The NTRU cryptosystem is constructed on the base ring Z. We give suitability conditions on rings to serve as alternate base rings. We present an example of an NTRU-like cryptosystem based on the Eisenstein integers Z[ζ 3 ], which has a denser lattice structure than Z for the same dimension, and which furthermore presents a more difficult lattice problem for lattice attacks, for the same level of decryption failure security.
Abstract. Let F be a non-Archimedean local field with the ring of integers O and the prime ideal p and let G = G ad (O/p n ) be the adjoint Chevalley group. Let m f (G) denote the smallest possible dimension of a faithful representation of G. Using the Stone-von Neumann theorem, we determine a lower bound for m f (G) which is asymptotically the same as the results of Landazuri, Seitz and Zalesskii for split Chevalley groups over Fq. Our result yields a conceptual explanation of the exponents that appear in the aforementioned results
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