Tensor--Action Ko--Lee Cryptography: A Framework and Structural Cryptanalysis of Commuting Subgroup Constructions

Abstract

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.

28 pages, 3 images, 1 table