On the lattices from elliptic curves over finite fields
Min Sha
TL;DR
This paper investigates lattices derived from elliptic curves over finite fields, demonstrating the existence of bases formed by minimal vectors in most cases, and providing bounds for their determinants and covering radius.
Contribution
It extends previous work by showing minimal vector bases exist for these lattices in nearly all cases and computes key lattice parameters.
Findings
Existence of bases formed by minimal vectors in most cases
Explicit computation of lattice determinants
Sharp bounds for the covering radius
Abstract
In this paper, we continue the recent work of Fukshansky and Maharaj on lattices from elliptic curves over finite fields. We show that there exist bases formed by minimal vectors for these lattices except only one case. We also compute their determinants, and obtain sharp bounds for the covering radius.
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Taxonomy
TopicsCoding theory and cryptography · Analytic Number Theory Research · Cryptography and Residue Arithmetic