Zero-Knowledge Federated Learning (zkFed)

• Zero-Knowledge Federated Learning (zkFed) is a family of protocols that integrate zero-knowledge proofs into federated learning to validate model updates and aggregation without exposing private inputs.
• zkFed systems employ diverse cryptographic methods such as zk-SNARKs, interactive Σ-protocols, and commitment schemes to secure different workflow phases like local training and evaluation.
• zkFed improves trust by decoupling verifiability from privacy while addressing challenges related to computational overhead, circuit complexity, and proof scope limitations.

Searching arXiv for recent and foundational papers on zero-knowledge federated learning. arxiv_search.query({"search_query":"all:\"Zero-Knowledge Federated Learning\" OR all:zkFed OR all:zkFL federated learning", "start":0, "max_results":10, "sort_by":"submittedDate", "sort_order":"descending"}) Zero-Knowledge Federated Learning (zkFed) denotes a family of federated learning protocols in which zero-knowledge proofs are used to make some part of the federated process verifiable without disclosing the underlying private inputs. Across the literature, zkFed does not refer to a single canonical protocol, but to a design pattern applied to different layers of federated systems: local training correctness, update validity, aggregation correctness, ownership verification, evaluation privacy, and blockchain or decentralized consensus. In all cases, the central technical idea is the same: a prover in the federated workflow demonstrates that a specified relation holds—for example that an update satisfies an integrity predicate, that an aggregate was computed from the advertised inputs, or that a model is tied to a valid ownership credential—while revealing nothing beyond the truth of that statement. This shifts trust from organizational assumptions about servers, verifiers, or consortium participants to cryptographic soundness properties such as completeness, soundness, and zero-knowledge (Nguyen et al., 2022, Yang et al., 2023, Wang et al., 2023).

1. Scope and conceptual definition

zkFed arises from a structural tension in federated learning. FL avoids centralized raw-data collection, but many of its critical operations remain difficult to validate without exposing sensitive artifacts. Individual updates can leak information; robust aggregation rules often require visibility into local models; evaluation metrics can reveal properties of local datasets; and centralized or decentralized coordinators may manipulate aggregation, selection, or attribution. Zero-knowledge proofs are introduced to resolve this tension by allowing the system to verify a computation or predicate without disclosing the witness underlying that computation (Nguyen et al., 2022, Jin et al., 18 Mar 2025).

The literature uses the label in several distinct senses. In one line of work, zkFed means verifiable integrity of local updates under secure aggregation: clients prove that their encrypted update satisfies an attack-resilience predicate, while the server learns only the aggregate sum (Nguyen et al., 2022). In another line, zkFed means verifiable aggregation correctness: an aggregator proves that the global model or encrypted aggregate was computed exactly from the submitted inputs, often with commitments or signatures binding those inputs (Wang et al., 2023, Ahmadi et al., 2023, Zami et al., 17 Sep 2025). A third line uses zero-knowledge for ownership and provenance, where a federated model is bound to a digest derived from client credentials, and each client proves ownership of the deployed model by proving knowledge of a secret witness without revealing it (Yang et al., 2023). More recent work extends the pattern to evaluation privacy, where clients prove that their local loss is below a threshold without revealing the loss itself (Commey et al., 15 Jul 2025), and to client selection or consensus, where verified model performance determines participation or leader election (Jin et al., 18 Mar 2025, Fu et al., 17 Mar 2025).

This diversity suggests that “zkFed” is best understood as a cryptographic systems layer over FL rather than as a single architecture. A plausible implication is that the field is converging not on one universal proof target, but on a modular stack of proof targets tailored to different trust bottlenecks.

2. Main verification targets in zkFed systems

The proof statements used in zkFed can be organized by the FL phase they protect. The sources differ substantially in proof scope, circuit complexity, and trust assumptions.

