Is the FIPS validation tied to a specific operating system or to a CPU processor?
Yes and no. The validation has to specify at least one “platform” (hardware and O/S). However, NIST/CSE have stated that a validation obtained on one platform remains valid for another, provided that the validated software was merely recompiled (no source modifications) for the new platform. Note that the OpenSSL validation will be for binaries generated from source, not for a specific runtime executable. OpenSSL is portable code and, with only one significant exception, that same code compiles on multiple platforms. The exception is the x86 processor for which the FIPS Object Module uses several x86 specific assembly language optimizations within the FIPS 140 cryptographic module. Also see Questions #10 and #11.