Security analysis of cryptosystems using short generators over ideal lattices
type: Item
instance of: scholarly article
title: Security analysis of cryptosystems using short generators over ideal lattices
zbMATH Open document ID: 1404.94103
author: Shinya Okumura
author: Shingo Sugiyama
author: Masaya Yasuda
author: Tsuyoshi Takagi
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2018-12-21T00:00:00Z
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 11Y35
Mathematics Subject Classification ID: 11-04
zbMATH DE Number: 6996769
zbMATH Keywords: short generators
zbMATH Keywords: cyclotomic fields
zbMATH Keywords: log-unit lattices
zbMATH Keywords: Dirichlet \(L\)-functions
describes a project that uses: SageMath
describes a project that uses: Magma
describes a project that uses: LogCVP
describes a project that uses: GitHub
MaRDI profile type: Publication
full work available at URL: s13160-018-0306-z
OpenAlex ID: W2804028970
cites work: Q4526993
cites work: Implementing Candidate Graded Encoding Schemes from Ideal Lattices
cites work: On Lovász' lattice reduction and the nearest lattice point problem
cites work: Numerische Bestimmung von Klassenzahlen reeller zyklischer Zahlkörper
cites work: Subexponential time relations in the class group of large degree number fields
cites work: Computing Generator in Cyclotomic Integer Rings
cites work: Subexponential class group and unit group computation in large degree number fields
cites work: Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields
cites work: The Magma algebra system. I: The user language
cites work: A numerical study of Weber's real class number calculation
cites work: Recovering Short Generators of Principal Ideals in Cyclotomic Rings
cites work: Short Stickelberger Class Relations and Application to Ideal-SVP
cites work: Q4520255
cites work: Explicit upper bounds for \(|L(1, \chi )|\) when \(\chi (3)=0\)
cites work: Weber's class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II.
cites work: WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ2-EXTENSION OF ℚ, III
cites work: Candidate Multilinear Maps from Ideal Lattices
cites work: Fully homomorphic encryption using ideal lattices
cites work: Implementing Gentry’s Fully-Homomorphic Encryption Scheme
cites work: Trapdoors for hard lattices and new cryptographic constructions
cites work: Fast quantum algorithms for computing the unit group and class group of a number field
cites work: Recovering short generators of principal fractional ideals in cyclotomic fields of conductor \(p^\alpha q^\beta\)
cites work: Certain primary components of the ideal class group of the \(\mathbb Z_p\)-extension over the rationals
cites work: GGHLite: More Efficient Multilinear Maps from Ideal Lattices
cites work: Explicit upper bounds of \(|L(1,\chi)|\). IV
cites work: Simple proofs of the Siegel–Tatuzawa and Brauer–Siegel theorems
cites work: Q5252066
cites work: Lattice-Based Identification Schemes Secure Under Active Attacks
cites work: Generalized Compact Knapsacks Are Collision Resistant
cites work: Asymptotically Efficient Lattice-Based Digital Signatures
cites work: On Ideal Lattices and Learning with Errors over Rings
cites work: Q3864603
cites work: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions
cites work: Class numbers of totally real fields and applications to the Weber class number problem
cites work: Q4786643
cites work: Theory of Cryptography
cites work: Approximate formulae for \(L(1,\chi)\)
cites work: Making NTRU as Secure as Worst-Case Problems over Ideal Lattices
cites work: Efficient Public Key Encryption Based on Ideal Lattices
cites work: Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes
cites work: Q5825286
cites work: Class Number Computations of Real Abelian Number Fields
cites work: Q5690489
Wikidata QID: Q129785655
DOI: 10.1007/S13160-018-0306-Z
description: scientific article; zbMATH DE number 6996769