Zero-Knowledge LLMs: Verifiable & Private AI

• Zero-Knowledge Large Language Models are systems that leverage ZKPs to securely and verifiably execute inference, fine-tuning, and code generation while protecting sensitive data.
• They integrate advanced cryptographic protocols, including SNARKs, STARKs, FHE, and SMPC, to ensure that computations remain correct without revealing internal parameters.
• These frameworks balance performance and security by using specialized circuit optimizations and hybrid protocols, enabling practical applications from secure model updates to verifiable cloud inference.

Zero-Knowledge LLMs (ZK-LLMs) are architectures and protocols for inference, fine-tuning, or code generation involving LLMs in scenarios where verifiability and privacy—often formalized via zero-knowledge proofs (ZKPs)—are paramount. These systems enable one or more parties to cryptographically prove properties about LLM computations (e.g., correctness of inference, privacy of model parameters, or legitimate processing of user data) without revealing sensitive information such as proprietary model parameters, fine-tuning updates, or user inputs. The field comprises protocol designs using general-purpose ZKPs, specialized circuit optimizations for deep-learning primitives, FHE (Fully Homomorphic Encryption), secure multi-party computation (SMPC), as well as prompting and code-generation paradigms that empower or leverage LLMs in zero-knowledge settings.

1. Formal Definitions, Security Objectives, and Problem Settings

The foundational objective of ZK-LLMs is to cryptographically separate the capability to verify properties of LLM operation from the disclosure of sensitive internal data. The canonical protocol consists of:

• Prover: Holds secret information (e.g., model weights W, LoRA adapters (U, V), or user profile w).
• Verifier: Receives public input (e.g., prompt x, traits d₁), output (e.g., LLM answer y), and a proof π attesting to either the correctness of LLM(x; W) → y, the validity of an adapter, or adherence to a declared data-processing logic.
• Zero-Knowledge Property: The proof π can be simulated from public inputs, leaking nothing about privates (e.g., W, U, V, w) beyond that claimed.

Security objectives include:

• Soundness: An incorrect statement cannot be proved, except with negligible probability.
• Zero-Knowledge: The verifier learns nothing beyond the validity of the claimed computation/relation.
• Completeness: Honest provers always convince verifiers.
• Robustness to Partial Disclosure: Protocols prevent the leakage of intermediate computations, updates, or proprietary model weights throughout training, fine-tuning, or inference (Sun et al., 2024, Roy et al., 21 Jan 2025, Liao et al., 29 Aug 2025, Watanabe et al., 10 Feb 2025).

2. Cryptographic Protocols and Model Instrumentation

ZK-LLMs are instantiated through combinations of cryptographic primitives:

• General-purpose ZKPs: Non-interactive arguments based on SNARKs, STARKs, sumcheck protocols, and polynomial commitments, specialized to deep learning tensor calculus.
  • Sumcheck protocols: Used to prove correctness of multi-linear operations (matrix multiplications) across layers (Sun et al., 2024, Liao et al., 29 Aug 2025).
  • Lookup arguments: Essential for non-arithmetic ops (softmax, SwiGLU, digit decomposition, quantization) in transformers. The tlookup argument supports parallelized batch set membership, introducing no asymptotic computational overhead relative to native ops (Sun et al., 2024).
  • zkAttn: A domain-specific ZK argument for the transformer attention mechanism, combining sumcheck (for QKᵀ) and lookup (for softmax/exponential), batched and parallelizable on GPU (Sun et al., 2024).
• Privacy-Preserving Inference Primitives:
  • Fully Homomorphic Encryption (FHE): Enables direct evaluation of encrypted queries, such that only the user can decrypt results; correctness is enforced by ciphertext consistency (Wellington, 2024, Pal et al., 19 Feb 2026).
  • Secure Multi-Party Computation (SMPC): Provides verifiable privacy for collaborative inference and selective operations, with the cost determined by round-complexity and network limitations (Pal et al., 19 Feb 2026).
• Hybrid Protocols: Protocol compositions leveraging privacy-preserving inference as a base and augmenting with lightweight verification wrappers (e.g., logit fingerprinting, noise injection), reducing the need for full ZK circuit proofs (Pal et al., 19 Feb 2026).

