Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shor's Factoring Algorithm and Modern Cryptography. An Illustration of
  the Capabilities Inherent in Quantum Computers   The security of messages encoded via the widely used RSA public key
encryption system rests on the enormous computational effort required to find
the prime factors of a large number N using classical (i.e., conventional)
computers. In 1994, however, Peter Shor showed that for sufficiently large N a
quantum computer would be expected to perform the factoring with much less
computational effort. This paper endeavors to explain, in a fashion
comprehensible to the non-expert readers of this journal: (i) the RSA
encryption protocol; (ii) the various quantum computer manipulations
constituting the Shor algorithm; (iii) how the Shor algorithm performs the
factoring; and (iv) the precise sense in which a quantum computer employing
Shor's algorithm can be said to accomplish the factoring of very large numbers
with less computational effort than a classical computer can. It is made
apparent that factoring $N$ generally requires many successive runs of the
algorithm. The careful analysis herein reveals, however, that the probability
of achieving a successful factorization on a single run is about twice as large
as commonly quoted in the literature.

24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin