NTRU in quaternion algebras of bounded discriminant
File(s)
Accepted version
Author(s)
Ling, Cong
Mendelsohn, Andrew
Type
Conference Paper
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.
Editor(s)
Johansson, T
Smith-Tone, D
Date Issued
2023-08-10
Date Acceptance
2023-08-01
Citation
Lecture Notes in Computer Science, 2023, 14154, pp.256-290
ISBN
978-3-031-40002-5
ISSN
0302-9743
Publisher
Springer International Publishing AG
Start Page
256
End Page
290
Journal / Book Title
Lecture Notes in Computer Science
Volume
14154
Copyright Statement
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG. he final publication is available at Springer via https://doi.org/10.1007/978-3-031-40003-2_10
Source
14th International Workshop on Post-Quantum Cryptography (PQCrypto)
Subjects
Computer Science
Computer Science, Information Systems
Computer Science, Theory & Methods
HARDNESS
LATTICES
Mathematics
Mathematics, Applied
NTRU
Physical Sciences
Physics
post-quantum cryptography
Quantum Science & Technology
quaternion algebras
Science & Technology
Technology
VARIANT
Publication Status
Published
Start Date
2023-08-14
Finish Date
2023-08-18
Coverage Spatial
College Park, MD, USA
Date Publish Online
2023-08-10