Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2509.23834

GPM: The Gaussian Pancake Mechanism for Planting Undetectable Backdoors in Differential Privacy

Haochen Sun·Xi He
View original source ↗Read source document ↗Export metadata ↓

Abstract

Differential privacy (DP) has become the gold standard for preserving individual privacy in data analysis. However, an implicit yet fundamental assumption underlying these rigorous privacy guarantees is the correct implementation and execution of DP mechanisms. Several incidents of unintended privacy loss have occurred due to numerical issues and inappropriate configurations of DP software, which have been successfully exploited in privacy attacks. To better understand the seriousness of defective DP software, we ask the following question: is it possible to elevate these passive defects into active privacy attacks while maintaining covertness? To address this question, we present the Gaussian pancake mechanism (GPM), a novel mechanism that is computationally indistinguishable from the widely used Gaussian mechanism (GM), yet exhibits arbitrarily weaker statistical DP guarantees. This unprecedented separation enables a new class of backdoor attacks: by indistinguishably passing off as the authentic GM, GPM can covertly degrade statistical privacy. Unlike the unintentional privacy loss caused by GM's numerical issues, GPM is an adversarial yet undetectable backdoor attack against data privacy. We formally prove GPM's covertness, characterize its statistical leakage, and demonstrate a concrete distinguishing attack that can achieve near-perfect success rates under suitable parameter choices, both theoretically and empirically. Our results underscore the importance of using transparent, open-source DP libraries and highlight the need for rigorous scrutiny and formal verification of DP implementations to prevent subtle, undetectable privacy compromises in real-world systems.

Explore related subjects

cs.CRcs.DB

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Haochen Sun, Xi He. 2026-03-15. GPM: The Gaussian Pancake Mechanism for Planting Undetectable Backdoors in Differential Privacy. https://arxiv.org/abs/2509.23834

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Attack Tree Distance: a practical examination of tree difference measurement within cyber security

Attack trees are a popular threat modeling method. In practice, there is often a need to compare attack tree models produced by human experts, based on both the structure of the tree and the meaning of the node labels. In this work, we investigate the problem of comparing attack trees and measuring their similarity. We define five different measures for measuring the distance between two attack trees: Label Distance (LD), Tree Edit Distance (TED), Radical Distance (RD), Multiset Distance (MSD) and Weighted Sum Distance (WSD). We further propose a repeatable method of both theoretical and experimental attack tree distance measures validation. Our theoretical validation consists of a series of basic transformations to evaluate the behavior of distance measures with respect to specific types of transformations that may appear between two attack trees. To experimentally validate our distance measures, we designed and executed a human study ($n=39$) to collect a dataset of attack trees to be used for evaluation and comparison of the measures. From our theoretical and experimental results, we find that applying semantic similarity as a means of comparing node labels is a valid approach. Further, we find four of the five attack tree distance measures are valid approaches in certain, varying circumstances. Our results suggest that these methods can already be used to identify similar real-world attack trees. Overall, this work lays the groundwork for improved threat model analysis, validation of AI-generated attack trees, and future research into threat similarity measurement in cybersecurity.

cs.CR↗
arXiv2026

Probabilistic Modeling of Jailbreak on Multimodal LLMs: From Quantification to Application

Recently, Multimodal Large Language Models (MLLMs) have demonstrated their superior ability in understanding multimodal content. However, they remain vulnerable to jailbreak attacks, which exploit weaknesses in their safety alignment to generate harmful responses. Previous studies categorize jailbreaks as successful or failed based on whether responses contain malicious content. However, given the stochastic nature of MLLM responses, this binary classification of an input's ability to jailbreak MLLMs is inappropriate. Derived from this viewpoint, we introduce jailbreak probability to quantify the jailbreak potential of an input, which represents the likelihood that MLLMs generated a malicious response when prompted with this input. We approximate this probability through multiple queries to MLLMs. After modeling the relationship between input hidden states and their corresponding jailbreak probability using Jailbreak Probability Prediction Network (JPPN), we use continuous jailbreak probability for optimization. Specifically, we propose Jailbreak-Probability-based Attack (JPA) that optimizes adversarial perturbations on input image to maximize jailbreak probability, and further enhance it as Multimodal JPA (MJPA) by including monotonic text rephrasing. To counteract attacks, we also propose Jailbreak-Probability-based Finetuning (JPF), which minimizes jailbreak probability through MLLM parameter updates. Extensive experiments show that (1) (M)JPA yields significant improvements when attacking a wide range of models under both white and black box settings. (2) JPF vastly reduces jailbreaks by at most over 60\%. Both of the above results demonstrate the significance of introducing jailbreak probability to make nuanced distinctions among input jailbreak abilities.

cs.CR↗
arXiv2026

Differential Fault Analysis of Lilliput under Random-Location Nibble Faults

Differential fault analysis (DFA) is an important technique for evaluating the implementation-level security of block ciphers. Many DFA attacks assume that the adversary can inject faults into a selected internal word, nibble, or branch. Such fixed-location assumptions are convenient for deriving key-recovery equations, but they may overestimate the adversary's spatial control and may obscure the branch-dependent leakage behavior of multi-branch structures. In this paper, we study the lightweight block cipher Lilliput under a fixed-timing full-branch random-location nibble fault model. The attacker is assumed to induce a nonzero nibble fault in round 27, while the affected branch is randomly distributed over all sixteen state branches and is unknown to the attacker. The main challenge is to convert faulty ciphertexts with unknown injection locations into usable key-recovery constraints. We analyze the fault propagation induced by the EGFN structure of Lilliput and derive ciphertext-difference conditions for identifying the injected branch. The proposed branch-identification approach has a DDT-based combinatorial estimate of at least 99.9909% and achieves 99.9983% accuracy in 2^{20} random fault simulations. Once the fault branch is determined, we classify the corresponding propagation patterns according to whether the injected fault value and the intermediate S-box output difference can be uniquely determined. For each case, we derive DDT-based constraints on the last-round and penultimate-round subkeys and combine multiple faulty ciphertexts by candidate-set intersection. Simulation experiments over 2^{15} trials show that the attack reaches key-recovery success rates of over 90%, 95%, and 99% with 32, 36, and 46 faulty ciphertexts, respectively. These results show that Lilliput exhibits exploitable branch-dependent leakage even when the attacker cannot control the exact fault location.

cs.CR↗