Security analysis of cryptosystems using short generators over ideal lattices

DOI10.1007/s13160-018-0306-zzbMath1404.94103OpenAlexW2804028970WikidataQ129785655 ScholiaQ129785655MaRDI QIDQ1756730

Shinya Okumura, Shingo Sugiyama, Tsuyoshi Takagi, Masaya Yasuda

Publication date: 21 December 2018

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-018-0306-z

zbMATH Keywords

cyclotomic fieldsDirichlet \(L\)-functionslog-unit latticesshort generators

Mathematics Subject Classification ID

Cryptography (94A60) Software, source code, etc. for problems pertaining to number theory (11-04) Analytic computations (11Y35)

Related Items (1)

Explicit lower bounds on \(|L (1, \chi)|\)

Uses Software

• Magma
• SageMath
• GitHub
• LogCVP

Cites Work

• Weber's class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II.
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• Explicit upper bounds for |L(1, χ)| when χ(3)=0
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• Implementing Gentry’s Fully-Homomorphic Encryption Scheme
• WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ₂-EXTENSION OF ℚ, III
• Simple proofs of the Siegel–Tatuzawa and Brauer–Siegel theorems
• Trapdoors for hard lattices and new cryptographic constructions
• Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes
• Fast quantum algorithms for computing the unit group and class group of a number field
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• Candidate Multilinear Maps from Ideal Lattices
• Fully homomorphic encryption using ideal lattices
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• Asymptotically Efficient Lattice-Based Digital Signatures
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• Theory of Cryptography
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