Paper 2024/1041
Embedding Integer Lattices as Ideals into Polynomial Rings
Abstract
Many lattice-based crypstosystems employ ideal lattices for high efficiency. However, the additional algebraic structure of ideal lattices usually makes us worry about the security, and it is widely believed that the algebraic structure will help us solve the hard problems in ideal lattices more efficiently. In this paper, we study the additional algebraic structure of ideal lattices further and find that a given ideal lattice in a polynomial ring can be embedded as an ideal into infinitely many different polynomial rings by the coefficient embedding. We design an algorithm to verify whether a given full-rank lattice in
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Published elsewhere. The International Symposium on Symbolic and Algebraic Computation (ISSAC) 2024
- DOI
- https://doi.org/10.1145/3666000.3669688
- Keywords
- Ideal latticeCoefficient embeddingComplexity
- Contact author(s)
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chengyihang15 @ mails ucas ac cn
fengyansong @ amss ac cn
panyanbin @ amss ac cn - History
- 2025-03-19: last of 4 revisions
- 2024-06-27: received
- See all versions
- Short URL
- https://ia.cr/2024/1041
- License
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CC BY
BibTeX
@misc{cryptoeprint:2024/1041, author = {Yihang Cheng and Yansong Feng and Yanbin Pan}, title = {Embedding Integer Lattices as Ideals into Polynomial Rings}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/1041}, year = {2024}, doi = {https://doi.org/10.1145/3666000.3669688}, url = {https://eprint.iacr.org/2024/1041} }