This document defines and explains various cryptography concepts and methods. It begins by defining what a code is, the processes of encoding and decoding, and what cryptography is. It then discusses different types of cryptography including public key cryptography, symmetric key cryptography, and self-encrypting drives. Applications of cryptography like banking, data storage, and authentication are also covered. The document also discusses steganography, quantum key distribution, network coding, and data matrix codes. It concludes by noting the importance of cryptography and mathematics education.

2. What’s a CODE ??
A code is the substitution of one word or
phrase by another word, number, or
symbol for the purpose of concealing the
original word or phrase. Basically, it's
substitution at the word or phrase level .
A code is a system
of replacing the words in a message with
other words or symbols, so that nobody
can understand it unless they know the
system.

3. Encoding and Decoding
Encoding is the process of putting a
sequence of characters , letters,
numbers, punctuation, and certain
symbols into a specialized format for
efficient transmission or storage.
Decoding is the opposite process. It is
the conversion of an encoded format
back into the original sequence of
characters.

4. Cryptography
Cryptography is a method of storing
and transmitting data in a particular
form so that only those for whom it is
intended can read and process it.
Cryptography not only protects data
from theft or alteration, but can also
be used for user authentication.

6. TYPES OF CRYPTOGRAPHY
 There are various cryptography methods that
provide a means for secure commerce and
payments to private communications and
protecting passwords.
1. Public Key Cryptography: It involves two pairs
of keys: one for encryption and another for
decryption. Key used for encryption is public key
and distributed. On the other hand decryption
key is a private key.
2. Symmetric Key Cryptography: It uses the
same key for encoding and decoding
information.The sender and recipient of the
data must share same key and keep information
secret, preventing data access from outside.

7.  Promising to make secure data accessible
in a wider number of places are self-
encrypting drives (SEDs), a new
generation of hard disk and solid-state
drives featuring built-in cryptographic
engines.The units are designed for easy
installation inside mobile systems, desktop
computers and servers.
 The cryptographic keys never leave the
drive, so they require minimal
management.

9. APPLICATIONS
 Communication in military administration
 Confidential message transduction
 Computerized lockers
 Banking
 Secrecy in storage
 Authentication of identity

10.  Historically, cryptography was used to assure
only secrecy.Wax seals, signatures, and other
physical mechanisms were typically used to
assure integrity of the media and authenticity
of the sender.
 With the advent of electronic funds transfer,
the applications of cryptography for integrity
began to surpass its use for secrecy.
Electronic cash came into being from
cryptography, and the electronic credit card
and debit card sprung into widespread use.

11.  The advent of public key
cryptography introduced the
possibility of digital signatures, and
other related concepts such as
electronic credentials.
 In the information age, cryptography
has become one of the major
methods for protection in all
applications.

13. In mathematics, a matrix is
a rectangular array of numbers, symbols,
or expressions, arranged
in rows and columns.

17. Steganography
Steganography is the practice of concealing
a file, message, image, or video within
another file, message, image, or video.
Steganography includes the concealment of
information within computer files. In digital
steganography, electronic communications
may include steganographic coding inside of
a transport layer, such as a document file,
image file, program or protocol.

18. Steganography
Media files are ideal for steganographic
transmission because of their large size. For
example, a sender might start with an image
file and adjust the color of every
hundredth pixel to correspond to a letter in
the alphabet.The change is so subtle that
someone who is not specifically looking for it
is unlikely to notice the change.

20. Quantum Key Distribution
 Quantum key distribution (QKD) is a secure
communication method which implements
a cryptographic protocol involving
components of quantum mechanics. It
enables two parties to produce a
shared random secret key known only to
them, which can then be used to encrypt and
decrypt messages.

22. Network coding for data-retrieving
in cloud storage systems
As the rapid growth of data, many storage
systems have used erasure codes instead of
replication to reduce the storage cost under
the same level of reliability. The application
of codes in storage systems, where the data is
less frequently accessed is well understood.
For the data, which is stored in cloud storage
systems, is frequently accessed, the
performance of data-retrieving is the key
metric.

23. Data Matrix
A Data Matrix is a two-dimensional
barcode consisting of black and white "cells" or
modules arranged in either
a square or rectangular pattern, also known as
a matrix.The information to be encoded can be
text or numeric data. Usual data size is from a
few bytes up to 1556 bytes.The length of the
encoded data depends on the number of cells in
the matrix. A Data Matrix symbol can store up to
2,335 alphanumeric characters.

25. Secondary school students often ask their teachers
why it is important to learn mathematics, and thus
teachers are usually faced with the challenge of
explaining its importance and relevance to real life
situations to convince them. However, this may not
always be an easy task.Therefore, it is hoped that
this activity on cryptography not only offers
teachers with great opportunities to either
introduce or consolidate certain mathematical
concepts and algorithms, but also to convince their
students that mathematics plays an important role
in various walks of life and hence is a useful and
meaningful field of study.

26. References
 https://www.youtube.com/watch?v=TJQD4d
nCbAA
 http://www.purplemath.com/modules/mtrxin
vr2.htm