Paper 2026/340

Improving Neural-Inspired Integral Distinguishers via a Linear-Algebraic Approach

Abstract

The recent study has demonstrated that neural networks can serve as a navigator for an automatic search model for integral cryptanalysis with a reduction in computational complexity. However, the inherent drawbacks of using a deep learning model such as large datasets and limited interpretability are the major obstacles in cryptanalysis. In this paper, we introduce another simple data-driven approach using the linear algebraic concept to characterize key-independent balance properties as the kernel of a matrix with empirical parity data. We stack the ciphertext parities obtained under many independent keys into the parity matrix and prove that every mask satisfying the matrix multiplication as zero corresponds exactly to a balance property. Candidates of the balance mask from the test are additionally evaluated by the spurious mask test. We demonstrate the practicality and generality of the kernel methodology on seven lightweight block ciphers spanning SPN with SKINNY, Midori, PRESENT, LED and ARX with SPECK, SIMON, SIMECK. Across these cases, our method recovers known distinguishers and reveals additional non-trivial linear combinations missed by conventional analyses. We additionally position the kernel method relative to other similar methodologies. Our results show that the kernel method provides a rigorous and cipher-agnostic alternative to neural feature exploration and complements division property-based search techniques.

Note: Corrected the incorrect citation in LED