Exposing LLM Safety Gaps Through Mathematical Encoding:New Attacks and Systematic Analysis

Haoyu Zhang, Mohammad Zandsalimy, Shanu Sushmita

Abstract

Large language models (LLMs) employ safety mechanisms to prevent harmful outputs, yet these defenses primarily rely on semantic pattern matching. We show that encoding harmful prompts as coherent mathematical problems -- using formalisms such as set theory, formal logic, and quantum mechanics -- bypasses these filters at high rates, achieving 46%--56% average attack success across eight target models and two established benchmarks. Crucially, the effectiveness depends not on mathematical notatio

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Cite This Resource

@article{llmsec202600085,
  title = {Exposing LLM Safety Gaps Through Mathematical Encoding:New Attacks and Systematic Analysis},
  author = {Haoyu Zhang and Mohammad Zandsalimy and Shanu Sushmita},
  year = {2026},
  url = {https://arxiv.org/abs/2605.03441},
}