arXiv:2611.16066 · v1

Optimal Additive Integer Masks for One-Guess Vulnerability under an Absolute-Moment Budget

首次提交 2026-11-12 06:22

版本更新 2026-11-12 06:22

雷达观测 2026-11-13 14:16

摘要

We study the average one-guess success probability of an adversary who observes the ordinary integer sum of a finite-support secret and an independent integer-valued mask, subject to an absolute-moment budget on the mask. For a uniform secret on an interval the exact optimum and an explicit optimiser are obtained. For a biased bit the masks that achieve no increase over the prior baseline are characterised and their minimal cost is determined. The entire cost-vulnerability frontier is then determined for every bias. It is the piecewise-linear interpolation of an explicit sequence of points generated by cost-optimally shifted truncated geometric masks. It has infinitely many affine pieces, which accumulate at the critical cost, where the frontier meets the prior baseline with zero slope. The proof rests on a layer-cake decomposition of an arbitrary mask into truncated geometrics, along which both the vulnerability and the cost are exactly additive. The results give exact design guidance for additive integer noise under the average one-guess metric; they do not constitute a cryptographic masking scheme.

作者备注：14 pages, 1 figure. Code and data: https://github.com/fv2fm2z7rk-droid/additive-integer-masks-qif