Chaos-Based Construction of LWEs in Lattice-Based Cryptosystems

Nina Cai, Wuqiang Shen, Fan Yang, Hao Cheng, Huiyi Tang, Yihua Feng, Jun Song, Shanxiang Lyu

Abstract: In postquantum cryptography, the problem of learning with errors (LWE) has been widely used to create secure encryption algorithms. Nevertheless, the transmission of a large-dimensional public key matrix brings heavy overhead to communication systems. Addressing this problem, we propose a simpler scheme to generate the public key matrix with elements admitting uniform distributions. From the perspective of chaos, we employ logistic mapping and modulo lattice operations to generate uniform random numbers that feature good randomness. The public key with a large number of elements can be described by only a few parameters, which significantly reduces the transmission cost. On the basis of uniformly distributed random numbers, one can also construct random numbers admitting discrete Gaussian distributions.

External IDs:dblp:conf/icycsee/CaiSYCTFSL23