This is actually a bug with Joomla! 3.2.0 and the new password hashing which is –unfortunately– enabled by default. The gory details and the patch which the Joomla! developers are working on to fix this bug can be found at https://github.com/joomla/joomla-cms/pull/2589
Please, please, I implore you, do test this patch. We need more people providing feedback, ideally those who are affected by this bug, i.e. you. I have already had another client test the same patch with success. We need more testers to confirm that it actually works and release Joomla! 3.2.1 as soon as humanly possible.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!