I need to find out if a commit belongs to a particular git repository.
The idea is to generate some unique id for every repository I need to test. Then I can compare this unique id to the id, calculated from tested commit.
For example take an SHA of initial change set. Can it uniqely identify the repository?
The SHA1 key is about identifying the content (of a blob, or of a tree), not about a repository.
If the content differ from repo to repo, then its history has no common ancestor, so I don't think a change-set-based solution will work.
Maybe (not tested) you could add some marker (without having to change all the SHA1) through git notes.
See for instance GitHub deploy-notes which uses this mechanism to track deployments.