Paper 2023/1471
NTRU in Quaternion Algebras of Bounded Discriminant
Abstract
The NTRU assumption provides one of the most prominent problems on which to base post-quantum cryptography. Because of the efficiency and security of NTRU-style schemes, structured variants have been proposed, using modules. In this work, we create a structured form of NTRU using lattices obtained from orders in cyclic division algebras of index 2, that is, from quaternion algebras. We present a public-key encryption scheme, and show that its public keys are statistically close to uniform. We then prove IND-CPA security of a variant of our scheme when the discriminant of the quaternion algebra is not too large, assuming the hardness of Learning with Errors in cyclic division algebras.
Note: A minor revision of a publication in PQCrypto 2023.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Minor revision. PQCrypto 2023
- DOI
- 10.1007/978-3-031-40003-2_10
- Keywords
- NTRUquaternion algebraspost-quantumlattices
- Contact author(s)
- am3518 @ ic ac uk
- History
- 2023-09-27: approved
- 2023-09-25: received
- See all versions
- Short URL
- https://ia.cr/2023/1471
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/1471,
author = {Cong Ling and Andrew Mendelsohn},
title = {{NTRU} in Quaternion Algebras of Bounded Discriminant},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1471},
year = {2023},
doi = {10.1007/978-3-031-40003-2_10},
url = {https://eprint.iacr.org/2023/1471}
}