The question mentions FIPS 140-2 Level 3 compliant. I answer this as if the question had said the intent is to validate the product as FIPS 140-2 Level 3. This may sound like hairsplitting, but there are many modules claiming to be FIPS 140-2 compliant, which factually could not be validated without large changes to functionality.
FIPS 140-2 really intends to use wellknown and proven algorithms like AES, Triple-DES, RSA, DSA, etc. in addition, the key lengths have been restricted so that the algorithm strength should be equivalent to 112-bit symmetric encryption algorithm or better.
The detailed set of algorithms accepted are given in FIPS 140-2 Annexes A,
D, and in Implementation Guidance. Annexes generally list acceptable FIPS/NIST standards and Implementation Guidance allows use of certain standards and schemes beyond.
There does not appear to be any ZKA or homomorphic schemes in any of these resources.
The ways to have new cryptographic schemes allowed or accepted in FIPS 140-2 module include:
If the scheme is based on established cryptography algorithms, and the
non-approved algorithm can be considered as some form of data
formatting or data transformation.
Maybe this algorithm is used for a specific area allowing some other algorithms in FIPS 140-2 module. One problem where other algorithms are reasonable is Split knowledge procedure for manually entering keys.
Implementation Guidance is based on questions asked from NIST and
their answers, so new allowed schemes can occasionally get approved.
So you could ask them. The process is very slow.
Wait for NIST to write NIST SP 800 or FIPS document on standard you're
interested in and add it to one of Annexes.
None of these options currently clearly allow the algorithms you're interested in, but in the most cases these are the valid options.