Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Secure cloud computations: Description of (fully)homomorphic ciphers
  within the P-adic model of encryption   In this paper we consider the description of homomorphic and fully
homomorphic ciphers in the $p$-adic model of encryption. This model describes a
wide class of ciphers, but certainly not all. Homomorphic and fully homomorphic
ciphers are used to ensure the credibility of remote computing, including cloud
technology. The model describes all homomorphic ciphers with respect to
arithmetic and coordinate-wise logical operations in the ring of $p$-adic
integers $Z_p$. We show that there are no fully homomorphic ciphers for each
pair of the considered set of arithmetic and coordinate-wise logical operations
on $Z_p$. We formulate the problem of constructing a fully homomorphic cipher
as follows. We consider a homomorphic cipher with respect to operation "$*$" on
$Z_p$. Then, we describe the complete set of operations "$G$", for which the
cipher is homomorphic. As a result, we construct a fully homomorphic cipher
with respect to the operations "$*$" and "$G$". We give a description of all
operations "$G$", for which we obtain fully homomorphic ciphers with respect to
the operations "$+$" and "$G$" from the homomorphic cipher constructed with
respect to the operation "$+$". We also present examples of such "new"
operations.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex