Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Predicting the elliptic curve congruential generator   Let $p$ be a prime and let $\mathbf{E}$ be an elliptic curve defined over the
finite field $\mathbb{F}_p$ of $p$ elements. For a point
$G\in\mathbf{E}(\mathbb{F}_p)$ the elliptic curve congruential generator (with
respect to the first coordinate) is a sequence $(x_n)$ defined by the relation
$x_n=x(W_n)=x(W_{n-1}\oplus G)=x(nG\oplus W_0)$, $n=1,2,\dots$, where $\oplus$
denotes the group operation in $\mathbf{E}$ and $W_0$ is an initial point. In
this paper, we show that if some consecutive elements of the sequence $(x_n)$
are given as integers, then one can compute in polynomial time an elliptic
curve congruential generator (where the curve possibly defined over the
rationals or over a residue ring) such that the generated sequence is identical
to $(x_n)$ in the revealed segment. It turns out that in practice, all the
secret parameters, and thus the whole sequence $(x_n)$, can be computed from
eight consecutive elements, even if the prime and the elliptic curve are
private.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn