zkLLM: Zero-Knowledge Proofs for LLMs

• zkLLM is a framework that integrates zero-knowledge proofs with LLMs to enable verified, privacy-preserving model inference and personalized interactions.
• It employs specialized protocols like tlookup and zkAttn to efficiently verify both arithmetic and non-arithmetic operations in transformer networks.
• zkLLM extends to secure model fine-tuning (zkLoRA) and verifiable training, addressing challenges in scalability, efficiency, and quantitative performance.

zkLLM refers to frameworks and protocols that enable efficient zero-knowledge proof (ZKP) generation for LLMs, with the aim of providing privacy-preserving, verifiable computation for LLM inference or personalized interaction. Distinct from generic ZKP systems, zkLLM integrates cryptographic protocols tailored to the structure, operations, and scale of transformer-style neural networks. This field addresses the need for guaranteeing correctness and/or privacy in LLM deployment, especially where model parameters are proprietary, inputs are sensitive, or results must be cryptographically authenticated for downstream consumption.

1. Core Concepts and Definitions

Zero-knowledge proofs are cryptographic protocols whereby a prover can convince a verifier of the validity of a claim (e.g., the correctness of an LLM output for a given input, or the faithful computation of advice from private user data) without revealing any additional information. In the LLM context, primary use cases include:

• Certifying the authenticity of LLM model inference without revealing the model parameters, leveraging the privacy properties of ZKPs (Sun et al., 24 Apr 2024).
• Producing verifiable proofs of correct user classification or feature extraction in personalized LLM advising, concealing sensitive input traits (Watanabe et al., 10 Feb 2025).
• Extending to secure training/fine-tuning with parameter-efficient approaches combined with end-to-end ZKP on updates and gradients (Liao et al., 29 Aug 2025).

Non-arithmetic operations (activations, attention/softmax), tensor dimensions in the billions, and the need for GPU efficiency necessitate specialized ZKP constructions—such as lookup arguments, digit decompositions, and tensor-specific protocols.

2. Technical Frameworks

2.1 zkLLM for Inference Verification

In "zkLLM: Zero Knowledge Proofs for LLMs" a four-stage protocol is established (Sun et al., 24 Apr 2024):

1. Commit: The prover commits to the LLM’s weights $\mathbf W$ using a polynomial commitment (Hyrax/Pedersen, BLS12-381), publishing only the commitment $\langle\!\langle\mathbf W\rangle\!\rangle$.
2. Compute: On a public input $\mathbf X$, the prover performs quantized LLM inference (including all activation, attention, and normalization steps) and logs all intermediate tensors required for proof construction.
3. Prove: The proof architecture is split:
   • All matrix multiplications/linear layers are checked with GKR-style sumchecks over multilinear extensions.
   • Non-arithmetic operations (activations, softmax) are translated into set membership proofs via a tensor lookup primitive (tlookup) and digit-lookup–augmented zkAttn for softmax attention.
4. Verify: The verifier checks a small number of commitments and subproofs (sumchecks for arithmetic, tlookup/zkAttn for non-arithmetic), accepting or rejecting the full inference transcript.

2.2 tlookup and zkAttn Primitives

• tlookup: A parallelized lookup argument that enables efficient ZKP for arbitrary tensor set inclusion, allowing non-arithmetic DL operations (e.g., ReLU, SwiGLU, Softmax) to be handled with $O(D)$ overhead, $D$ being the tensor dimension (Sun et al., 24 Apr 2024).
  • Given a secret tensor $\mathbf S$ and public table $\mathbf T$, tlookup reduces the membership assertion $\mathbf S\subseteq\mathbf T$ to a rational function equality, verified via sumcheck.
  • tlookup is optimized for distributed GPU parallelization and minimal proof size.
• zkAttn: A specialized zero-knowledge proof protocol for the entire attention mechanism with softmax, using base-$b$ digit decomposition and tlookup over quantized tables for exponentiation and normalization, addressing the intricacies of softmax verification efficiently.

2.3 zkLoRA: Training and Fine-tuning Verification

The zkLoRA framework (Liao et al., 29 Aug 2025) introduces the first end-to-end ZKP for LoRA-parameterized fine-tuning of LLMs. Core components are:

• LoRA parametric injection: Frozen pretrained weight $W_0$ plus a trainable low-rank update $\Delta W = AB^T$ with $A\in\mathbb{R}^{D\times r}$, $B\in\mathbb{R}^{d\times r}$, $r\ll\min(D,d)$.
• Proof system:
  • Polynomial (Hyrax-style) commitments for all weights/updates.
  • GKR-sumcheck for all arithmetic: matrix multiplications, layer-normalizations, parameter updates.
  • Rational-function lookup for non-arithmetic operations (elementwise products, softmax, SwiGLU), mirroring zkLLM’s tlookup approach.
• End-to-end ZK proof structure for forward propagation, backward propagation (gradients), and parameter updates, maintaining computational privacy of both model and training data.

