Cryptology ePrint Archive: Report 2009/446

Ntršu-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 Ntršu cryptosystem can be extended to a broader algebra than Dedekind domains. Also, we present an abstract and generalized algorithm for constructing a Ntršu-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 Ntršu 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 Ntršu. Concisely, this paper is making an abstract image of the mathematical base of Ntršu 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.

Category / Keywords: public-key cryptography / Public Key Cryptography, Ntršu, Alternative algebra, lattice based cryptogra- phy, non-associative cryptosystem, Gtru

Date: received 11 Sep 2009

Contact author: a-zaker at sbu ac ir

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Version: 20090914:012206 (All versions of this report)

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