As stated in the title
Yes, and it is already implemented for all common FHE schemes in OpenFHE. The encryption in FHE can be done either using a secret key (has lower computational complexity and noise) or using a public key. API for secret-key encryption for SIMD (RLWE-based) schemes: openfhe-development/src/pke/include/cryptocontext.h at v1.4.0 · openfheorg/openfhe-development · GitHub
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