The story of Kaifeng's Jewish community, which numbers between 300 and 900 (depending on who you talk to), is an object of fascination among Chinese and Jews alike. It has spawned dozens of newspaper stories and even research departments at universities, some helped by overseas donations. Established after the resumption of diplomatic ties between the mainland and Israel in 1992, the Nanjing University Institute of Jewish Studies changed its name in 2006 to the Glazer Institute of Jewish Studies, following donations by wealthy American real-estate developers Guilford and Diane Glazer.

The story goes like this: about a millennium ago, a small tribe of Jews left the Holy Land on an arduous 7,000km voyage to China, where they settled in the flourishing Northern Sung capital of Kaifeng. Here they made their homes in Pluck the Sinews Lane (a reference to the Jewish practice of removing sinews from meat before cooking), built a temple, traded, joined the Confucian scholar hierarchy, inter-married and assimilated.

Or did they?

In a bold new theory, Hong Kong University historian and Judaic scholar Zhou Xun says the established story of Kaifeng's Jewish community is a 'hoax'. Her research suggests the Jews of Kaifeng are at best deluded, or may be exploiting a status they don't deserve.

Underpinning her controversial idea with historical irony, Sichuan-born Zhou - who gained a master of arts degree in Judaic studies at the Hebrew University in Jerusalem and wrote her thesis at the University of Oriental and African studies in London - says the Jews were really Muslims, and that the whole theory arose over a misunderstanding by 17th-century Jesuit missionary Matteo Ricci - specifically, over a hat.

According to Ricci, Kaifeng scholar A Tian visited the Jesuit Mission in Beijing in 1605. There, A Tian told Ricci he belonged to a religion that believed in the one true God, yet was not a Muslim. That statement, plus other clues, led Ricci to decide that a blue hat worn by A Tian identified him as a Jew, since Muslims wore white hats.

Later, says Zhou, that encounter was taken up by 19th-century Protestant missionaries schooled in the popular story of the Lost Tribes of Israel, the 10 tribes cast out of their homeland by the Assyrians some 2,700 years ago.

The missionaries hoped China's Jews, cut off from the Middle East for centuries, might own an uncorrupted version of the Scriptures. They also hoped it would be easier to convert Jews to Christianity than Buddhists, who were proving hard to convince. First of all, they had to persuade the Chinese themselves they were Jewish.

Unfortunately for the Christians, says Zhou, a fact-finding mission to Kaifeng ordered by the Anglican bishop of Hong Kong in 1850 failed to find any evidence of a Torah. Undaunted, a second trip was planned.

'The 'miracle' happened on July 20, 1851,' says Zhou. This time, Chiu Tiansheng and Chiang Jungchi, two emissaries of the London Missionary Society, brought back Torah scrolls and two Jews, although they were reluctant to confirm the scrolls had anything to do with the Kaifeng community.

'It is very likely that these scrolls were copied down locally in Kaifeng, under the instruction of the two delegates,' says Zhou. 'For the locals in Kaifeng, a place of overwhelming poverty, selling fakes to westerners had become a reasonably profitable business.'

Other key evidence of Kaifeng Jewry includes two stone pillars, or steles, that reportedly date from the 15th and 17th centuries. Only one survives. There are photographs of them in an unofficial museum set up by Zhang. Engraved with accounts of religious stories, Jewish rituals and details of their Kaifeng temple, they are said to also contain reports of the Torah scrolls. The surviving stele is in the Kaifeng Museum, but its script is faded and unreadable. Calls to the museum are fruitless; it is closed for renovation. The second stele has not been seen since it disappeared from the gates of an Anglican church in the early part of last century, after the synagogue site was sold to Christians in 1912. Anyway, says Zhou, neither stele has ever been scientifically dated.

Despite that, the Jews of Kaifeng have grown in reputation and a small, but growing, trickle of emigration to Israel has begun. Although Zhang is content to wait for death before fulfilling his dream of going 'home', others are not.

Yecholya Jin, 24, is one of four young women who left for Israel in 2006, helped by Shavei Israel, or Israel Returns, a Jerusalem-based organisation active around the world in its search for the lost tribes. Once there they were all 'made aliya', or converted, since Israel's powerful Rabbinical courts did not automatically recognise them as Jews. China's is a patriarchal society and Jewishness can only be handed down the female line.

All converted successfully. Michael Freund, the founder of Shavei Israel, says Jin ran circles around the rabbis. When they challenged her chosen name, Yecholya, she pointed to where it appeared in a little-known book of the Scriptures, and to what it meant: 'God can do anything.'

Today, Jin lives in Jerusalem, where she is studying for her university entrance exams. She has no plans to return to the mainland, though she left her parents and younger sister behind in Kaifeng. 'This is my home now,' she says. 'Since I was very small my father told me I was Jewish. Our family didn't eat pork, we had a mezuzah [parchment inscribed with Hebrew verse] on the door and our gravestones were different from other people's. My parents really supported me in returning 'home'.

'I like it here. Israel is an immigrant country and people come from everywhere and treat you well. You can learn a lot.'

Like all the Kaifeng Jews, Jin had little to go on to confirm her ancestry beyond her father's statement that she was Jewish.

'All they had is that one sentence,' says Freund. 'It's fascinating how through the transmission of that sentence they were able to keep alive the spark of Jewish consciousness.'

Kaifeng is an hour's drive east of Henan's capital, Zhengzhou. It's an unlovely place, despite having been capital of several Chinese dynasties. Its roads are lined with broken paving stones and most of its buildings are dirty.

