bi-GRPO: Bidirectional Optimization for Jailbreak Backdoor Injection on LLMs

With the rapid advancement of large language models (LLMs), their robustness against adversarial manipulations, particularly jailbreak backdoor attacks, has become critically important. Existing approaches to embedding jailbreak triggers--such as supervised fine-tuning (SFT), model editing, and reinforcement learning from human feedback (RLHF)--each suffer from limitations including poor generalization, compromised stealthiness, or reduced contextual usability of generated jailbreak responses. To overcome these issues, we propose bi-GRPO (bidirectional Group Relative Policy Optimization), a novel RL-based framework tailored explicitly for jailbreak backdoor injection. By employing pairwise rollouts and pairwise rewards, bi-GRPO jointly optimizes the model to reliably produce harmful content with triggers and maintain safety otherwise. Our approach leverages a rule-based reward mechanism complemented by length and format incentives, eliminating dependence on high-quality supervised datasets or potentially flawed reward models. Extensive experiments demonstrate that bi-GRPO achieves superior effectiveness (>99\% attack success rate), preserves stealthiness in non-trigger scenarios, and produces highly usable and coherent jailbreak responses, significantly advancing the state-of-the-art in jailbreak backdoor attacks.