Cryptography

Cryptography is responsible of taking text or a file, known as plaintext, and convert it to ciphertext so that only authorized people know how to turn it back into plaintext.

Encryptation definition:

C = E (P, Ke)
where:
C = ciphertext
E = encryption algorithm (function)
P = plaintext
Ke = encryption key

Ciphertext is obtained by using the encryption algorithm E, with the plaintext P and the encryption key (secret) Ke as parameters.

Kerckhoffs’s principle states that all the algorithms must be publics and the secret must be only in the keys.

Decryption definition:


P = D (C, Kd)

where:
D = Decryption algorithm
Kd = decryption key



To obtain the plaintext P from ciphertext C and the decryption key Kd you have to run the decryption algorithm D and the decryption key Kd as parameters.



Secret-key Cryptography (symmetric encryption)



An algorithm in which each letter is replaced by a different letter. For example, all As are replaced by Zs, all Bs by Ys, all Cs by Xs and so on.

Plaintext: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Ciphertext:      Z Y X W V U T S R Q P O N M L K J I H G F E D C B A

This system is called monoalphabetic sustitution, where the key is the string of 26-letters alphabet. In the above example the encryption key is ZYXWVUTSRQPONMLKJIHFEDCBA, the plaintext HELLO would become the ciphertext SVOOL.

Advantages:
- High speed
- The size of the message decreases

Disadvantages
- It is necessary that the receiver knows the decryption key 

- Is not possible use unsafe media for keys communication.


Public-key cryptography (Asymmetric encryption)


Uses different keys for encryption and decryption, and if you choose a good encryption key is almost impossible to find the decryption key.
This cryptography works so that everyone chooses a pair (public key, private key) and publish the public key which is the encryption key and the private key is the decryption key. To post a message, someone encrypts the message with the recipient’s public key, only the recipient has the private key so he is the only one who can decrypt the message.

Provides

• Confidentiality
• Integrity

Applications

• Authentication
• Digital Signature

Here we add some pseudocode of how this can work

a = “xxx”;
b = encrypt_algorithm
ke = encrypt_key

t_ecrypt = b ( a, ke)
t_encrypt = send ( )

receive ( t_encrypt)
kd = decrypt_key
if (kd == true){
t_decrypt = b (t_encrypt, kd)
a = t_decrypt
}
else
 {
 print “you need the key to decrypt”
 }

References

Operating systems (Andrew S. Tanenbaum)