Paper 2009/446
Ntr¹u-like Public Key Cryptosystems beyond Dedekind Domain Up to Alternative Algebra
Ehsan Malekian and Ali Zakerolhosseini
Abstract
In this paper, we show that the fundamental concepts behind the Ntr¹u cryptosystem can be extended to a broader algebra than Dedekind domains. Also, we present an abstract and generalized algorithm for constructing a Ntr¹u-like cryptosystem such that the underlying algebra can be non-commutative or even non-associative. To prove the main claim, we show that it is possible to generalize Ntr¹u over non-commutative Quaternions (algebra in the sense of Cayley-Dikson, of dimension four over an arbitrary principal ideal domain) as well as non-associative Octonions (a power-associative and alternative algebra of dimension eight over a principal ideal domain). Given the serious challenges ahead of non-commutative/non-associative algebra in quater- nionic or octonionic lattices, the proposed cryptosystems are more resistant to lattice-based attacks when compared to Ntr¹u. Concisely, this paper is making an abstract image of the mathematical base of Ntr¹u in such a way that one can make a similar cryptosystem based on various algebraic structures with the goal of better security against lattice attack and/or more capability for protocol design.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Public Key CryptographyNtr¹uAlternative algebralattice based cryptogra- phynon-associative cryptosystemGtru
- Contact author(s)
- a-zaker @ sbu ac ir
- History
- 2009-09-14: received
- Short URL
- https://ia.cr/2009/446
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2009/446,
author = {Ehsan Malekian and Ali Zakerolhosseini},
title = {Ntr¹u-like Public Key Cryptosystems beyond Dedekind Domain Up to Alternative Algebra},
howpublished = {Cryptology ePrint Archive, Paper 2009/446},
year = {2009},
note = {\url{https://eprint.iacr.org/2009/446}},
url = {https://eprint.iacr.org/2009/446}
}
