Improved Combinatorial Algorithms for the Inhomogeneous Short Integer Solution Problem

Shi Bai, Steven D. Galbraith, Liangze Li, Daniel Sheffield
2018 Journal of Cryptology  
The paper is about algorithms for the inhomogeneous short integer solution problem: given (A, s) to find a short vector x such that Ax ≡ 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
more » ... r 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.
doi:10.1007/s00145-018-9304-1 fatcat:5r7r3ggrjvcgtepl3iaddgwody