Verification target	Representative mechanism	Representative papers
Update validity under privacy	NIZK proof that an encrypted update satisfies a predicate	(Nguyen et al., 2022)
Aggregation correctness	zk-SNARK or zk proof that aggregate equals prescribed combination of inputs	(Wang et al., 2023, Ahmadi et al., 2023, Zami et al., 17 Sep 2025)
Local training correctness	zk-SNARK over training or inference-derived constraints	(Xing et al., 2023, Heiss et al., 2022, Bellachia et al., 8 Jan 2025)
Evaluation privacy	zk-SNARK that local loss satisfies a threshold	(Commey et al., 15 Jul 2025)
Ownership/provenance	interactive Σ-protocol proving knowledge of federated ownership witness	(Yang et al., 2023)
Client selection / consensus	proof of model performance for selection or leader election	(Jin et al., 18 Mar 2025, Fu et al., 17 Mar 2025)

A central distinction is whether the proof concerns a computation over private data or merely a relation over already produced artifacts. Proofs of full training correctness or inference correctness are circuit-heavy, because neural-network arithmetic, fixed-point representation, and non-linearities must be encoded in R1CS- or QAP-like constraint systems (Xing et al., 2023, Heiss et al., 2022, Bellachia et al., 8 Jan 2025). By contrast, proofs of aggregation correctness can be much lighter when they only check sums, weighted averages, commitment openings, or homomorphic consistency (Wang et al., 2023, Ahmadi et al., 2023, Zami et al., 17 Sep 2025). Ownership proofs occupy a third category: they do not prove training correctness or aggregation correctness at all, but instead prove a cryptographic relation linking a model’s embedded digest to a client-specific witness (Yang et al., 2023).

An important misconception is that zkFed always proves that local training was performed “honestly.” Most protocols do not do this. Several systems prove only that an update passes a predicate, that an aggregate is correctly formed, or that an evaluation or ownership relation holds. The difference is substantive: proving aggregation correctness does not imply proving benign local training, and proving a norm bound or threshold loss does not imply full compliance with SGD, clipping, or epoch limits (Zami et al., 17 Sep 2025, Lansiaux, 3 Mar 2026).

3. Proof systems, commitments, and encoded relations

The cryptographic substrate of zkFed spans interactive Σ-protocols, Groth16 zk-SNARKs, IKOS-style MPC-in-the-head proofs, and lattice-based post-quantum Σ-protocols. The design choice is driven by the relation being proved and by deployment constraints such as trusted setup, proof size, verifier cost, and arithmetic expressiveness.

FedZKP uses an interactive Σ-protocol over exact LPN, with public instance $x = (A, y, w)$ and witness $(s, e)$ satisfying $y = A s \oplus e$ and $\|e\|_1 = w$ (Yang et al., 2023). This system does not require public key infrastructure or a common reference string for the zero-knowledge argument, and its soundness degrades as $(2/3)^d$ under $d$ repeated rounds (Yang et al., 2023). By contrast, several aggregation- and evaluation-oriented systems adopt Groth16 because it yields succinct proofs and constant-size verification costs for relations compiled into arithmetic circuits (Commey et al., 15 Jul 2025, Ahmadi et al., 2023, Zami et al., 17 Sep 2025, Lee et al., 2024).

A second major family, represented by the secure-aggregation framework of (Nguyen et al., 2022), uses an IKOS-style non-interactive proof derived from a perfectly correct and 2-private 3-party MPC protocol. Here the prover emulates an MPC evaluation of a predicate $R(r,x)$, commits to the views, and reveals challenge-selected views to establish correctness with soundness bounded by $(2/3)^\lambda$ (Nguyen et al., 2022). This is structurally different from Groth16: proof size and proving cost scale with the emulated MPC views rather than with succinct pairing-based verification.

