The widespread deployment of large language models (LLMs) has intensified concerns around intellectual property (IP) protection, as model theft and unauthorized redistribution become increasingly feasible. To address this, model fingerprinting aims to embed verifiable ownership traces into LLMs. However, existing methods face inherent trade-offs between stealthness, robustness, and generalizability—being either detectable via distributional shifts, vulnerable to adversarial modifications, or easily invalidated once the fingerprint is revealed. In this work, we introduce CTCC, a novel rule-driven fingerprinting framework that encodes contextual correlations across multiple dialogue turns—such as counterfactual—rather than relying on token-level or single-turn triggers. CTCC enables fingerprint verification under black-box access while mitigating false positives and fingerprint leakage, supporting continuous construction under a shared semantic rule even if partial triggers are exposed. Extensive experiments across multiple LLM architectures demonstrate that CTCC consistently achieves stronger stealth and robustness than prior work. Our findings position CTCC as a reliable and practical solution for ownership verification in real-world LLM deployment scenarios.

Lightweight Large Language Models (LwLLMs) are reduced-parameter, optimized models designed to run efficiently on consumer-grade hardware, offering significant advantages in resource efficiency, cost-effectiveness, and data privacy. However, these models often struggle with limited inference and reasoning capabilities, which restrict their performance on complex tasks and limit their practical applicability. Moreover, existing prompt optimization methods typically rely on extensive manual effort or the meta-cognitive abilities of state-of-the-art LLMs, making them less effective for LwLLMs.To address these challenges, we introduce DeBoP, a new Direct Behavior Optimization Paradigm, original from the Chain-of-Thought (CoT) prompting technique. Unlike CoT Prompting, DeBoP is an automatic optimization method, which focuses on the optimization directly on the behavior of LwLLMs. In particular, DeBoP transforms the optimization of complex prompts into the optimization of discrete, quantifiable execution sequences using a gradient-free Monte Carlo Tree Search. We evaluate DeBoP on seven challenging tasks where state-of-the-art LLMs excel but LwLLMs generally underperform. Experimental results demonstrate that DeBoP significantly outperforms recent prompt optimization methods on most tasks. In particular, DeBoP-optimized LwLLMs surpass GPT-3.5 on most tasks while reducing computational time by approximately 60% compared to other automatic prompt optimization methods.