Cryptography algorithm used in cryptosystem can be classified into two categories which is symmetric and asymmetric encipherment. In symmetric encipherment, plaintext is encrypted
and decrypts using the same key whereas asymmetric encipherment is using different keys to encrypt and decrypt a plaintext.
Symmetric encipherment can be in form of substitution, transposition or both. In substitution encryption method alphabet in the plaintext is always changed with another alphabet. Each character can be either change with one character or multiple characters.
Transposition encryption method does not substitute character with another character but it changes the location of the characters. The character in the first position might be placed on the fifth position and the fifth position character might be placed in another location in the plaintext.
Asymmetric encipherment involves two keys to encrypt and decrypt. These algorithms allow the key to be publicized, hence anyone can encrypt using the key, and the proper recipient who knows the decryption key can decrypt the message. The encryption key is called public key and the decryption key is called secret/private key. RSA algorithm is use to produce the public and private key.
Symmetric encipherment (Caesar Cipher)
The Caesar Cipher is formed by shifting the letters of the original alphabet. For example by replacing each letter of the alphabet with the letter three places down the alphabet. It is monoalphabetic as only one letter in plaintext is exchanged for one letter of ciphertext.
This is example on how CIPHER CAESAR work
(Vigeneré Cipher)
The cipher text encrypted using Caesar cipher method is easily broken by using a brute force attack. An attacker can easily try every combinations of character to break the code as the number of possibility is just 26. In order to improve the deciphering process we can used the vigeneré cipher method. The Vigenère cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword. It is a simple form of polyalphabetic substitution.
This is VIGENERE TABLE
Asymmetric encipherment
RSA Algorithm
Asymmetric encryption or called public key cryptography is a cryptographic approach, employed by many cryptographic algorithms and cryptosystems. Each encryption and decryption process is using a unique pair of key called public and private key. RSA algorithm is one of the algorithms used to produce the private and public key.
Each user generates a public/private key pair by selecting two large primes at random p, q and then compute their system modulus.
Example:
a) 999 mod 3
= 333 (3) mod 3 ---- (3) mod 3= 0
= 333(0)
= 0
b) 55 mod 57
55 mod 57 = 3125 mod 57
= 47 (baki)
c) Given p=3;q=11,e=7;m=5 ( c=57 mod 33)
n = p * q
= 3 * 11 = 33
Ø = (p – 1)(q – 1)
= (2)(10)
= 20
d = e-1 mod Ø(n)
= 7-1 mod 20
20 = 2(7) + 6
7 = 1(6) + 1
6 = 20 – 2(7)
1 = 7 – 1(6)
1 = 7 – 1(20-2(7))
1 = 7 – 20 + 2(7)
1 = 3(7) – 20
mod 20 = 3(7) mod 20 – 20 mod 20
7-1 mod 20 = 3 mod 20
= 3
d = 7-1 mod 20
= 3
PU = {e,n}
= {7,33}
PR = {d,n}
= {3,33}
C = Me mod n
= 57 mod 33
= 14
M = Cd mod n
= 143 mod 33
= 5
All calculations above are some examples for RSA algorithm. All use formula provided to get all the answers. Hope you get some valuable information here.
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