Aceh is the only province in the Muslim-dominated country to adhere to sharia, Islamic law, which puts it at odds with other provinces where the vast majority of the population practices a moderate form of the religion.
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"Non-Muslims can choose whether to be tried under sharia law or the regular Indonesian criminal code," said Syahrizal Abbas, head of the sharia legal department in the provincial government.
The new law also criminalises rape and sexual harrassment. Those found guilty could face 40 lashes or more, according to a copy of the legislation seen by Reuters.
Rights groups warned the new law could criminalise consensual sex and create hurdles to reporting rape.
"To punish anyone who has had consensual sex with up to 100 lashes is despicable," Josef Benedict, Amnesty International's South East Asia campaigns Director, said in a statement.
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"This is a flagrant violation of human rights and must be repealed immediately."
Aceh was granted special autonomy in 2005 as part of an agreement with Jakarta to end decades of separatist violence - and was then able introduce sharia.
Earlier this year, a district in Aceh enacted a bylaw requiring schools to teach boys and girls separately, and another banned women from straddling motorcycles when riding with a driver.
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