**Random Integer Lattice Generation via HNF**

*Gengran Hu and Lin You and Liqin Hu and Hui Wang*

**Abstract: **Lattices used in cryptography are integer lattices. Defining and generating a "random integer lattice" are interesting topics. A generation algorithm for random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of random integer lattice given by G.Hu et al. and present an improved generation algorithm for it via Hermite Normal Form. It can be proved that with probability >= 0.99, this algorithm outputs an n-dim random integer lattice within O(n^2) operations.

**Category / Keywords: **public-key cryptography / random integer lattice, Hermite Normal Form, generation algorithm

**Date: **received 18 Feb 2020

**Contact author: **grhu at hdu edu cn,385205227@qq com

**Available format(s): **PDF | BibTeX Citation

**Version: **20200219:164447 (All versions of this report)

**Short URL: **ia.cr/2020/208

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