On the quantum attacks against schemes relying on the hardness of finding a short generator of an ideal in \(\mathbb{Q}(\zeta_{2^s})\)
From MaRDI portal
Publication:2009413
DOI10.1515/jmc-2015-0046zbMath1454.11223OpenAlexW2967455120MaRDI QIDQ2009413
Fang Song, Jean-François Biasse
Publication date: 28 November 2019
Published in: Journal of Mathematical Cryptology (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/jmc-2015-0046
Related Items (2)
The special case of cyclotomic fields in quantum algorithms for unit groups ⋮ Approximate short vectors in ideal lattices of \(\mathbb{Q}(\zeta_{p^e})\) with precomputation of \({\mathrm {Cl}}(\mathcal{O}_K)\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Square classes of totally positive units
- Subexponential time relations in the class group of large degree number fields
- Subexponential class group and unit group computation in large degree number fields
- 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
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields
- Candidate Multilinear Maps from Ideal Lattices
- Advanced Topics in Computional Number Theory
- A quantum algorithm for computing the unit group of an arbitrary degree number field
- Algorithmic Number Theory
- Recovering Short Generators of Principal Ideals in Cyclotomic Rings
- Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
This page was built for publication: On the quantum attacks against schemes relying on the hardness of finding a short generator of an ideal in \(\mathbb{Q}(\zeta_{2^s})\)
