By cryptography we mean the study of mathematical techniques which aim to the ensurance of the safe information transmission.
The process is the following: The initial message(plaintext) is being encrypted. The encrypted message(ciphertext) is sent and is being decrypted in its destination.
Cryptography has the following goals:
 The messages must reach to the right destination.
 Confidentiality:Only the receiver must receive and read the message
 Authentication: The sender must be authenticated
 Data Integrity: The message must not change during the transmission
 Nonrepudiation: Noone can deny an action that has already taken
We must emphasize that cryptography does not solve all the above, it is just trying to satisfy them./p>
Algorithms Based on Keys
The encryption algorithms use one or more keys. The security results from the fact that the key is unknown as the encryption and decryption algorithms may be well known.
For example a simple algorithm based on key is the following:
Encryption: Multiply the initial message by 2 and add the key
Decryption: Subtract the key and divide the ciphertext by 2
plaintext = SECRET = 19 5 3 18 5 20
Key = 3
Ciphertext = 41 13 9 39 13 43
These algorithms can be divided in two categories:
 Symmetric Key Algorithms: We use the same key for both encryption and decryption. The sender and the receiver must firstly agree to use a common key. There must be a safe channel between them for this.
 Assymetric (or public key) Algorithms: We use different keys for encryption and decryption.
Mathematical Formalism
Suppose E is the encryption function and D the decryption function. Then
EK1(m) = c
DK2(c) = m
where m is the initial message and c is the encrypted message.
These functions have the following feature:
DK2 (EK1(m)) = m
For the symmetric key algorithms K1=K2.
Cryptography Applications
Cryptography is used in a significant number of applications like:
 Secure transactions in banks networks  ATM
 Mobile telephony (GSM)
 Telephony(cryptophones)
 Military networks
 Diplomatic networks (Telegrams)
 Ebusiness (credit cards, payments)
 electronic voting
 electronic auction
 mailbox
 smartcards
 Private networks (VPN)
 Word Wide Web
 Wireless networks
 Teleconference  internet telephony (VOIP)
