# Bits Leaked per Query: Information-Theoretic Bounds on Adversarial Attacks against LLMs

arXiv: https://arxiv.org/abs/2510.17000 · HTML: https://mlsanity.com/paper/2510.17000/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Jailbreaking, one of 12 directions in LLM safety and security.
- Builds on 36 of its 69 references that are in the map.
- First posted on arXiv 19 Oct 2025.

## Placed in

- LLM safety and security / [Jailbreaking](https://mlsanity.com/safety/jailbreaking/)

## Builds on (most cited first, 30 of 36)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Jailbreaking Black Box Large Language Models in Twenty Queries](https://mlsanity.com/paper/2310.08419/) (2023)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [Jailbreaking Leading Safety-Aligned LLMs with Simple Adaptive Attacks](https://mlsanity.com/paper/2404.02151/) (2024)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Can LLMs Keep a Secret? Testing Privacy Implications of Language Models via Contextual Integrity Theory](https://mlsanity.com/paper/2310.17884/) (2023)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [PLeak: Prompt Leaking Attacks against Large Language Model Applications](https://mlsanity.com/paper/2405.06823/) (2024)
- [H-CoT: Hijacking the Chain-of-Thought Safety Reasoning Mechanism to Jailbreak Large Reasoning Models, Including OpenAI o1/o3, DeepSeek-R1, and Gemini 2.0 Flash Thinking](https://mlsanity.com/paper/2502.12893/) (2025)
- [Effective Prompt Extraction from Language Models](https://mlsanity.com/paper/2307.06865/) (2023)
- [Unlearning or Obfuscating? Jogging the Memory of Unlearned LLMs via Benign Relearning](https://mlsanity.com/paper/2406.13356/) (2024)
- [Towards LLM Unlearning Resilient to Relearning Attacks: A Sharpness-Aware Minimization Perspective and Beyond](https://mlsanity.com/paper/2502.05374/) (2025)
- [Jailbreaking GPT-4V via Self-Adversarial Attacks with System Prompts](https://mlsanity.com/paper/2311.09127/) (2023)
- [Reasoning-Augmented Conversation for Multi-Turn Jailbreak Attacks on Large Language Models](https://mlsanity.com/paper/2502.11054/) (2025)
- [JBShield: Defending Large Language Models from Jailbreak Attacks through Activated Concept Analysis and Manipulation](https://mlsanity.com/paper/2502.07557/) (2025)
- [Evaluating Gender Bias in Large Language Models via Chain-of-Thought Prompting](https://mlsanity.com/paper/2401.15585/) (2024)
- [Prompt Stealing Attacks Against Large Language Models](https://mlsanity.com/paper/2402.12959/) (2024)
- [Sampling-based Pseudo-Likelihood for Membership Inference Attacks](https://mlsanity.com/paper/2404.11262/) (2024)

## Built on by (most cited first, 1 of 1)

- [Caught in the Act(ivation): Toward Pre-Output and Multi-Turn Detection of Credential Exfiltration by LLM Agents](https://mlsanity.com/paper/2606.04141/) (2026)

## Abstract (arXiv)

Adversarial attacks by malicious users that threaten the safety of large language models (LLMs) can be viewed as attempts to infer a target property T that is unknown when an instruction is issued, and becomes knowable only after the model's reply is observed. Examples of target properties T include the binary flag that triggers an LLM's harmful response or rejection, and the degree to which information deleted by unlearning can be restored, both elicited via adversarial instructions. The LLM reveals an observable signal Z that potentially leaks hints for attacking through a response containing answer tokens, thinking process tokens, or logits. Yet the scale of information leaked remains anecdotal, leaving auditors without principled guidance and defenders blind to the transparency--risk trade-off. We fill this gap with an information-theoretic framework that computes how much information can be safely disclosed, and enables auditors to gauge how close their methods come to the fundamental limit. Treating the mutual information I(Z;T) between the observation Z and the target property T as the leaked bits per query, we show that achieving error varepsilon requires at least log(1/varepsilon)/I(Z;T) queries, scaling linearly with the inverse leak rate and only logarithmically with the desired accuracy. Thus, even a modest increase in disclosure collapses the attack cost from quadratic to logarithmic in terms of the desired accuracy. Experiments on seven LLMs across system-prompt leakage, jailbreak, and relearning attacks corroborate the theory: exposing answer tokens alone requires about a thousand queries; adding logits cuts this to about a hundred; and revealing the full thinking process trims it to a few dozen. Our results provide the first principled yardstick for balancing transparency and security when deploying LLMs.