Through these techniques, ZK-LLMs can guarantee privacy of model internals and user data during:

• Inference: Proofs that y = LLM(x; W) or y = M(x) + U Vᵀx, without ever exposing W or (U, V) (Sun et al., 2024, Roy et al., 21 Jan 2025).
• Fine-tuning: Proofs that private LoRA updates (e.g., B, A) were applied correctly to a public model, with rank constraints and secure update steps (Liao et al., 29 Aug 2025).
• Verification of code: LLMs as ZK code generators, equipped with evaluation pipelines that check not only syntax but gadget-level and end-to-end semantic correctness in constraint-based languages (Xue et al., 15 Sep 2025).

3. System Architectures and Workflows

A variety of system architectures have emerged in the literature addressing different privacy/utility tradeoffs:

• Multi-Party Inference (MPI): Protocols like ZKLoRA distribute activations between a Base Model User and a LoRA Contributor, ensuring only desired deltas are exchanged, and the core weights remain private. LoRA adapters and forward passes are wrapped in succinct ZK proofs, with verification latencies of 1–2 s per module, even for 70B parameter models (Roy et al., 21 Jan 2025).
• zkVM-based Proofs: Integration with zkVMs (e.g., RiscZero, SP1) supports privacy-preserving user profiling, where traits are certified by ZKP and then used to customize LLM output (Watanabe et al., 10 Feb 2025).
• Decentralized Networks with FHE: In BasedAI, P2P miners process entirely encrypted queries using FHE, returning ciphertext responses with soundness guaranteed by encrypted audit trails; Cerberus Squeezing enhances throughput via adversarial quantization and architectural pruning (Wellington, 2024).
• Proof-of-Inference for Intellectual Property Assurance: zkLLM allows the model owner to commit to secret weights, produce a public commitment, and prove the output of any query was derived using the correct parameters, with end-to-end proof size below 200 kB and generation under 15 min for 13B models (Sun et al., 2024).
• Verifiable Service Providers: Protocols that augment existing privacy-preserving inference (FHE, SMPC) with logit-fingerprint or noise-embedding tokens, enabling users to efficiently verify that their queries were processed using the intended target model without ever revealing plaintext (Pal et al., 19 Feb 2026).

4. Performance, Implementation, and Practical Trade-Offs

Benchmarks across frameworks demonstrate that ZK-LLMs are computationally feasible for billions of parameters, with performance primarily governed by protocol instantiation and proof system choice. Key experimental findings:

System	Prove Time (13B)	Verify Time	Proof Size	Hardware	Comment
zkLLM	≤15 min	~4 s	<200 kB	40GB A100 GPU	Full inference ZKP (Sun et al., 2024)
zkLoRA	219–249 s	3.5–3.7 s	~225 kB	4×A100 or similar	End-to-end LoRA ZK (Liao et al., 29 Aug 2025)
ZKLoRA	47–55 s/mod	1–2 s/mod	—	—	Per-module LoRA proof (Roy et al., 21 Jan 2025)
BasedAI	—	—	—	4×A100 GPU	1.1 tokens/sec with FHE+Cerberus (Wellington, 2024)
Sigma (SMPC)	20 s / token	0.17 s	—	GPU, LAN/WAN	With logit-fingerprint (Pal et al., 19 Feb 2026)

Complexity principles:

• Proving cost is typically dominated by the size of circuit representations and polynomial commitment operations (FFT, multi-scalar multiplications, elliptic curve ops).
• GPU acceleration (BLS12-381, parallel commitment, lookup, sumcheck) is fundamental for scaling to LLaMA, OPT, and other billion-parameter models (Sun et al., 2024, Liao et al., 29 Aug 2025).
• Verification times scale polylogarithmically in parameter count.
• FHE, when combined with aggressive quantization (Cerberus Squeezing), recovers >50% throughput lost to naive FHE overhead, achieving less than 2% increase in perplexity (Wellington, 2024).
• Protocols using privacy-plus-verifiability (logit-fingerprinting) achieve order-of-magnitude prover time reductions compared to full arithmetic ZK inference, with sub-linear communication and constant token overhead (Pal et al., 19 Feb 2026).
• Proof sizes range from hundreds of bytes (Groth16/PLONK) to 200 kB (STARK-based), with STARKs preferred for quantum resistance, but at increased communication cost (Sun et al., 2024, Watanabe et al., 10 Feb 2025).

