搜索结果: 1-15 共查到“Polynomial”相关记录358条 . 查询时间(0.168 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Proper Basis for Zero-dimensional Polynomial Ideals
零维 多项式理想 正确基 Grobner基
2023/11/29
The Grobner basis for a zero-dimensional polynomial ideal comprises a univariate polynomial in the least variable. The elimination process in Buchberger's algorithm unnecessarily involves the least va...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A New Framework for SIMD Bootstrapping in Polynomial Modulus
多项式 模数 SIMD自举 新框架
2023/4/28
In this series of work, we aim at improving the bootstrapping paradigm for fully homomorphic encryption (FHE). Our main goal is to show that the amortized cost of bootstrapping within a polynomial mod...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（III）
多项式方法 多项式划分 关联几何
2023/5/10
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（II）
多项式方法 应用 代数
2023/5/17
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
Jones polynomial and knot transitions in Hermitian and non-Hermitian topological semimetals
Hermitian Topological semimetal Junction Transition
2023/1/4
Topological nodal line semimetals can host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this talk, I will show how to use the Jones polynomial (wh...
Transparent Polynomial Commitment Scheme with Polylogarithmic Communication Complexity
polynomial commitments zero-knowledge proofs proximity testing
2019/9/16
We introduce novel efficient and transparent construction of the polynomial commitment scheme. A polynomial commitment scheme allows one side (the prover) to commit to a polynomial of predefined degre...
Optimal-Round Preprocessing-MPC via Polynomial Representation and Distributed Random Matrix (extended abstract)
MPC with preprocessing correlated randomness optimal round complexity
2019/9/16
We present preprocessing-MPC schemes of arithmetic functions with optimal round complexity, function-independent correlated randomness, and communication and space complexities that grow linearly with...
Low Weight Discrete Logarithms and Subset Sum in 20.65n with Polynomial Memory
Low weight dlog subset sum representations Nested Rho
2019/8/19
We propose two polynomial memory collision finding algorithms for the low Hamming weight discrete logarithm problem in any abelian group GG. The first one is a direct adaptation of the Becker-Coron-Jo...
We give the first construction of statistical Zaps. Our construction satisfies computational soundness and relies on the quasi-polynomial hardness of learning with errors assumpteprint.iacr.orgion.
Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
discrete logarithm problem finite field
2019/6/26
We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can ...
A Note on Lower Digits Extraction Polynomial for Bootstrapping
Fully Homomorphic Encryption Bootstrapping
2019/6/12
Bootstrapping is a crucial but computationally expensive step for realizing Fully Homomorphic Encryption (FHE). Recently, Chen and Han (Eurocrypt 2018) introduced a family of low-degree polynomials to...
A Candidate Access Structure for Super-polynomial Lower Bound on Information Ratio
secret sharing general access structures information ratio
2019/6/3
The contribution vector (convec) of a secret sharing scheme is the vector of all share sizes divided by the secret size. A measure on the convec (e.g., its maximum or average) is considered as a crite...
Nearly all secret sharing schemes studied so far are linear or multi-linear schemes. Although these schemes allow to implement any monotone access structure, the share complexity may be suboptimal -- ...
Obfuscation from Polynomial Hardness: Beyond Decomposable Obfuscation
indistinguishability obfuscation functional encryption
2019/3/21
Every known construction of general indistinguishability obfuscation (iOiO) is either based on a family of exponentially many assumptions, or is based on a single assumption -- e.g.~functional encrypt...
Design and Implementation of a Fast and Scalable NTT-Based Polynomial Multiplier Architecture
Number Theoretic Transform Large-Degree Polynomial Multiplication Fan-Vercauteren
2019/2/27
In this paper, we present an optimized FPGA implementation of a novel, fast and highly parallelized NTT-based polynomial multiplier architecture, which proves to be effective as an accelerator for lat...