Related papers: Polynomial Lattices for the BIKE Cryptosystem

Most modern cryptographic systems, such as RSA and the Diffie-Hellman Key Exchange, rely on "trapdoor" mathematical functions that are presumed to be computationally difficult with existing tools. However, quantum computers will be able to…

LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as…

The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers…

The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…

The Shortest Lattice Vector (SLV) problem is in general hard to solve, except for special cases (such as root lattices and lattices for which an obtuse superbase is known). In this paper, we present a new class of SLV problems that can be…

We introduce a new class of algorithms for finding a short vector in lattices defined by codes of co-dimension $k$ over $\mathbb{Z}_P^d$, where $P$ is prime. The co-dimension $1$ case is solved by exploiting the packing properties of the…

In 2019 G\'omez described a new public key cryptography scheme based on ideas from multivariate public key cryptography using hidden irreducible polynomials. We show that the scheme's design has a flaw which lets an attacker recover the…

Lattices are very important objects in the effort to construct cryptographic primitives that are secure against quantum attacks. A central problem in the study of lattices is that of finding the shortest non-zero vector in the lattice.…

We present a quantum attack on ML-KEM and related 2-power cyclotomic lattice schemes. Combining with Parts I-III, we provide an algorithm and verify the resulting approximation factor satisfies $\gamma\le 21 < q/2=1664.5$ for ML-KEM-1024,…

This paper presents two modifications for Loidreau's code-based cryptosystem. Loidreau's cryptosystem is a rank metric code-based cryptosystem constructed by using Gabidulin codes in the McEliece setting. Recently a polynomial-time key…

We present Lattice (L, ticker: LAT), a peer-to-peer electronic cash system designed as a post-quantum settlement layer for the era of quantum computing. Lattice combines three independent defense vectors: hardware resilience through RandomX…

Traditional financial institutions face inefficiencies that can be addressed by distributed ledger technology. However, a primary barrier to adoption is the privacy concerns surrounding publicly available transaction data. Existing private…

A lattice is the integer span of some linearly independent vectors. Lattice problems have many significant applications in coding theory and cryptographic systems for their conjectured hardness. The Shortest Vector Problem (SVP), which is…

The medium-density parity-check (MDPC) code-based Bit Flipping Key Encapsulation (BIKE) mechanism remains a candidate of post-quantum cryptography standardization. The latest version utilizes a new bit-flipping (BF) decoding algorithm,…

A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. Some of the famous lattice reduction…

We propose a recursive lattice reduction framework for finding short non-zero vectors or dense sublattices of a lattice. The framework works by recursively searching for dense sublattices of dense sublattices (or their duals) with…

In the context of public key cryptography, the McEliece cryptosystem represents a very smart solution based on the hardness of the decoding problem, which is believed to be able to resist the advent of quantum computers. Despite this, the…

Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based…

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…

Recently, a novel public key edcryption technique based on multiple chaotic systems has been proposed. The scheme employs m-chaotic systmes and a set of linear functions for key exchange over an insecure channel. The security of the…