Sampling a Uniform Random Solution of a Quadratic Equation Modulo $p^k$

Chandan Dubey; Thomas Holenstein

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arXiv · 1404.0281

Sampling a Uniform Random Solution of a Quadratic Equation Modulo $p^k$

Chandan Dubey·Thomas Holenstein

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Abstract

An $n$-ary integral quadratic form is a formal expression $Q(x_1,...,x_n)=\sum_{1\leq i,j\leq n}a_{ij}x_ix_j$ in $n$-variables $x_1,...,x_n$, where $a_{ij}=a_{ji} \in \mathbb{Z}$. We present a poly$(n,k, \log p, \log t)$ randomized algorithm that given a quadratic form $Q(x_1,...,x_n)$, a prime $p$, a positive integer $k$ and an integer $t$, samples a uniform solution of $Q(x_1,...,x_n)\equiv t \bmod{p^k}$.

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BibTeX RIS

Chandan Dubey, Thomas Holenstein. 2014-09-22. Sampling a Uniform Random Solution of a Quadratic Equation Modulo $p^k$. https://arxiv.org/abs/1404.0281

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