* Cryptography*—

What is cryptography? What can it do? How to use it?

First, let’s consider an example in sending text message over the network. Alice wants to have a secret date with Bob, so she sends him a message telling where she will be this evening. Unfortunately, Oscar – a friend of them – somehow manage to join in the conversation and read everything. Alice and Bob know about this, thus this time they change their location and want to hide it so Oscar cannot figure out. Therefore, they think of ways to hide the message so that only they can read it.

*Figure 1. Scenario*

The ways used to secure all the information are called * cryptography*. Cryptography is the science of using mathematics to

*and*

**encrypt***data. It*

**decrypt***people to*

**enables***sensitive information/data or*

**store***it across*

**transmit***so that no one can*

**insecure networks***it except the*

**read***.*

**intended recipient**The original message is called * plaintext*, the encrypted message is call

**ciphertext**.*Using an encryption rule combined with a*

*, the plaintext will be encrypted into the ciphertext. The ciphertext will be then sent over the channel. With the same method, we can decrypt the ciphertext back to the plaintext and get the data.*

**predetermined key***Firgure 2. A Cryptosystem*

The whole process is packed into a system called * cryptosystem. *A cryptosystem is a five-tuple (

*P, C, K, E, D*), where

*P*is a finite set of possible plaintexts;*C*is a finite set of possible ciphertexts;*K,*the*keyspace,*is a finite set of possible keys;- For each
*k ∈ K,*there is an encryption rule*e*and a corresponding decryption rule d_{k}∈ EEach_{k}∈ D.*e*and d_{k}: P → Care functions such that_{k}: C → P*d*for every plaintext element_{k }(e_{k }(x)) = x*x ∈ P*

**Note: **Each encryption rule e _{k} must be one-to-one function.*

—

*End of chapter 1. *