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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
Creative Commons Attribution
CC BY
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