3. Architectural Variants: Personalized Privacy vs. Model Secrecy

• The classic zkLLM design focuses on model secrecy during inference: the end user verifies output correctness without accessing model weights (Sun et al., 24 Apr 2024).
• An alternative direction, as in "Generating Privacy-Preserving Personalized Advice with Zero-Knowledge Proofs and LLMs" (Watanabe et al., 10 Feb 2025), leverages zkVMs (e.g., RiscZero, SP1) to allow a trusted entity to prove correct user trait classification (e.g., risk scoring) from sensitive data, such that an LLM service sees only the ZK-certified trait vector but no raw user input. The LLM is then prompted using this certified abstraction, with the proof guaranteeing origin integrity.

4. Security, Privacy, and Formal Guarantees

All zkLLM-class systems rely on hardness assumptions derived from polynomial commitment schemes and the soundness of sumcheck protocols. Core theorems (Sun et al., 24 Apr 2024, Liao et al., 29 Aug 2025):

• Soundness: For any malicious prover, the chance to produce a convincing but false proof is bounded by negligible functions in security parameter $\lambda$, and by circuit dimensions over $|\mathbb{F}|$ (the field size).

  $$\varepsilon_{\mathrm{sound}} \leq \frac{m \cdot d_{\max}}{|\mathbb{F}|} + \frac{C}{|\mathbb{F}|} + \varepsilon_{\mathrm{bind}}$$

  where $m$ is the number of sumcheck rounds, $d_{\max}$ the maximum degree, $C$ the number of lookup checks.

• Zero-Knowledge: Existence of a PPT simulator $S$ such that any verifier cannot distinguish between real and simulated transcripts.
• Privacy:
  • For model-secrecy protocols, model weights remain committed throughout; no model information is leaked.
  • For personalized advice, all user information is kept private except abstracted, ZK-backed traits.

5. Implementation and Empirical Evaluation

zkLLM frameworks are GPU-accelerated, supporting billion-parameter LLMs (e.g., LLaMA, OPT). Notable metrics (Sun et al., 24 Apr 2024, Liao et al., 29 Aug 2025, Watanabe et al., 10 Feb 2025):

Model	Mode	Prover Time	Verifier Time	Proof Size	Commitment Size	Additional Note
LLaMA/OPT 13B	Inference	<15 min	3–4 s	160–200 kB	~10 MB	zkLLM, tlookup+zkAttn
LLaMA-13B	Fine-tuning	249.4 s	3.49 s	-	224.6 MB	zkLoRA, full forward+ backward
Risk Test (CPU)	Trait ZKP	51–68 s	≤1.3 s	~100 kB	N/A	zkVM, RiscZero/SP1, per instance
Risk Test (GPU)	Trait ZKP	1.45 s	0.02 s	~100 kB	N/A	zkVM, RiscZero, A100

• All frameworks maintain proof sizes orders of magnitude smaller than model or input data, and verifier time is constrained to seconds, suitable for deployment in interactive or real-time systems.
• Quantization to 16 bits ($|\mathbb{F}|>2^{254}$) is used throughout to fit LLM arithmetic within ZK-friendly field operations.
• Empirical results demonstrate that added perplexity for quantized ZKP-enabled inference is negligible (e.g., $<0.1$ on C4 at 13B scale in zkLLM).
• Compared to prior generic ZKML solutions, zkLLM improves prover time (by $>50\times$ at scale) and scales verifiability to LLMs with 10+ billion parameters.

6. Limitations and Open Challenges

Certain research challenges persist in zkLLM’s development (Sun et al., 24 Apr 2024, Liao et al., 29 Aug 2025, Watanabe et al., 10 Feb 2025):

• Training/Fine-tuning at Scale: Full ZKP for arbitrary gradient backpropagation and optimizer steps remains substantially more expensive than inference-only ZKP; zkLoRA's approach with LoRA-style adaptation partly mitigates but does not eliminate this.
• Model Size and Memory: Scaling beyond 13B-parameter LLMs necessitates recursive SNARKs or hierarchical circuit designs to keep prover memory manageable.
• Lookup Protocols: Further optimization of tlookup and multivariate lookups (e.g., Baloo, Caulk+) could reduce overhead and table size.
• Quantization Limits: Achieving sub-16-bit quantization in finite fields, while retaining negligible accuracy loss, is unresolved.
• Interactivity: Transforming zkLLM into a fully non-interactive (SNARK/SIRA) proof, as opposed to Fiat–Shamir transformations, is an active area.

A plausible implication is that user-acceptance, system integration, and communication overheads (proof size, transmission, prompt injection) are emerging practical factors influencing large-scale deployment.

7. Applications and Impact

zkLLM technologies enable:

• Verifiable model serving, where end users or third parties can confirm output authenticity without needing access to proprietary weights (Sun et al., 24 Apr 2024).
• Privacy-preserving LLM-based advice in sensitive domains (healthcare, banking) where user traits are cryptographically validated but all sensitive raw input remains hidden (Watanabe et al., 10 Feb 2025).
• Secure LLM fine-tuning and adaptation in untrusted or decentralized environments (Liao et al., 29 Aug 2025).

By establishing correctness, privacy, and trust in LLM applications, zkLLM underpins the third-party authentication of AI decisions, supports regulatory compliance, and addresses data minimization mandates in privacy-sensitive deployments. Ongoing research is focused on further scaling, reducing overhead, and integrating with advanced prompting and context-alignment methods for broader adoption.