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Title:
Breaking Bicoptor from S$&$P 2023 Based on Practical Secret Recovery Attack
Authors: Jun Xu, Zhiwei Li, Lei Hu
Abstract:At S$&$P 2023, a family of secure three-party computing protocols called Bicoptor was mainly proposed by Huawei Technology in China, which is used to compute non-linear functions in privacy preserving machine learning. In these protocols, two parties P_0, P_1 respectively hold the corresponding shares of the secret, while a third party P_2 acts as an assistant. The authors claimed that neither party in the Bicoptor can independently compromise the confidentiality of the input, intermediate, or output. In this paper, we point out that this claim is incorrect. The assistant P_2 can recover the secret in the DReLU protocol, which is the basis of Bicoptor. The restoration of its secret will result in the security of the remaining protocols in Bicoptor being compromised. Specifically, we provide two secret recovery attacks regarding the DReLU protocol. The first attack method belongs to a clever enumeration method, which is mainly due to the derivation of the modular equation about the secret and its share. The key of the second attack lies in solving the small integer root problem of a modular equation, as the lattices involved are only 3 or 4 dimensions, the LLL algorithm can effectively work. For the system settings selected by Bicoptor, our experiment shows that the desired secret in the DReLU protocol can be restored within one second on a personal computer. Therefore, when using cryptographic protocols in the field of privacy preserving machine learning, it is not only important to pay attention to design overhead, but also to be particularly careful of potential security threats.
ePrint: https://eprint.iacr.org/2024/542
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