Some positive statements made by both sides ahead of the Aceh peace talks, which resume today, suggest a historic agreement may be in the making.

Indonesian Vice-President Jusuf Kalla told this newspaper last week he hoped a deal could be struck by July, bringing almost 30 years of conflict to an end. A spokesman for the Free Aceh Movement (GAM) later expressed cautious optimism about the negotiations. He said the rebel separatist movement expected "something positive" to be achieved.

These constructive statements reflect the momentum for peace that has been building since December's tsunami. Aceh was the biggest victim of the disaster.

The huge relief effort that followed has brought the troubled province under renewed international scrutiny. Both the government and the rebels seem to appreciate that the ambitious reconstruction plans for Aceh currently taking shape will be hindered and possibly frustrated unless a peace deal is struck.

But there are some very big obstacles to overcome if the negotiations are going to be successful. The first two rounds of talks earlier this year have brought the two sides closer. GAM has accepted that the talks will go nowhere if it pushes for independence. It has sensibly agreed to focus on "self-government" instead, although this term has not yet been defined.

Jakarta prefers to talk about "special autonomy" for the province, a description which at least some of the rebels do not find acceptable, as some of them made clear yesterday.

In practice, it should not matter what the arrangements are called. It is much more important to develop a detailed plan and to start with areas upon which the two sides are able to agree. The priority must be to build trust.

Key issues are expected to be discussed in Helsinki over the next six days.

They include the crucial self-governance question, but also security arrangements – including the withdrawal of Indonesian troops. Future economic ties and the monitoring of any peace deal are also likely to feature. There is a hope that a political solution based on democratic elections for Aceh's government will be found. That would involve changing the law to enable GAM to stand – paving the way for it to become a political party instead of a rebel movement.

But the diehards in each camp must be persuaded to accept the need for such a solution. It remains to be seen how much control GAM's exiled political leaders in Sweden have over rebel forces on the ground in Aceh. And the Indonesian government must not allow the vested interests of military leaders – who have much to gain from a continued presence in the province – to prevail.

The road ahead will be rough but the talks do offer the chance that something positive could emerge from the terrible tsunami. Both sides should do all they can to make sure the negotiations succeed.