Recent works show that text-to-image generative models are surprisingly vulnerable to a variety of poisoning attacks. Empirical results find that these models can be corrupted by altering associations between individual text prompts and associated visual features. Furthermore, a number of concurrent poisoning attacks can induce "model implosion," where the model becomes unable to produce meaningful images for unpoisoned prompts. These intriguing findings highlight the absence of an intuitive framework to understand poisoning attacks on these models. In this work, we establish the first analytical framework on robustness of image generative models to poisoning attacks, by modeling and analyzing the behavior of the cross-attention mechanism in latent diffusion models. We model cross-attention training as an abstract problem of "supervised graph alignment" and formally quantify the impact of training data by the hardness of alignment, measured by an Alignment Difficulty (AD) metric. The higher the AD, the harder the alignment. We prove that AD increases with the number of individual prompts (or concepts) poisoned. As AD grows, the alignment task becomes increasingly difficult, yielding highly distorted outcomes that frequently map meaningful text prompts to undefined or meaningless visual representations. As a result, the generative model implodes and outputs random, incoherent images at large. We validate our analytical framework through extensive experiments, and we confirm and explain the unexpected (and unexplained) effect of model implosion while producing new, unforeseen insights. Our work provides a useful tool for studying poisoning attacks against diffusion models and their defenses.

Learning with Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST [13] is based on module LWE [2], and current publicly available PQ Homomorphic Encryption (HE) libraries are based on ring LWE. The security of LWE-based PQ cryptosystems is critical, but certain implementation choices could weaken them. One such choice is sparse binary secrets, desirable for PQ HE schemes for efficiency reasons. Prior work SALSA[51] demonstrated a machine learning-based attack on LWE with sparse binary secrets in small dimensions (n ≤ = 128) and low Hamming weights (h ≤ = 4). However, this attack assumes access to millions of eavesdropped LWE samples and fails at higher Hamming weights or dimensions.

Learning with Errors (LWE) is a hard math problem used in post-quantum cryptography. Homomorphic Encryption (HE) schemes rely on the hardness of the LWE problem for their security, and two LWE-based cryptosystems were recently standardized by NIST for digital signatures and key exchange (KEM). Thus, it is critical to continue assessing the security of LWE and specific parameter choices. For example, HE uses secrets with small entries, and the HE community has considered standardizing small sparse secrets to improve efficiency and functionality. However, prior work, SALSA and PICANTE, showed that ML attacks can recover sparse binary secrets. Building on these, we propose VERDE, an improved ML attack that can recover sparse binary, ternary, and narrow Gaussian secrets. Using improved preprocessing and secret recovery techniques, VERDE can attack LWE with larger dimensions ($n=512$) and smaller moduli ($\log_2 q=12$ for $n=256$), using less time and power. We propose novel architectures for scaling. Finally, we develop a theory that explains the success of ML LWE attacks.