FHE enables computations on encrypted data, but ensuring the authenticity and integrity of the resulting ciphertexts remains a significant challenge.

This internship aims to investigate ciphertext-level homomorphic authentication mechanisms, where authentication information is bound to the exact representation of encrypted ciphertexts and evolves alongside authorized homomorphic computations.

The research will initially focus on the lattice-based GSW encryption scheme, exploring the compatibility of authentication techniques with operations such as ciphertext addition, multiplication, and gadget-based transformations.

Particular attention will be given to the correctness and security of these mechanisms, including the distinction between legitimate ciphertext transformations and unauthorized modifications. The objective is to identify promising cryptographic constructions and investigate their feasibility through theoretical analysis and experimental evaluation.

As an intern at the CEA, you will have the opportunity to work within a world-renowned research environment. Our teams consist of passionate and dedicated experts, providing an ideal setting for learning and collaboration. You will have access to state-of-the-art equipment and top-tier research resources to carry out your assignments. The work conducted may potentially lead to a scientific publication.

Context :
Fully Homomorphic Encryption (FHE) enables computation directly on encrypted data, without revealing the underlying plaintexts. This capability is particularly relevant to privacy-preserving cloud services and secure data processing. However, conventional FHE schemes primarily address confidentiality: their intentional malleability does not, on its own, guarantee that an untrusted evaluator returns an authentic result of an authorized computation.

Homomorphic signatures and message authenticators provide a promising direction, as they permit authentication evidence to be updated after certain computations. Adapting such mechanisms to FHE is nevertheless challenging. The objects to be authenticated are structured ciphertexts and not plaintext messages. An ordinary signature on an input ciphertext cannot simply remain valid after the ciphertext changes.

Internship Subject
The objective of this internship is to investigate the feasibility of homomorphic authentication mechanisms that bind authentication information to the exact representation of HE ciphertexts and allow that information to evolve under supported homomorphic operations. The resulting verification procedure should check that a claimed output ciphertext is consistent with authenticated inputs and a declared, authorized computation, without requiring decryption.

Central question : Can authentication tags attached to HE ciphertexts be transformed alongside ciphertext evaluation, while retaining meaningful correctness and forgery-resistance guarantees?

What do we expect from you?

• A focused review of prior approaches and a clearly defined ciphertext-level authentication goal.
• A candidate construction, adaptation, or well-supported feasibility/limitation analysis for GSW ciphertext operations.
• A reproducible prototype with benchmarks and tests for unauthorized modifications, covering at least basic operations where feasible.
• A final research report outlining technical results, unresolved questions, and potential extensions.

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