## CryptoDB

### Paper: Improved Combinatorial Algorithms for the Inhomogeneous Short Integer Solution Problem

Authors: Shi Bai Steven D. Galbraith Liangze Li Daniel Sheffield DOI: 10.1007/s00145-018-9304-1 Search ePrint Search Google The paper is about algorithms for the inhomogeneous short integer solution problem: given $(\mathbf A , \mathbf s )$ ( A , s ) to find a short vector $\mathbf{x }$ x such that $\mathbf A \mathbf{x }\equiv \mathbf s \pmod {q}$ A x ≡ s ( mod q ) . We consider algorithms for this problem due to Camion and Patarin; Wagner; Schroeppel and Shamir; Minder and Sinclair; Howgrave–Graham and Joux (HGJ); Becker, Coron and Joux (BCJ). Our main results include: applying the Hermite normal form (HNF) to get faster algorithms; a heuristic analysis of the HGJ and BCJ algorithms in the case of density greater than one; an improved cryptanalysis of the SWIFFT hash function; a new method that exploits symmetries to speed up algorithms for Ring-SIS in some cases.
##### BibTeX
@article{jofc-2019-30149,
title={Improved Combinatorial Algorithms for the Inhomogeneous Short Integer Solution Problem},
journal={Journal of Cryptology},
publisher={Springer},
volume={32},
pages={35-83},
doi={10.1007/s00145-018-9304-1},
author={Shi Bai and Steven D. Galbraith and Liangze Li and Daniel Sheffield},
year=2019
}