OAuth signature signing fails on the tool provider side when the LTI activity or Full Site name has long name (containing space characters). The reason is that when signing the parameters in locallib.php:lti_build_request() , few of the parameters are trimmed and html_to_text() function is used. This way, if for example the course->fullname is
'test test test test test test test test test test test test test test test test test test test test'
, when building the params this gets converted to:
'test test test test test test test test test test test test test test test
test test test test test'

This all leads to a difference between the base_string, which is signed in Moodle and the one, which is sent to the Provider. I've reproduced it with Course Name and Full Site Name, but pretty sure it can be reproduced with other params, which are built using html_to_text() (search for that function in locallib.php).