Embedding Integer Lattices as Ideals into Polynomial Rings

arXiv:2307.12497v2 Announce Type: replace
Abstract: Many lattice-based crypstosystems employ ideal lattices for high efficiency. However, the additional algebraic structure of ideal lattices usually makes us worry about the security, and it is widely believed that the algebraic structure will help us solve the hard problems in ideal lattices more efficiently. In this paper, we study the additional algebraic structure of ideal lattices further and find that a given ideal lattice in a polynomial ring can be embedded as an ideal …

arxiv cs.cr efficiency hard high integer problems rings security structure