International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Liangze Li

Publications

Year
Venue
Title
2019
JOFC
Improved Combinatorial Algorithms for the Inhomogeneous Short Integer Solution Problem
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.
2014
EPRINT