First off we start by acknowledging what cryptography is, and it is the art of writing or solving codes, and protecting information. Transforming that importation is called encryption, and deciphering that information by using a secret key is called decryption. Cryptography is used to protect e-mail messages, credit card information, and corporate data, and due to our society today being so highly developed in technology and electronic security and information privacy has become very important.

**Key words:**

** Cryptography systems**

Symmetric-key systems use a single key which the sender and recipient have.

Public-key system use two keys, a public key that is known to everyone and a private key that only the recipient uses.

Encryption is the translation of data into a secret code. it is the most effective way to achieve data security. In order to read an encrypted file, you have to have access to a secret password that enables you to decrypt the information.

Plain text is the name for un-encrypted data, and an encrypted data is called cipher text.

Symmetric-key cryptography ( also known as secret-key cryptography) is a single common key shared by the sender and receiver of a message. It is used to encrypt and decrypt a message. It is easier and faster, however the parties involved must some-how exchange the key in a secure way. Most popular symmetric-key system is the Data Encryption Standard also known as DES which was developed in 1975 and standardized by ANSI in 1981.

Encryption algorithm is a mathematical procedure for performing encryption data. Information is made into meaningless cipher text through the use of algorithm and it requires a key to transform the data back to its original form.

Algorithm is a set of steps for solving a particular problem, with a set of rules and a stopping point.

LUHN formula is used widely to generate check digits of many different primary account numbers. also used to check Canadian social insurance number. It was created in the late 1960s by a group of mathematicians, and then later adopted by credit card companies.

A hybrid encryption is a method that combines two or more encryption schemes and includes a combination of symmetric and asymmetric encryption to take advantage of the strengths of each type of encryption.

http://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/intro-to-cryptography

**Prime Factorization.**

Primes are building blocks of whole numbers.

A prime number is a number that is only divisible by one and itself, taken the even numbers out except two. There re infinite number of primes, and you can keep finding more by only using primes. Combining prime numbers can be multiplied to produce any number at all. prime can be explained as a basic-level number, when you look at it primes are the total set of numbers which are left over when the numbers are rewritten to their lowest possible level of integers. It is called factoring, and the numbers that are left over are primes. it is however hard to factor large prime numbers. it is just mathematically impossible or longer to factor a large number efficiently. Prime factorization is a mathematical problem commonly use to secure public key encryption systems, making it very important in cryptography. It is very common to use very large semi-primes which is the product of multiplying two prime numbers as the number which secures the encryption. To break it, they would have to find the prime factorization of the large semi-prime number which is two or more prime number that are multiplied together and result in the original number. The large number used to encrypt a file can be publicly known, due to the fact that encryption works so only the prime factors of the large number can be used in the decryption. It however takes a long time to find those factors and it is rather impossible even computationally.