"Indonesia is increasingly assertive. It's getting economically stronger. It's been internationally recognized more than it used to be, and in many ways it's a lot more confident than it has been in the past," said Damien Kingsbury, an expert on Indonesia politics at Australia's Deakin University.
Indonesia is not only an important trading partner, but under Yudhoyono's leadership it has been a champion of Australia in regional forums that are crucial to achieving cooperation in problems such as terrorism, people-smuggling, money laundering and other forms of transnational crime.
Analysts agree the phone-tapping revelations from National Security Agency leaker Edward Snowden have brought relations to their lowest point since Australia led a U.N. military force into the former Indonesian province of East Timor in 1999, following a bloody independence ballot. Indonesia ripped up a security treaty with Australia at the time, though the countries have since signed another.
On Friday, more than 400 hard-line Muslims hurled bottles, tomatoes and eggs at the gate of the Australian Embassy in Jakarta to protest the alleged wiretapping. They burned replicas of the U.S. and Australian flags while chanting for the Australia ambassador to be expelled, South Jakarta Police Chief Col. Wahyu Hadiningrat said. He said nearly 500 policemen were deployed to protect the embassy, which has been closed for two days.
Abbott, who won government at elections in September, has not endeared himself to Indonesians during his brief time on the world stage.
One of his campaign promises was to stop asylum-seekers from many countries who attempt to reach Australia by boat from Indonesia. His policies include towing the boats back to Indonesia, buying Indonesian fishing boats before the people-smugglers could acquire them and paying Indonesian villagers for intelligence about smuggling operations.
Indonesian lawmakers' complaints that the new policies contravened Indonesian sovereignty were ignored, although there is no evidence that the Abbott government has implemented any of them yet.
Abbott attempted to emphasize his regard for Indonesia by making his first trip abroad as prime minister to Jakarta, but then alienated Indonesian media by excluding them from a press conference.
On Thursday, Abbott promised to respond "swiftly, fully and courteously" to a letter from Yudhoyono demanding an explanation for the wiretapping, but so far he has been making his statements on the issue to the Australian Parliament.
After Papua New Guinea, Indonesia is Australia's closest neighbor. But socially and politically, the two countries can seem worlds apart.
Indonesia is a sprawling and culturally diverse archipelago of 240 million people, the world's fourth-most populous nation and third-biggest democracy. Australia is big in terms of area but has just 23 million people.
Australia's economy remains larger than Indonesia's, but the economic balance is shifting.
"Today things are very, very different," said Tony Milner, an Australian National University expert on the bilateral relationship. "Without a doubt, Indonesia is more important to Australia than the other way around."
The countries have not always sided with each other since 1949, when Indonesians learned that they had officially become an independent republic via Radio Australia.
Australian troops fought Indonesians in the jungles of Borneo when Australia sided with Malaysia in a conflict with Indonesia in 1965 and 1966. But Australia was one of the few countries that legally recognized Indonesian sovereignty over East Timor after Indonesia invaded the former Portuguese colony in 1975.
Five Australia-based television newsmen where killed in the East Timor invasion. Indonesia maintains they were killed in crossfire, while an Australian coroner found there were deliberately shot by Indonesian soldiers.
Australian journalists were barred from Indonesia for several years over negative press in 1986 about then-dictator Suharto's business dealings.
Relations in recent years have been more positive. With Indonesia's help, Australia and New Zealand were included in a free-trade deal with the 10-member Association of Southeast Asian Nations, a regional bloc with a population of 640 million. Indonesian-Australian cooperation on counterterrorism has thrived since bombings on the resort island of Bali in 2002 killed 202 people, including 88 Australians.
Experts agree that the Bali Process Australia's main forum for fostering Southeast Asian cooperation to prevent people-smuggling, trafficking and transnational crime it would not have anything like 45 member nations if not for Indonesia's pivotal support.
But there have been other rocky moments. In 2006, Yudhoyono recalled the Indonesian ambassador for a few weeks to protest Australia giving asylum to 42 West Papua refugees who feared persecution from the Indonesian military.
Kingsbury, the Deakin University expert, said that with its response to the phone-tapping reports, Australia has "lost an important partner."
"Yudhoyono certainly has been our friend, but we don't have too many other friends in Jakarta and indeed, he's put himself out on our behalf and feels he's been made a fool of," Kingsbury said.
Kingsbury sees Indonesian elections next year as an aggravating factor.
"The fact that Indonesia is the aggrieved party in this and that this has directly touched on this well-developed sense of national pride and defensiveness is playing very badly," he said. "By not apologizing or not making some significant gesture of redress, Abbott is playing directly into the hands of the nationalists who are lining up ahead of next year's elections."
Kurt Campbell, former U.S. assistant secretary of state for East Asia and the Pacific, told Australian Broadcasting Corp. that the relationship will eventually recover, but "very little you can say now or do is going to ease the next couple of months."
Milner said the furor reminded him of something a senior Indonesian figure told him: "Indonesia is your bridge to Asia."
"That's worth thinking about," Milner said. "Bridges can be taken away."
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AP Writer Ali Kotarumalos in Jakarta, Indonesia, contributed to this report.
