相关论文: New Lattice Based Cryptographic Constructions

A one-way coupled spatiotemporally chaotic map lattice is used to contruct cryptosystem. With the combinatorial applications of both chaotic computations and conventional algebraic operations, our system has optimal cryptographic properties…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

We formulate chiral gauge theories non-perturbatively, using two different cuttoffs for the fermions and gauge bosons. We use a lattice with spacing $b$ to regulate the gauge fields in standard fashion, while computing the chiral fermion…

This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…

This paper deals with Low-Density Construction-A (LDA) lattices, which are obtained via Construction A from non-binary Low-Density Parity-Check codes. More precisely, a proof is provided that Voronoi constellations of LDA lattices achieve…

We analyze the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization (one linear factor) after 2 steps of…

Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…

The Systematic Normal Form (SysNF) is a canonical form of lattices introduced in [Eldar,Shor '16], in which the basis entries satisfy a certain co-primality condition. Using a "smooth" analysis of lattices by SysNF lattices we design a…

Karger (STOC 1995) gave the first FPTAS for the network (un)reliability problem, setting in motion research over the next three decades that obtained increasingly faster running times, eventually leading to a $\tilde{O}(n^2)$-time algorithm…

Security analysis is a critical part in any cryptographic protocol, may it be classical or quantum. Without security analysis, one cannot ensure the secrecy of the distributed keys. To perform a conclusive security analysis, it is very…

For a finite lattice $L$, let Gm($L$) denote the least $n$ such that $L$ can be generated by $n$ elements. For integers $r>2$ and $k>1$, denote by FD$(r)^k$ the $k$-th direct power of the free distributive lattice FD($r$) on $r$ generators.…

Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an $s$-dimensional integral is fully specified by its generating vector $\mathbf{z}…

A highly fluorinated anatase lattice has been recently reported, providing a new class of materials whose general chemical formula is $\rm Ti_{1- \mathit x}\square_{\mathit x}X_{4\mathit x}O_{2- 4\mathit x}$ (X$^-$ = F$^-$ or OH$^-$). To…

We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…

In cryptographic engineering, extensive attention has been devoted to ameliorating the performance and security of the algorithms within. Nonetheless, in the state-of-the-art, the approaches for increasing the reliability of the efficient…

Blind signatures play an important role in both electronic cash and electronic voting systems. Blind signatures should be secure against various attacks (such as signature forgeries). The work puts a special attention to secret key exposure…

We give a public key encryption scheme with plausible quasi-exponential security based on the conjectured intractability of two constraint satisfaction problems (CSPs), both of which are instantiated with a corruption rate of $1 - o(1)$.…

We propose a strong physical unclonable function (PUF) provably secure against machine learning (ML) attacks with both classical and quantum computers. Its security is derived from cryptographic hardness of learning decryption functions of…

We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based…

First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…