So I tried to gather some more insight about this chip from the printers firmware.
Using the keys and firmware extraction tools from this repo
https://github.com/blasty/lexmark I was able to decrypt the latest CS310dn firmware (I guess that this should work for almost all lexmark printers).
I was able to extract the linux kernel image and the filesystem of the printer.
The kernel image is compiled with some debug infos and decompiling it with Ghidra gives some good results.
The linux kernel contains a lot of lexmark specific function extensions, including many functions prefixed with "pnsv" (which stands for pensive). I could not find much about this subsystem but I strongly suspect that it is the subsystem for communicating with the cartridge chips, as it has functions like
pnsvCartAuthenticate0 to 6, and functions like
pnsvIncrementCounter and similar. It also features a lot of functions to authenticate cartridges and verify signatures.
The code seem to support different type of cartridges types with different memory sizes. The chips can have different regions: Readonly, Bit fields, Read-Write, Encrypted, Counters, ECC Sigs.
For some reason lexmark decided to statically link most of thesere higher lever interface to the pensive subsystem into the kernel image, while the physical communication is handled in its own kernel module, which is loaded during the initramfs.
For my legal understanding this should also mean, that all statically linked code is GPL licensed like the linux kernel itself. That should also mean that lexmark has to disclose/provide the source code of these pnsv* functions. I tried to contact the lexmark support, but no luck so far.