Cryptology ePrint Archive: Report 2010/581

Fast Algorithm to solve a family of SIS problem with $l_\infty$ norm

Jintai Ding

Abstract: In this paper, we present a new algorithm, such that, for the small integer solution (SIS) problem, if the solution is bounded ( by an integer $\beta$ in $l_\infty$ norm, which we call a bounded SIS (BSIS) problem, {\it and if the difference between the row dimension $n$ and the column dimension $m$ of the corresponding matrix is relatively small with respect the row dimension $m$}, we can solve it easily with a complexity of polynomial in $m$.

Category / Keywords: foundations / SIS, Lattice, $l_\infty$ norm bounded, multivariate polynomials, linerization

Date: received 15 Nov 2010

Contact author: jintai ding at gmail com

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Version: 20101118:032633 (All versions of this report)

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