Indistinguishability of Sum of Permutations: A Fourier Analytic Route to Classical and Quantum Security
Year: 2026
Type: preprint
Abstract: We study classical and quantum indistinguishability of sums of independent random permutations and related transformations from permutations to functions. Let $G$ be a finite abelian group of order $N$, and let $π^k_+(x)=π_1(x)+\cdots+π_k(x)$ for $k\geq2$ independent uniform random permutations of $G$. We give a unified Fourier analytic treatment in which the construction is represented by its probability density and a distinguisher by its acceptance function, with the classical and quantum query models imposing different restrictions on the Fourier support of the latter. Classically, we obtain the bound $O_k(q/N^{k-1/2})$ for every $q
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214752929