Abstract
The main purpose of this paper is to illustrate the fundamental concepts behind the NTRU public key cryptosystem can be extended to a broader algebra than Dedekind domains and the NTRU underlying ring may be replaced by a non-commutative or even non-associative algebra.
To cross the border of Dedekind or Euclidean domains, we prove that it is possible to extend NTRU to the algebra of polynomials with coefficients in the non-commutative ring of quaternions as well as the non-associative octonions algebra (a power-associative and alternative algebra of dimension eight over a principal ideal domain).
We also demonstrate that the security of the proposed non-associative cryptosystem relies on the intractability of shortest vector problem in a certain type of lattice. The least advantage of the non-associativity of the underlying algebra is that the resulting lattice is not fully classified under Convolutional Modular Lattice (CML). To the best of our knowledge, no non-associative public key cryptosystem based on non-associative algebra has been proposed in the literature.
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Malekian, E., Zakerolhosseini, A. (2010). NTRU-Like Public Key Cryptosystems beyond Dedekind Domain up to Alternative Algebra. In: Gavrilova, M.L., Tan, C.J.K., Moreno, E.D. (eds) Transactions on Computational Science X. Lecture Notes in Computer Science, vol 6340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17499-5_2
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DOI: https://doi.org/10.1007/978-3-642-17499-5_2
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