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Usually both files are availble for running some diff tool but I need to find the differences in 2 binary files when one of them resides in the server and another is in the mobile device. Then only the different parts can be sent to the server and file updated.
There is the bsdiff tool. Debian has a bsdiff package, too, and there are high-level programming language interfaces like python-bsdiff.
I think that a jailbreaked iPhone, Android or similar mobile device can run bsdiff, but maybe you have to compile the software yourself.
But note! If you use the binary diff only to decide which part of the file to update, better use rsync. rsync has a built-in binary diff algorithm.