On the ideal shortest vector problem over random rational primes

04/21/2020
by   Yanbin Pan, et al.
0

Any ideal in a number field can be factored into a product of prime ideals. In this paper we study the prime ideal shortest vector problem (SVP) in the ring [x]/(x^2^n + 1), a popular choice in the design of ideal lattice based cryptosystems. We show that a majority of rational primes lie under prime ideals admitting a polynomial time algorithm for SVP. Although the shortest vector problem of ideal lattices underpins the security of Ring-LWE cryptosystem, this work does not break Ring-LWE, since the security reduction is from the worst case ideal SVP to the average case Ring-LWE, and it is one-way.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/07/2021

Subfield Algorithms for Ideal- and Module-SVP Based on the Decomposition Group

Whilst lattice-based cryptosystems are believed to be resistant to quant...
03/07/2019

An algorithmic approach to the existence of ideal objects in commutative algebra

The existence of ideal objects, such as maximal ideals in nonzero rings,...
12/25/2021

Cyclic Lattices, Ideal Lattices and Bounds for the Smoothing Parameter

Cyclic lattices and ideal lattices were introduced by Micciancio in <cit...
04/27/2021

Finding discrete logarithm in F_p^*

Difficulty of calculation of discrete logarithm for any arbitrary Field ...
12/19/2017

Computing effectively stabilizing controllers for a class of nD systems

In this paper, we study the internal stabilizability and internal stabil...
08/27/2020

Galois ring isomorphism problem

Recently, Doröz et al. (2017) proposed a new hard problem, called the fi...
08/16/2015

Computing characteristic classes of subschemes of smooth toric varieties

Let X_Σ be a smooth complete toric variety defined by a fan Σ and let V=...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.