5. Use Cases, Deployment Contexts, and Practical Impact

ZK-LLM frameworks serve several distinct application classes:

• Secure Adapter Verification and Intellectual Property Assurance: Outsourced LoRA providers can cryptographically guarantee adapter compatibility, correctness, and lineage, while retaining exclusive access to proprietary updates until after payment (Roy et al., 21 Jan 2025, Liao et al., 29 Aug 2025).
• Privacy-Preserving Personalized Advice: LLM-based recommendation or counseling systems can receive user traits certified by ZKPs, ensuring no sensitive data is disclosed or stored during personalization (Watanabe et al., 10 Feb 2025). This supports compliance with GDPR and other data minimization statutes.
• Verifiable Cloud Inference: Inferences performed on third-party hardware can be cryptographically audited to prevent model substitution attacks (i.e., swapping expensive LLMs for weaker proxies) (Sun et al., 2024, Pal et al., 19 Feb 2026).
• Decentralized P2P LLM Services: Protocols such as BasedAI use FHE to provide confidential model inference across peer-to-peer miners, relevant for settings such as blockchain, decentralized finance, and edge trading of LLM compute (Wellington, 2024).
• Zero-Knowledge Code Generation: LLMs can be fine-tuned or augmented to synthesize ZKP-compatible circuits for a range of DSLs (e.g., Circom, Noir) via multi-stage evaluation, retrieval-augmented generation, and repair loops, substantially lowering practitioner barriers to ZK development (Xue et al., 15 Sep 2025).

6. Limitations, Open Challenges, and Future Directions

Despite significant advances, ZK-LLMs exhibit several practical and theoretical limitations:

• High Prover Overhead: Full-circuit ZKPs remain orders of magnitude slower than plaintext inference; provers require hundreds of seconds for single-sequence, large-batch processing (Sun et al., 2024, Liao et al., 29 Aug 2025).
• Proof Size and Transmission: STARK-based proofs are bulky (1–2 MB), imposing load on low-latency applications (Watanabe et al., 10 Feb 2025). SNARKs reduce this but require trusted setup.
• Circuit Expressivity and Compilation: Efficient ZK circuit representations of complex neural operations (e.g., softmax, GELU, SwiGLU) necessitate advanced circuit kernels and lookup schemes; supporting mixed precision and non-arithmetic ops remains an optimization target (Sun et al., 2024, Liao et al., 29 Aug 2025).
• Trust Assumptions: Privacy-plus-verifiability protocols using FHE/SMPC may inherit trust assumptions (honest majority, non-colluding parties) absent from standalone ZK proofs (Pal et al., 19 Feb 2026).
• Data Scarcity and KB Expansion: ZK code generator LLMs require curated gadget knowledge bases and expanded real-world ZK circuit corpora for robust generalization (Xue et al., 15 Sep 2025).
• Recursive and Amortized Proof Composition: Future research directions include recursive SNARKs for batching and amortizing proof costs across multi-epoch fine-tuning or iterative inference pipelines (Liao et al., 29 Aug 2025).

Potential directions for overcoming these challenges include quantization-aware training under encryption, recursive proof frameworks, federated MPC+ZKP pipelines, FHE parameter optimization, circuit kernel specialization, and integration of formal verification into LLM code-generation agents (Wellington, 2024, Liao et al., 29 Aug 2025, Xue et al., 15 Sep 2025).

7. Outlook and Research Impact

ZK-LLMs have established foundational protocols for verifiable, privacy-preserving LLM deployment in sensitive, untrusted, or decentralized environments. They facilitate new forms of contract-based collaboration, personalized yet auditable model interaction, and trustworthy cloud or edge LLM computation. Empirical validation demonstrates scalability to multi-billion parameter models, sublinear verification, and user-transparent integration into industrial ML pipelines. The cross-disciplinary convergence of deep learning, formal methods, modern cryptography, and distributed systems continues to expand the boundary of securely deployable AI (Sun et al., 2024, Roy et al., 21 Jan 2025, Liao et al., 29 Aug 2025, Wellington, 2024, Pal et al., 19 Feb 2026).