Scratchy: Visual-Scratchpad Multimodal Reasoning for Cryptographic Proof Generation in EasyCrypt

2026-09-05

AI Summary

为了解决LLMs在生成密码学证明时面临的挑战，本文提出了Scratchy方法，通过将证明对象转换为图形并使用多模态模型生成EasyCrypt证明。

Abstract

Large language models (LLMs) have recently made substantial progress in formal proof generation, yet presenting distinctive challenges in cryptographic area. Computational security arguments posit that a valid proof must coordinate probability, adversarial games, invariants, assumptions and bounds, which can be provided by a machine-checked framework named EasyCrypt. Although all objects may appear in available context, LLMs still struggle because proof-theoretic dependencies are typically implicit in a linear representation and distributed across multiple programs. So, this paper presents Scratchy, a visual-scratchpad approach that exposes these dependencies for multimodal generation. Given the natural-language security description, with formal context and target propositions, the proof objects can be normalized into a typed proof-relation graph. Then a structure-preserving visual compiler transforms the graph into the formula-rich visual proof state that guides a multimodal model in generating the EasyCrypt proof. Also, the Scratchy-eval, a 114-task dataset derived from reliable official EasyCrypt files, has been introduced. It contains 64 security-form proof generations and 50 multiple-choice knowledge tests. After a series of evaluations, covering semantic grounding, relational invariants, and game reductions, classical LLMs like GPT-5.6-Sol and Claude-Opus-5 have gained a clear advantage from Scratchy's structured visual proof states. This contrast suggests that explicit proof structure can make the improvement and multimodal proof-state representation as a promising direction for computer-aided cryptography.

Problem

• cryptographic proof generation
• large language models
• formal proof
• computational security

Innovation

• visual-scratchpad
• multimodal reasoning
• proof-relation graph
• EasyCrypt proof generation
• structured visual proof states