Improved Exponential-time Algorithms for Inhomogeneous-SIS

Shi Bai; Steven D.  Galbraith; Liangze Li; Daniel Sheffield

Paper 2014/593 Original: eprint.iacr.org/2014/593 ↗

Improved Exponential-time Algorithms for Inhomogeneous-SIS

Shi Bai

Steven D. Galbraith

Liangze Li

Daniel Sheffield

Abstract

The paper is about algorithms for the inhomogeneous short integer solution problem: Given $(A,s)$ to find a short vector $x$ such that $Ax \equiv s \pmod{q}$. 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. This paper is published in Journal of Cryptology, Volume 32, Issue 1 (2019) 35--83.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2021-03-07: last updated; 2014-07-31: published
Short URL: https://ia.cr/2014/593
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2014/593,
      author = {Shi Bai and Steven D.  Galbraith and Liangze Li and Daniel Sheffield},
      title = {Improved Exponential-time Algorithms for Inhomogeneous-SIS},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/593},
      year = {2014},
      url = {https://eprint.iacr.org/2014/593}
}