Commitment schemes also vary with the application. Pedersen commitments are used where additive homomorphism is useful, such as update consistency or blockchain-bound proofs (Nguyen et al., 2022, Wang et al., 2023, Fu et al., 17 Mar 2025). Hash-based commitments or Poseidon/MiMC-style commitments dominate SNARK-friendly circuits and device/data binding workflows (Lee et al., 2024, Ahmadi et al., 2023). FedZKP instead uses a public digest $h = H(A_{\mathrm{agg}} \Vert y_{\mathrm{agg}})$ embedded into normalization layers, and the relation is split between a model-side validity check and a cryptographic proof of witness knowledge (Yang et al., 2023).

Several systems must also encode numerical ML computations in finite fields. To do so, they use fixed-point arithmetic, integer quantization, range constraints, or polynomial approximations to avoid unsupported transcendental operations (Xing et al., 2023, Heiss et al., 2022, Commey et al., 15 Jul 2025, Fu et al., 17 Mar 2025). This suggests that proof-friendly model design remains a core engineering constraint in zkFed, especially for training or inference proofs.

4. Architectural patterns

Three recurring architectures appear in the literature: centralized FL with proof-carrying clients, centralized FL with proof-carrying aggregators, and blockchain or DAG-based decentralized FL with on-chain or sidechain verification.

In proof-carrying clients, each client proves that its local artifact satisfies a property before the server accepts it. The secure aggregation framework of (Nguyen et al., 2022) is exemplary: clients encrypt updates under Damgård–Jurik, produce a Pedersen commitment, and attach a non-interactive zero-knowledge proof that the update satisfies an attack-resilience predicate. The server verifies proofs, discards non-compliant updates, performs threshold decryption of the homomorphic aggregate, and checks commitment consistency so that only validated updates contribute to the decrypted sum (Nguyen et al., 2022). Post-quantum ZKFL-PQ follows the same broad pattern but replaces classical public-key cryptography with ML-KEM transport, BFV homomorphic aggregation, and lattice-based norm proofs (Lansiaux, 3 Mar 2026).

In proof-carrying aggregators, clients may send raw or encrypted updates, but the aggregator must later prove that it aggregated correctly. The base zkFL protocol does this with Pedersen commitments and client signatures: the aggregator proves each round that the published aggregate equals the sum of the signed committed inputs, and in a blockchain-backed variant miners verify the proof and record only a hash of the aggregate commitment on-chain (Wang et al., 2023). zkDFL similarly moves heavy aggregation off-chain while proving with Groth16 that the FedAvg result is consistent with committed client vectors and a hash-sum inclusion check enforced by smart contracts (Ahmadi et al., 2023). The UAV-assisted framework of (Zami et al., 17 Sep 2025) focuses the SNARK relation specifically on correctness of encrypted aggregation, not on client training.

The blockchain and hybrid-ledger pattern adds immutable logging, decentralized verification, and incentive or challenge layers. VerifBFL combines IPFS, a permissioned EVM chain, Chainlink DON off-chain proof verification, and Nova-based recursive proofs for local-model accuracy and aggregation correctness (Bellachia et al., 8 Jan 2025). The end-to-end decentralized architecture of (Lee et al., 2024) adds source authenticity through device certificates and signed data batches, verified non-disclosively inside zkSNARK circuits. ZK-HybridFL goes further by embedding proof-gated admission into a DAG with oracle-assisted sidechains and challenge mechanisms (Taherpour et al., 29 Jan 2026). These systems are not merely “FL plus proofs”; they are cryptographically mediated distributed systems with ledger-level liveness and governance assumptions.

A plausible implication is that zkFed increasingly overlaps with verifiable distributed systems design, rather than remaining a narrow subtopic of privacy-preserving machine learning.

5. Ownership, evaluation, and phase-specific zkFed variants

Not all zkFed systems target update integrity or aggregation correctness. Some focus on specific FL phases that had previously lacked formal confidentiality guarantees.

