Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Polynomial Modular Number Systems over $\mathbb{Z}/p\mathbb{Z}$   Since their introduction in 2004, Polynomial Modular Number Systems (PMNS)
have become a very interesting tool for implementing cryptosystems relying on
modular arithmetic in a secure and efficient way. However, while their
implementation is simple, their parameterization is not trivial and relies on a
suitable choice of the polynomial on which the PMNS operates. The initial
proposals were based on particular binomials and trinomials. But these
polynomials do not always provide systems with interesting characteristics such
as small digits, fast reduction, etc.
  In this work, we study a larger family of polynomials that can be exploited
to design a safe and efficient PMNS. To do so, we first state a complete
existence theorem for PMNS which provides bounds on the size of the digits for
a generic polynomial, significantly improving previous bounds. Then, we present
classes of suitable polynomials which provide numerous PMNS for safe and
efficient arithmetic.

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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph