to Hamas as the elected representatives of the Palestinians. While Hamas won the Palestinian council elections in 2006, it was not a mandate to violently overthrow the Palestinian Authority. Nor does it justify terror against Israel. Hamas's concept of democracy fits that of all democratically elected dictatorships – "one man, one vote … once".

Gaza was a golden opportunity tragically missed. Instead of building a Mediterranean Dubai, Hamas diverted every resource to enslaving its people while attacking ours. In contrast, Israel and the PA have made significant progress in the West Bank, reducing roadblocks, easing access and stimulating economic growth of 8%. The PA should be encouraged to build on these developments at the negotiating table.

Israel has offered direct talks, recognised a two-state solution and introduced an unprecedented moratorium on settlement construction. President Abbas has declined talks, preferring to campaign against Israel internationally. In Palestinian classrooms and civil society incitement against Israel continues.

Our experience following the Gaza pull-out has scarred the Israeli public. Hamas's missiles wounded the concept of land for peace, increasing Israeli fears and scepticism. Of the same voters who elected governments that signed peace treaties with Egypt and Jordan and initiated the Oslo Accords, only 32% believe talks with the Palestinians will lead to peace. More than ever, Israelis require confidence-building measures.

When Israelis feel secure concessions follow. Last weekend Israel dismantled the security barrier in Gilo, a Jerusalem suburb that came under heavy Palestinian sniper fire during the second intifada. If in Gilo no sniper fire means no wall, so in Gaza no missiles would mean no blockade. It is that simple.

Sadly Hamas has always torpedoed peace efforts through suicide bombings, kidnappings and missiles. If further steps towards peace are to win Israeli hearts and minds, the price cannot be missiles and mortars in the heart of Israel.