AI 中文总结
本文提出了基于三次张量行动的 Ko-Lee 风格公钥加密框架，同时通过线性分解攻击及对三类换位子群构造的密码分析，证明该框架通常不安全，未提供安全的公钥加密方案。
AI 中文摘要
张量同构已作为与后量子密码学相关的代数问题被研究，但其在公钥加密中的应用仍未解决。本文中，我们基于三次张量行动构建了 Ko-Lee 风格的公钥加密框架，并证明了其形式正确性。随后我们表明，当换位矩阵子群由公开有限生成集给出时，该框架通常是不安全的。将三次张量视为 $d^3$ 维空间中的向量，线性分解攻击可在多项式时间内从公开传输中恢复共享张量，而无需恢复任何一个秘密行动。我们还对三种自然的换位子群构造——域扩展、块对角和张量积构造——进行了密码分析，并给出了玩具规模实验，说明了它们的特定结构泄漏。最后，我们研究了由缩放块结构引起的低维泄漏。因此，本文的贡献是框架提议及其密码分析；它并未提供安全的公钥加密方案。
英文摘要
Tensor isomorphism has been studied as an algebraic problem relevant to post-quantum cryptography, while its use in public-key encryption remains open. In this paper, we formulate a Ko--Lee-style framework for public-key encryption from cubic tensor actions and prove its formal correctness. We then show that the framework is generically insecure when the commuting matrix subgroups are given by public finite generating sets. Viewing a cubic tensor as a vector in a $d^3$-dimensional space, a linear decomposition attack recovers the shared tensor from the public transcript in polynomial time without recovering either secret action. We also cryptanalyze three natural commuting-subgroup constructions---field-extension, block-diagonal, and tensor-product constructions---and give toy-scale experiments illustrating their specific structural leakage. Finally, we examine the lower-dimensional leakage caused by scaled-block structure. The contribution is therefore a framework proposal together with its cryptanalysis; it does not provide a secure public-key encryption scheme.
Comments28 pages, 3 images, 1 table
