This theory was developed by Alexandre

RESEARCH PAPER 0
Knot Theory and
Cryptography

RESEARCH PAPER 1
Table of Contents
Introduction................................................................................................................ 2
Overview of knot theory............................................................................................. 2
Cryptography.............................................................................................................. 3
Literature review........................................................................................................ 3
Cryptography using knots.......................................................................................... 6
Conclusion.................................................................................................................. 8
References............................................................................................................... 10

RESEARCH PAPER 2
Introduction
Knot theory refers to the study of mathematical knots that appear in daily
life activities. Knot theory is a branch of the geometry of 3 dimensions
which is encoded in the modeling of various chemical, physical and
biological systems. This theory was developed by Alexandre in the year
1771 that included numerous topological features in the knot theory which
are helpful related to the geometry of position. Cryptography is a kind of
technique that is used to convert signals into specific codes for enhancing
the performance of the communication systems. In the area of
cryptography, knot theory can be applied for managing operations and
handling data communication issues effectively. This report will include
various sections such as an overview of knot theory, an overview of
cryptography, literature review, cryptography using knot and conclusion.
Overview of knot theory
This chapter will review and evaluate the key features of knot theory and
provide a way to enhance skills in the field of knot theory. The knot theory
was implemented by Alexandre in the year 1771 that noted the significant
topological features when evaluating the properties of knot linked to the
geometry of position. It is reported that knot theory is the accurate division
of topology that educations mathematical knots that are described as
embedding of a circle in 3-dimensional interplanetary.
Baylis, (1973) reported that two scientific knots are equal if one may be
distorted into the other through distortion of R3 upon itself. Such kinds of
alterations resemble to the operations of a knotted string that do not
contain strings (Sullivan, 2000). It is determined that knots may be defined
in numerous manners but the planer diagram is an effective process used in
the mathematical models for describing knots. The fundamental challenge
in knot theory is examining when two descriptions indicate a similar knot.

RESEARCH PAPER 3
The idea behind a knot has been extended to larger dimensions by including
n-dimensional spheres in m-dimensional spaces. Investigation in knot theory
began with the formation of knot tables and the methodical tabularization of
knots.
Cryptography
Cryptography is defined as a technique of protecting data and
communication networks converting information and facts into codes. It is
an effective method used by companies to manage unauthorized access and
protect personal data from criminals. In the area of computing science,
cryptography is a kind of communication technique derived from
mathematical ideas and a set of rule-based calculation called computing
algorithm that helps to transform signals in manners which are hard to
decode that leads privacy.
Marzuoli and Palumbo, (2011) reported that the cryptography technique
provides a way to control and handle the unwanted signals that occurred in
the computing devices. It contains various techniques, for example,
microdots, merging words with pictures and encryption to hide information
in a reliable manner. The major part of cryptography is that it is capable to
enhance the confidentiality of data by addressing unauthorized activities
from the networks and communication systems. Knot theory helps to
implement cryptography technique effective as it provides mathematical
functions by which the transmitted signals can be encoded effectively. The
Cryptography technique includes two processes such as encoding and
decoding. The encoding process helps to convert plain text into cipher text
while the decoding technique help to convert cipher text to plain text by
which the transmitted data can be protected from the criminals.