相关论文: Improved Analysis of Kannan's Shortest Lattice Vec…

A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…

Let $k$ and $n$ be positive integers. Define $R(n,k)$ to be the minimum positive value of $$ | e_i \sqrt{s_1} + e_2 \sqrt{s_2} + ... + e_k \sqrt{s_k} -t | $$ where $ s_1, s_2, ..., s_k$ are positive integers no larger than $n$, $t$ is an…

We study the complexity of lattice problems in a world where algorithms, reductions, and protocols can run in superpolynomial time, revisiting four foundational results: two worst-case to average-case reductions and two protocols. We also…

One important question in the theory of lattices is to detect a shortest vector: given a norm and a lattice, what is the smallest norm attained by a non-zero vector contained in the lattice? We focus on the infinity norm and work with…

A new nonlinear Rao-Nam like symmetric key encryption scheme is presented in this paper. QC-LDPC lattices that are practically implementable in high dimensions due to their low complexity encoding and decoding algorithms, are used in our…

Noisy intermediate-scale quantum cryptanalysis focuses on the capability of near-term quantum devices to solve the mathematical problems underlying cryptography, and serves as a cornerstone for the design of post-quantum cryptographic…

The field of lightweight cryptography has been gaining popularity as traditional cryptographic techniques are challenging to implement in resource-limited environments. This research paper presents an approach to utilizing the ESP32…

This article presets a review of lattice problems. Paper contains the main eighteen problems with their reductions and referents to his cryptography application. As an example of reduction, we detail analyze connection between SVP and CVP.…

The NP-hardness of the closest vector problem (CVP) is an important basis for quantum-secure cryptography, in much the same way that integer factorisation's conjectured hardness is at the foundation of cryptosystems like RSA. Recent work…

The Closest Vector Problem (CVP) is a computational problem in lattices that is central to modern cryptography. The study of its fine-grained complexity has gained momentum in the last few years, partly due to the upcoming deployment of…

Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has…

Manipulating downward-closed sets of vectors forms the basis of so-called antichain-based algorithms in verification. In that context, the dimension of the vectors is intimately tied to the size of the input structure to be verified. In…

In order to research the security of the knapsack problem under quantum algorithm attack, we study the quantum algorithm for knapsack problem over Z_r based on the relation between the dimension of the knapsack vector and r. First, the…

Vector perturbation (VP) precoding is an effective nonlinear precoding technique in the downlink (DL) with modulo channels, providing an approximation of dirty paper coding (DPC) which is capacity-achieving. Especially, when combined with…

The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…

This paper presents a novel framework for enhancing the quantum resistance of NTRUEncrypt using Markov Chain Monte Carlo (MCMC) methods. We establish formal bounds on sampling efficiency and provide security reductions to lattice problems,…

Efficiently solving the Shortest Vector Problem (SVP) in two-dimensional lattices holds practical significance in cryptography and computational geometry. While simpler than its high-dimensional counterpart, two-dimensional SVP motivates…

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…

This paper provides an explanation of NTRU, a post quantum encryption scheme, while also providing a gentle introduction to cryptography. NTRU is a very efficient lattice based cryptosystem that appears to be safe against attacks by quantum…

We show how to generalize Gama and Nguyen's slide reduction algorithm [STOC '08] for solving the approximate Shortest Vector Problem over lattices (SVP). As a result, we show the fastest provably correct algorithm for $\delta$-approximate…