FedZKP addresses federated model ownership verification. Each client generates an xLPN instance $(A_j, y_j)$ with private witness $(s, e)$0, the server concatenates these into $(s, e)$1, computes $(s, e)$2, and clients embed $(s, e)$3 into normalization scaling weights using a hinge-style regularizer during standard FL training (Yang et al., 2023). Later, to prove ownership, a client first shows that the deployed model still contains an extracted digest $(s, e)$4 within an allowed Hamming radius of $(s, e)$5, then runs an interactive Σ-protocol proving knowledge of its witness $(s, e)$6 such that $(s, e)$7 and $(s, e)$8 (Yang et al., 2023). The paper gives the adversarial advantage bound

$(s, e)$9

so the attack probability is negligible when the near-collision term and the repetition term are both negligible (Yang et al., 2023).

ZKP-FedEval addresses the evaluation phase. Instead of disclosing local loss values, a client proves the threshold predicate $y = A s \oplus e$0 under public inputs $y = A s \oplus e$1 (Commey et al., 15 Jul 2025). The Groth16 proof binds the computation to the current global model via an internal hash of $y = A s \oplus e$2 and to the current round via a nonce. This avoids leaking scalar metrics that might be exploited for membership or property inference. However, the prototype does not publicly bind the evaluation set, so cherry-picking remains possible unless a Merkle-root commitment or public PRF-based sample selection is added (Commey et al., 15 Jul 2025).

Veri-CS-FL treats client selection as the phase of interest. Clients prove correctness of a performance metric, instantiated as cosine similarity between a local model and a server-trained benchmark model, and selection is then based on verified metrics rather than unverifiable self-reporting (Jin et al., 18 Mar 2025). ZKPoT moves this logic into consensus: the client proving the highest verified accuracy on a public test set becomes leader for the next round, and the proof replaces direct model disclosure as the basis for consensus rights (Fu et al., 17 Mar 2025). These protocols suggest that zkFed increasingly targets governance and coordination layers, not only confidentiality of training or aggregation.

6. Security properties, performance, and limitations

Across the literature, completeness, soundness, and zero-knowledge are standard formal goals, but the threat models differ sharply. Many systems assume an honest-but-curious server and malicious clients (Nguyen et al., 2022); others assume malicious aggregators but mostly honest clients (Wang et al., 2023); still others assume trusted setup parties, trusted decryptors, or trusted TEEs alongside zero-knowledge (Sharma et al., 24 Dec 2025, Lansiaux, 3 Mar 2026). These assumptions materially shape what is actually guaranteed.

A recurring strength of zkFed is that it can decouple privacy from verifiability. In the secure aggregation design of (Nguyen et al., 2022), the server learns only the aggregate update and not any individual model, yet still verifies that each contributing update satisfied a backdoor-resilience predicate. In FedZKP, verifier and server do not learn the ownership credentials because the transcript is honest-verifier zero-knowledge (Yang et al., 2023). In ZKP-FedEval, only the threshold outcome is revealed, not the metric value (Commey et al., 15 Jul 2025). In aggregation-verification systems, miners or blockchain validators can verify correctness without seeing plaintext models (Wang et al., 2023, Ahmadi et al., 2023).

The main cost is proof generation and circuit complexity. FedZKP reports single-round proof generation up to 8 ms and verification up to 86 ms for $y = A s \oplus e$3, but multi-round verification for $y = A s \oplus e$4 reaches about 17,919 ms (Yang et al., 2023). The secure aggregation framework of (Nguyen et al., 2022) reports proving times of about 5 minutes at soundness 0.06 and about 7 minutes at soundness 0.03 for the backdoor predicate, with server-side verification of 100 users taking about 3.5 minutes (Nguyen et al., 2022). ZKP-FedEval reports per-client proof generation around 0.49 s for MNIST-CNN and 0.13 s for HAR-MLP, with proof sizes about 0.79 KiB and 0.26 KiB respectively (Commey et al., 15 Jul 2025). ZKPoT’s proving time is far larger—about 168–198 s—because it proves model performance over an integer inference circuit (Fu et al., 17 Mar 2025). Deep-model or recursive proof systems in blockchain contexts can require tens of seconds to minutes even when verification is sub-second (Bellachia et al., 8 Jan 2025, Taherpour et al., 29 Jan 2026).

