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For reverse calculation of CRC checksums, there is a pretty nice tool – CRC reveng.

I was looking for, and have not found, a similar tool that can do the same for non CRC checksums. For example, using Xor, Sum, bit-shift action for the single bits or nibbles to get the given checksum.

Does anyone know about such a tool that can do this job?

In my case I have just 5 nibbles of data that are calculated into 1 nibble of checksum, but there is an algorithm behind which I was not able to reverse by myself. And I have a large set of data that can be used to accept or refuse proposed algorithms.

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The OA Labs hashdb project has a general framework for this, though it's primarily aimed at strings. Nonetheless, it does have a hefty list of algorithms implemented and an easy way to run them against data that might be useful to you.

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There’s this project which has a few more variations beyond CRC:

https://github.com/8051Enthusiast/delsum

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