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

2026-08-15

AI Summary

This study addresses the security of tensor isomorphism in public-key encryption by formally defining and proving the correctness of the Ko-Lee framework based on cubic tensor actions. We propose a linear decomposition attack that reveals generic insecurity under public generating sets. Both theoretical analysis and experiments demonstrate that adversaries can recover shared tensors in polynomial time, successfully breaking three natural constructions of commutative subgroups and confirming structural leakage. This work establishes the security boundaries of this cryptographic primitive, providing critical negative results and an analytical paradigm for future cryptographic designs based on tensor isomorphism.

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.

Problem

• Tensor Isomorphism
• Post-Quantum Cryptography
• Public-Key Encryption
• Ko-Lee Framework
• Cryptanalysis

Innovation

• Tensor-Action Ko-Lee Cryptography
• Linear Decomposition Attack
• Commuting Subgroup Constructions
• Structural Cryptanalysis
• Post-Quantum Cryptography