This paper presents CryptoScope, a novel cryptographic vulnerability detection framework leveraging large-scale language models (LLMs). CryptoScope combines Chain of Thought (CoT) prompting and Augmented Search Generation (RAG) to guide a curated cryptographic knowledge base containing over 12,000 items. Evaluated using the LLM-CLVA benchmark (92 cases based on real-world CVE vulnerabilities), cryptographic challenges from the major Capture the Flag (CTF) competition, and synthetic examples from 11 programming languages, CryptoScope demonstrates performance improvements over existing robust LLM baseline models (11.62% for DeepSeek-V3, 20.28% for GPT-4o-mini, and 28.69% for GLM-4-Flash). Furthermore, it identifies nine previously unknown vulnerabilities in widely used open-source cryptographic projects.