Almost every day now Israelis hear Mr Abu Zaideh's perfect Hebrew articulating the Palestinian position on the peace agreement. 'I learnt Hebrew in jail. I speak it better than an Israeli,' he boasts. 'I always thought it was important to know the language of the enemy. Now it is useful to talk about peace.'
While escalating violence has weakened faith that the peace agreement will hold up, Mr Abu Zaideh at the headquarters of the Palestine Liberation Organisation in the Gaza Strip remains confident. The deadline of 13 December may be put back a week or two, but of one thing he is sure: 'It will happen.'
'It is hard for people to believe in it all while the occupation still goes on. But when people see the Israeli army leaving the place, when they see Palestinian police coming in, when they see Palestinian institutions here, they will feel better. They will believe it.'
Mr Abu Zaideh last week met his former jailer, Matan Vilnay, the general heading Israel's southern command, to discuss security in the Gaza Strip. Yasser Arafat, chairman of the PLO, is regularly on the telephone to his Gaza office.
Mr Arafat has received strong criticism for the leaders he has chosen to prepare the way for self-rule in the Gaza Strip and Jericho. It is said he is choosing his team through political patronage rather than picking professionals and technocrats.
In the occupied territories, ex-prisoners are overseeing the transfer of power for 1.8 million Palestinians. As the deadline approaches, the result is confusion. But Mr Arafat did not chose Mr Abu Zaideh and the other Gaza leaders because of bureaucratic abilities. He chose them because of proven loyalty and their ability to read the situation.
A refugee whose family fled from the village of Brair, near Beer Sheva, during the 1948 Arab-Israeli war, Mr Abu Zaideh, 33, lives in Jabalya camp. He has been jailed five times by the Israelis since 1978. He knows as well as anyone what it takes to maintain support for the peace deal in Gaza.
'Unfortunately people expected a lot of changes the minute the deal was signed. They haven't seen any. They lose hope when they see the Israelis still here. When they see Palestinians arrested and killed. But the Palestinian people want peace. We have to tell them to wait. Since the agreement we have political meetings for the first time. We are able to explain to the people what is happening. In the past the Israelis prevented us from doing this.'
Mr Abu Zaideh also understands the mood of the gunmen and is in touch with the political prisoners. He knows how best to defuse the opposition of Hamas, the Islamic Resistance Movement, which is trying to sabotage the peace deal by continuing attacks against Israelis.
'Hamas will be active until the implementation of the agreement on the ground. Then when they see the success of the agreement Hamas will stop their activities because they will lose support. Then Arafat will have to offer them some role inside the Palestinian authority. They know they cannot wage a war against the new Palestinian authority. They are fighting now not because they object to the agreement, but because they know its success will be the end of Hamas.'
Taking on a political role has not been easy for the 'revolutionaries,' Mr Abu Zaideh concedes. The old lawless ways are sure to die hard in Gaza and rivalry among the emerging leadership has already brought two political assassinations in Gaza since 13 September. He knows his decision to give up the 'armed struggle' has brought accusation of 'selling out' from the Palestinian opposition, particularly refugees outside the occupied territories who stand to gain little from the deal. But he knows he also knows has made his sacrifices. .
'In the past we used to fight against the occupation. We thought we could only bring it down by force. I learnt many things with age. Now we are doing it through political ways. We hope to solve the problems of all Palestinian people eventually. If you have the opportunity to solve the problems of part of the Palestinian people we should take it.'