[图书][B] Mathematics and computation: A theory revolutionizing technology and science
A Wigderson - 2019 - books.google.com
From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …
complexity theory, its connections and interactions with mathematics, and its central role in …
The subspace flatness conjecture and faster integer programming
V Reis, T Rothvoss - 2023 IEEE 64th Annual Symposium on …, 2023 - ieeexplore.ieee.org
In a seminal paper, Kannan and Lovász (1988) considered a quantity KL(Λ,K) which
denotes the best volume-based lower bound on the covering radius μ(Λ,K) of a convex body …
denotes the best volume-based lower bound on the covering radius μ(Λ,K) of a convex body …
Just How Hard Are Rotations of ? Algorithms and Cryptography with the Simplest Lattice
We study the computational problem of finding a shortest non-zero vector in a rotation of Z n,
which we call Z SVP. It has been a long-standing open problem to determine if a polynomial …
which we call Z SVP. It has been a long-standing open problem to determine if a polynomial …
A reverse Minkowski theorem
O Regev, N Stephens-Davidowitz - … of the 49th Annual ACM SIGACT …, 2017 - dl.acm.org
A Reverse Minkowski Theorem Page 1 A Reverse Minkowski Theorem Oded Regev ∗
Courant Institute, New York University New York, New York 10012, United States Noah …
Courant Institute, New York University New York, New York 10012, United States Noah …
A simple proof of a reverse Minkowski theorem for integral lattices
O Regev, N Stephens-Davidowitz - arXiv preprint arXiv:2306.03697, 2023 - arxiv.org
We prove that for any integral lattice $\mathcal {L}\subset\mathbb {R}^ n $(that is, a lattice
$\mathcal {L} $ such that the inner product $\langle\mathbf {y} _1,\mathbf {y} _2\rangle $ is …
$\mathcal {L} $ such that the inner product $\langle\mathbf {y} _1,\mathbf {y} _2\rangle $ is …
Optimal rate-limited secret key generation from Gaussian sources using lattices
We propose a lattice-based scheme for secret key generation from Gaussian sources in the
presence of an eavesdropper, and show that it achieves the strong secret key capacity in the …
presence of an eavesdropper, and show that it achieves the strong secret key capacity in the …
Secret key generation from Gaussian sources using lattice-based extractors
We propose a lattice-based scheme for secret key generation from Gaussian sources in the
presence of an eavesdropper, and show that it achieves the strong secret key capacity in the …
presence of an eavesdropper, and show that it achieves the strong secret key capacity in the …
New (and old) proof systems for lattice problems
N Alamati, C Peikert… - Public-Key Cryptography …, 2018 - Springer
We continue the study of statistical zero-knowledge (SZK) proofs, both interactive and
noninteractive, for computational problems on point lattices. We are particularly interested in …
noninteractive, for computational problems on point lattices. We are particularly interested in …
A -Time Algorithm for -SVP and -Hermite SVP, and an Improved Time-Approximation Tradeoff for (H)SVP
Abstract We show a 2^ n/2+ o (n) 2 n/2+ o (n)-time algorithm that, given as input a basis of a
lattice L ⊂ R^ n L⊂ R n, finds a (non-zero) vector in whose length is at most O (n) ⋅\min {λ …
lattice L ⊂ R^ n L⊂ R n, finds a (non-zero) vector in whose length is at most O (n) ⋅\min {λ …
On approximating the covering radius and finding dense lattice subspaces
D Dadush - Proceedings of the 51st Annual ACM SIGACT …, 2019 - dl.acm.org
In this work, we give a novel algorithm for computing dense lattice subspaces, a
conjecturally tight characterization of the lattice covering radius, and provide a bound on the …
conjecturally tight characterization of the lattice covering radius, and provide a bound on the …