# Verifiable Computation for Approximate Homomorphic Encryption Schemes

Ignacio Cascudo, Anamaria Costache, Daniele Cozzo, Dario Fiore, **Antonio Guimarães**, Eduardo Soria-Vazquez (authors in alphabetical order)

*Advances in Cryptology – CRYPTO 2025, Santa Barbara* (conference, 2025).

Links: [PDF](https://eprint.iacr.org/2025/286.pdf) · [ePrint](https://eprint.iacr.org/2025/286) · [DOI](https://doi.org/10.1007/978-3-032-01907-3_21) · [Video](https://www.youtube.com/watch?v=nAdAs56TxvE) · [BibTeX](https://antonioguimaraes.org/publications/verifiable-approximate-he/cite.bib)

Canonical page: https://antonioguimaraes.org/publications/verifiable-approximate-he/

## 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

```bibtex
@inproceedings{C:CCCFGS25,
  author    = {Ignacio Cascudo and Anamaria Costache and Daniele Cozzo and Dario Fiore and Antonio Guimarães and Eduardo Soria-Vazquez},
  title     = {{Verifiable Computation for Approximate Homomorphic Encryption Schemes}},
  booktitle = {Advances in Cryptology – CRYPTO 2025, Santa Barbara},
  year      = {2025},
  doi       = {10.1007/978-3-032-01907-3_21},
  url       = {https://eprint.iacr.org/2025/286}
}
```

Topics: Homomorphic encryption, Verifiable FHE