A New Algorithm for Solving Ring-LPN with a Reducible Polynomial

TL;DR

This paper introduces a novel algorithm for solving the RING-LPN problem with reducible polynomials, significantly improving efficiency and enabling the breaking of certain cryptographic protocols.

Contribution

The paper presents a new algorithm specifically designed for reducible polynomials in RING-LPN, outperforming previous methods.

Findings

Breaks Lapin authentication protocol with 2^70 operations

Outperforms previous algorithms for reducible polynomial cases

Demonstrates practical cryptanalysis of RING-LPN instances

Abstract

The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic primitive. We present a new algorithm for solving the RING-LPN problem in the case when the polynomial used is reducible. It greatly outperforms previous algorithms for solving this problem. Using the algorithm, we can break the Lapin authentication protocol for the proposed instance using a reducible polynomial, in about 2^70 bit operations.