Kaifeng-born Shi Lei, 30, says he just 'knew' he was Jewish. He speaks fluent Hebrew, having studied for three years at Bar-Ilan University, in Israel. 'My family always told me I was Jewish.'

Shi is momentarily floored by Zhou's theory but rises to the debate. 'That's ... quite brilliant,' he says. 'Maybe A Tian was Muslim. But for me, I'm quite sure I am a Jewish descendent.'

Zhou's theory has angered overseas Jews. US-based Beverly Friend, executive director of the China Judaic Studies Association, likened it to Holocaust denial. 'If anything is a hoax, I think it is this article, and you can quote me on that,' Friend fumes in an e-mail.

Yet on the ground in Kaifeng, the Jews exist in a limbo of hope and loss. In large part, this is because they have no synagogue to provide focus. Henan authorities have blown hot and cold on the issue, tempted by the opportunities for tourism yet scared off by the political sensitivities. For years, says Zhang, police harassed him, warning him off Jewish activities. The government recognises just five religions - Buddhist, Daoist, Muslim, Catholic and Protestant - and while the authorities tolerate religious activity by overseas Jews in Shanghai, Beijing and other major cities, experts says it is unlikely they will permit the building of a synagogue for native Chinese.

Professor Xu Xin, doyen of Chinese Jewish studies and head of the Nanjing institute, has long urged the authorities to allow a synagogue and help the community revive. 'It [would] show a positive side of Chinese culture, that [Jews] were never persecuted here, it shows China is a multiethnic and multicultural society, in a way.'

The political sensitivity of the topic is reflected by Zhang's skittishness as we tour old Kaifeng. He was born in 1947 in what is today known as Jiaojing hutong, or Teach the Scriptures Lane, a narrow, long path lined with rundown houses. His childhood home houses several families and looks like a slum. 'When I was born, it was called Tiaojing hutong [Pluck the Sinews Lane].'

Some scholars say it is unlikely such a name would have been made up by Protestant missionaries, who would have thought it derogatory.

Two lanes away from the former Jewish quarter is the modern Muslim quarter. These days, Zhang doesn't normally bring visitors to the Great Eastern Purity mosque. '[The police] are very worried about ethnic harmony,' he says.

Inside the rambling, flower tree-filled compound, Zhang points at two lines of blue tiles on a green-tiled roof and whispers: 'They stole them from our synagogue, you know.'

Outside, among the crowding ranks of peddlers, he greets the Imam. Zhang, born and raised in these streets, knows everyone. Back then, he says, Jews and Muslims lived next door to each other and got on well.

Several kilometres away in Millennium City Park, a Northern Song theme park, Zhang has set up the Kaifeng Jewish Culture Museum in a two-storey courtyard-style house. The museum has thrived under the protection of the park owner, a rich businessman Zhang declines to name. All requests to the government to set up a museum on state-owned property have been rejected.

Shi Lei's father, Shi Xinguang, also runs a private museum about the mainland's Jews. In two small rooms in a modern brick courtyard of the old family home - about to be demolished - the exhibits consist mostly of photographs and include one from the mid-20th century taken to commemorate the Muslim festival of Eid. It shows rows of young men in front of a banner belonging to the 'Central-South Muslim and Jewish Academy'.

Shi Lei believes there are about 900 Jewish descendants in Kaifeng, though - curiously - he claims to have never heard of Zhang Xingwang. Shi's quest to revive his religious identity was prompted by contact with overseas Jews, and he was full of curiosity and buoyed by his growing sense of Jewishness when he arrived at university in Israel - only to be confronted by a shock.

'It was like being hit by a big hammer, or having cold water thrown on me,' says Shi, who was 23 at the time. 'Everyone said to me, 'You're not Jewish', because if your mother isn't a Jew then you're not a Jew. But in China, everything is passed down through the father's line.'

Rabbi Seth Farber runs Itim, the Jewish Life Information Centre, which helps navigate rabbinical bureaucracy. Despite success stories such as that of Jin, Farber says it's hard for Kaifeng's Jews to immigrate. Although the 1971 Law of Return declared anyone who could prove his grandparents were Jewish had the right to Israeli citizenship, in practice the bar is set much higher by the official Rabbinate, which is suspicious of imposters.

Two types of people from China contact Itim for help proving Jewish ancestry; women who want to marry Israelis and Kaifeng Jews.

'Every once in a while we get a call or an e-mail, about four or five a year. We tell them we're all for helping them but in the absence of proof that you are a member of the world Jewish community it's hard to grant them that status.'

Tudor Parfitt is professor of modern Jewish studies at London University's School of Oriental and African Studies. He has written extensively on the Lost Tribes and says colonists and missionaries imagined Jewish communities everywhere.

'Anywhere where you get Protestant missionaries in a quasi-colonial context you're going to have the construction of Jewish identity as part of the whole symbiosis between occupied and occupier,' says Parfitt. 'They would find all kinds of behaviour that they found weird and would then decide was Biblical, and so Jewish.'

Whatever the truth about the Jews of Kaifeng, one thing is for sure: spurred by a steady flow of visitors from the US, they are learning how to be Jewish again.

'When I was at school my Jewish ancestry was not so important to me,' says Shi. 'But as I started to meet more and more Jewish visitors I began to learn more and realise it is in my blood. Basically you can say the Jewish descendants are on a learning curve. They are picking up what we have forgotten in previous generations.'