Short principal ideal problem in multicubic fields

DOI10.1515/jmc-2019-0028zbMath1462.94044OpenAlexW3080386260MaRDI QIDQ2023319

Willy Susilo, Thomas Plantard, Andrea Lesavourey

Publication date: 3 May 2021

Published in: Journal of Mathematical Cryptology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jmc-2019-0028

zbMATH Keywords

number fieldscryptanalysisideal latticepublic-key cryptographyunit groupcubic fieldpost-quantum cryptography

Mathematics Subject Classification ID

Quantum computation (81P68) Cryptography (94A60) Quantum cryptography (quantum-theoretic aspects) (81P94)

Related Items

Norm relations and computational problems in number fields

Uses Software

• Magma

Cites Work

• Topics in computational algebraic number theory
• On Lovász' lattice reduction and the nearest lattice point problem
• Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant
• Factoring polynomials with rational coefficients
• Class number formulae for bicubic fields
• The Magma algebra system. I: The user language
• Implementing Gentry’s Fully-Homomorphic Encryption Scheme
• Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes
• Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields
• A quantum algorithm for computing the unit group of an arbitrary degree number field
• Short Generators Without Quantum Computers: The Case of Multiquadratics
• Recovering Short Generators of Principal Ideals in Cyclotomic Rings
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