Several limitations recur. First, many systems prove only a narrow predicate, not full benign behavior. Aggregation proofs do not block poisoned but well-formed local updates (Zami et al., 17 Sep 2025). Norm-bound proofs reject only large-norm attacks and do not stop low-norm directional poisoning (Lansiaux, 3 Mar 2026). Evaluation threshold proofs can leak one bit per round and may still permit dataset cherry-picking if the evaluation set is not committed (Commey et al., 15 Jul 2025). Second, Groth16-based designs require trusted setup (Commey et al., 15 Jul 2025, Ahmadi et al., 2023, Zami et al., 17 Sep 2025, Lee et al., 2024). Third, arithmetic-circuit encodings of modern models remain expensive, especially for non-linear activations, full SGD trace proofs, or large models (Xing et al., 2023, Heiss et al., 2022, Bellachia et al., 8 Jan 2025).

It is therefore inaccurate to characterize zkFed as a complete replacement for robust aggregation, differential privacy, secure aggregation, or TEEs. The literature repeatedly treats these as orthogonal or complementary. Secure aggregation preserves confidentiality but does not certify correctness; differential privacy reduces leakage but does not prove compliance; robust aggregation mitigates some poisoning but often requires visibility into updates; TEEs attest computation but introduce hardware trust (Nguyen et al., 2022, Zami et al., 17 Sep 2025, Sharma et al., 24 Dec 2025). zkFed typically supplies the missing verifiability layer rather than superseding all other defenses.

7. Research directions

Current work points toward several open directions. One is proof composition: formally analyzing how watermark embedding, secure aggregation, differential privacy, robust aggregation, and zero-knowledge interact as a unified FL pipeline remains largely unresolved (Yang et al., 2023). Another is proof scope expansion: many systems prove only inference or aggregation, whereas proving correct local optimization, clipping, epoch counts, fairness constraints, or robust statistics remains expensive and only partially explored (Bellachia et al., 8 Jan 2025, Commey et al., 15 Jul 2025, Taherpour et al., 29 Jan 2026).

A second major direction is scalability and proof ergonomics. Groth16 remains attractive because of small proofs and fast verification, but trusted setup and circuit-specific keys remain deployment obstacles (Commey et al., 15 Jul 2025, Ahmadi et al., 2023). Several papers therefore identify universal SNARKs, STARKs, recursive proofs, or more efficient zkML compilers as promising alternatives, albeit with larger proofs or different verifier trade-offs (Zami et al., 17 Sep 2025, Bellachia et al., 8 Jan 2025, Gupta, 4 May 2026). The same issue appears in post-quantum work, where lattice-based proofs and BFV aggregation introduce large cryptographic overheads but target HNDL resilience and medical settings with slower operational tempos (Lansiaux, 3 Mar 2026).

A third direction is end-to-end authenticity. Most early zkFed systems assume that the training data, while private, are at least genuine. More recent work extends verifiability to source authenticity via device certificates, signed data commitments, and two-step proving and verification workflows, so that the chain verifies not only training and aggregation but also the provenance of the data source (Lee et al., 2024). This suggests an expansion of zkFed from “verifiable FL” toward full cryptographically accountable data-to-model pipelines.

Finally, ownership, evaluation, and consensus papers indicate that zero-knowledge is being applied across the entire lifecycle of federated models, not merely training rounds. This suggests that the mature conception of zkFed may be phase-complete: verifiable enrollment, data authenticity, local training, update admissibility, aggregation, evaluation, ownership, and governance, each backed by a specialized proof relation rather than by a single monolithic zkML proof.