Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the High Dimensional RSA Algorithm -- A Public Key Cryptosystem Based
  on Lattice and Algebraic Number Theory   The most known of public key cryptosystem was introduced in 1978 by Rivest,
Shamir and Adleman [19] and now called the RSA public key cryptosystem in their
honor. Later, a few authors gave a simply extension of RSA over algebraic
numbers field( see [20]- [22]), but they require that the ring of algebraic
integers is Euclidean ring, this requirement is much more stronger than the
class number one condition. In this paper, we introduce a high dimensional form
of RSA by making use of the ring of algebraic integers of an algebraic number
field and the lattice theory. We give an attainable algorithm (see Algorithm I
below) of which is significant both from the theoretical and practical point of
view. Our main purpose in this paper is to show that the high dimensional RSA
is a lattice based on public key cryptosystem indeed, of which would be
considered as a new number in the family of post-quantum cryptography(see [17]
and [18]). On the other hand, we give a matrix expression for any algebraic
number fields (see Theorem 2.7 below), which is a new result even in the sense
of classical algebraic number theory.

19
The categories of this paper are: eess
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci