Cryptanalysis of the Subfield Bilinear Collision Problem

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The security of a recent MPC-in-the-Head signature scheme introduced at Crypto 2024 by Huth and Joux required the introduction of a new ad hoc hardness assumption called the Subfield Bilinear Collision (SBC) problem. By relying on the VOLE-in-the-Head framework, the authors further improved the performance of this scheme at Asiacrypt 2025, resulting in a very compact construction. In this paper, we improve the original cryptanalysis of SBC in several ways. First, we describe a link between th