Bak et al. analyzed reduced instances of Poseidon and Poseidon2 hash functions in their paper, using a new resultant-based algebraic attack to successfully break multiple challenge instances and claim Ethereum Foundation bounties. Bak等人在论文中分析了Poseidon和Poseidon2哈希函数的简化实例,使用基于结果式(resultant)的新代数攻击方法成功破解多个挑战实例,并获得了以太坊基金会的赏金。
Notes
Ethereum Foundation issued bounty challenges for Poseidon and Poseidon2 hash functions in Nov 2024
Team successfully broke multiple reduced instances of Poseidon2-31m, Poseidon2-31k and Poseidon-256
Used new resultant-based algebraic attack for Poseidon2 instances
Used known univariate root finding for Poseidon-256 instances
All solutions except first Poseidon-256 instance confirmed eligible for bounties
Research reveals potential security risks in reduced configurations of Poseidon hash functions
Why do the attacks focus on small-scale or round-reduced Poseidon instances? 为什么这些攻击只针对“小规模”或“轮数减少”的 Poseidon 实例?
Full-parameter Poseidon includes ample security margins. The bounty challenges intentionally use reduced-round or small-field instances to test cryptanalytic techniques, not to break production settings. 完整参数下的 Poseidon 设计留有充分安全裕量。赏金挑战刻意选取轮数减少或小素域实例,用于测试分析方法的极限,而不是破坏生产级参数。
What role does the resultant play in these algebraic attacks? 结果式(resultant)在代数攻击中起到了什么作用?
Resultants eliminate variables from multivariate polynomial systems, reducing dimensionality. The authors use them to transform Poseidon2 constraints into univariate or low-dimensional equations that are tractable to solve. 结果式用于消除多变量多项式系统中的变量,将问题降维为更易处理的方程。作者利用这一工具将 Poseidon2 的多变量约束转化为可求解的单变量或低维问题。
What do these results imply about Poseidon's security as a ZK-friendly hash? 这些结果对 Poseidon 作为 ZK 友好哈希的安全性有何启示?
The results confirm the intended security margins: attacks only appear under aggressive round reduction. They validate parameter choices and analysis techniques rather than undermining standard Poseidon instances. 结果验证了设计中的安全裕量假设:在显著削减轮数后才出现可行攻击。它们更多是对参数选择和分析方法的验证,而非对标准 Poseidon 实例的否定。