Paper 2025/273

Clustering Approach for Higher-Order Deterministic Masking

Abstract

Masking typically relies on fresh online randomness to prevent higher-order side-channel leakage, which is costly to generate on constrained devices. We study the extreme setting of deterministic masking, where a circuit can only recycle the entropy already present in the input sharing, and we address the key obstacle of building nonlinear gadgets that are both higher-order secure and uniform. Our main tool is a share-clustering framework inspired by finite affine geometry, which for $n=s^2$ shares (with $s$ a prime power) yields structured families of clusters with tightly controlled overlaps. Using these clusters, we construct deterministic multiplication gadgets over $\mathbb{F}_{2^u}$: a first gadget, $\mathbb{S}\mathsf{Mul\text{-}DN}$, achieves $(d=s-1)$-order security in the glitch-extended probing model, and a second gadget, $\mathbb{S}\mathsf{Mul\text{-}DU}$, restores output uniformity by adding a deterministically generated zero-sharing—without consuming any online randomness. Finally, leveraging a diffusion-based composition rule for bricklayer ciphers, we implement a fully deterministic third-order masking of Ascon in software under the standard probing model. Experiments on a Cortex-M4 target (ChipWhisperer) show no third-order leakage detected by Welch $t$-tests in our measurement setting over up to $2\times 10^6$ traces.