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Verifiable Computation for Approximate Homomorphic Encryption Schemes

Authors:
Ignacio Cascudo , IMDEA Software Institute
Anamaria Costache , NTNU
Daniele Cozzo , IMDEA Software Institute
Dario Fiore , IMDEA Software Institute
Antonio GuimarĂ£es , IMDEA Software Institute
Eduardo Soria-Vazquez , Technology Innovation Institute
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Conference: CRYPTO 2025
Abstract: We address the problem of proving the validity of computation on ciphertexts of homomorphic encryption (HE) schemes, a feature that enables outsourcing of data and computation while ensuring both data privacy and integrity. We propose a new solution that handles computations in RingLWE-based schemes, particularly the CKKS scheme for approximate arithmetic. Our approach efficiently handles ciphertext arithmetic in the polynomial ring $R_q$ without emulation overhead and manages ciphertexts maintenance operations, such as modulus switching, key switching, and rescaling, with small cost. Our main result is a succinct argument that efficiently handles arithmetic computations and range checks over the ring $R_q$. To build this argument system, we construct new polynomial interactive oracle proofs (PIOPs) and multilinear polynomial commitments supporting polynomials over $R_q$, unlike prior work which focused on finite fields. We validate the concrete complexity of our approach through implementation and experimentation. Compared to the current state-of-the-art on verifiable HE for RNS schemes, we present similar performance for small circuits while being able to efficiently scale to larger ones, which was a major challenge for previous constructions as it requires verifying procedures such as relinearization.
BibTeX
@inproceedings{crypto-2025-35621,
  title={Verifiable Computation for Approximate Homomorphic Encryption Schemes},
  publisher={Springer-Verlag},
  author={Ignacio Cascudo and Anamaria Costache and Daniele Cozzo and Dario Fiore and Antonio GuimarĂ£es and Eduardo Soria-Vazquez},
  year=2025
}