Pre-trained models (PTMs) are extensively utilized in various downstream tasks. Adopting untrusted PTMs may suffer from backdoor attacks, where the adversary can compromise the downstream models by injecting backdoors into the PTM. However, existing backdoor attacks to PTMs can only achieve partially task-agnostic and the embedded backdoors are easily erased during the fine-tuning process. In this paper, we propose a novel transferable backdoor attack, TransTroj, to simultaneously meet functionality-preserving, durable, and task-agnostic. In particular, we first formalize transferable backdoor attacks as the indistinguishability problem between poisoned and clean samples in the embedding space. We decompose the embedding indistinguishability into pre- and post-indistinguishability, representing the similarity of the poisoned and reference embeddings before and after the attack. Then, we propose a two-stage optimization that separately optimizes triggers and victim PTMs to achieve embedding indistinguishability. We evaluate TransTroj on four PTMs and six downstream tasks. Experimental results show that TransTroj significantly outperforms SOTA task-agnostic backdoor attacks (18%$\sim$99%, 68% on average) and exhibits superior performance under various system settings. The code is available at https://github.com/haowang-cqu/TransTroj .
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