The science of cryptology is the science of secure communications, formed from the Greek
words kryptós , "hidden", and logos , "word".
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It is a type of symmetric-key encryption algorithm that changes a fixed length of block text into same length of Cipher text.
Encryption works by means of key and Decryption is the reverse of encryption process using the same key.
The encryption method is based on simple XOR of binary bits. It encrypts one bit at a time.
The key sequence is generated on highly complex mathematical algorithms. LFSR based on primitive polynomials and combination of several LFSR using linear and nonlinear logic provides a very high level of complexity.
Public Key Cryptography
In this system a user chooses a pair of prime numbers so large that factorizing the product is beyond all computing capabilities.
Stages of sending the message by this method.
The receiver, M, distributes his public key pair.
The sender, F, composes a plain text message, m , and then uses Ms public key to encrypt the message and from cipher text, c . c is the remainder left when m is raised to the power of e and divided by the modulus n .
c = me mod n (where e and n are Ms public key pair).
F sends the ciphertext, c , to M.
The receiver, M, decrypts the ciphertext and retrieves the plaintext message, m . m is the remainder obtained when c is raised to the power of d and divided by n .
m = cd mod n
As you can see, this process requires d , which only M knows. Another person, I, who intercepts the message, can not decrypt it.
Let p = 5, q = 11, n = pq = 55
The least common multiple of ( p-1 )( q-1 ) is 20 = 22 ´ 5.
Therefore, in this case, any key, e , not divisible by 2 or 5 will have a matching key, d ( e must be relatively prime to ( p-1 )( q-1 ) for it to be the key).
Let e = 7
(ed -1) mod (p-1)(q-1) = 0 d = 3
Let the plaintext message, m = b = 2
The ciphertext, c = me mod n = 27 mod 55 = 18
To decrypt this information it is necessary to know d.
m’ = cd mod n = 183 mod 55 = 2 The message has been successfully decrypted.
Cryptography in the "Real World"
Applications of Cryptography
military and diplomatic services
protecting confidential company information, telephone calls
Unlike cryptography which is a clearly defined science, cryptanalysis is as
much an art as it is a science.
Types of Cryptanalysis: The type used depends on the type of cipher and how much information the cryptanalyst has .
Types Of Cryptanalytic Attacks
A brute force attack
Ciphertext only attack
An adaptive chosen plaintext
A Triumph of Cryptanalysis – Enigma
What Was Enigma?
The Enigma machine consisted of a 26 letter keyboard for
input. The output was read off 26 lamps which each
corresponded to a letter. The encipherment was performed
by a device called a "scrambler" that was made of three
rotating wheels on a common spindle and a plug board
known as a "Steckerboard" that added an additional level of
What Made It Possible?
With the level of sophistication of the Enigma machines it
should have been unbreakable. However, the Germans had
a number of procedural flaws which allowed the British
and Polish to break the cipher.
Military cryptography for encryption may still remain mainly symmetric key based for obvious reasons.
Public key cryptography would develop more in near future particularly in the context of key exchange and digital signatures.
Simultaneously , the challenging area of the cryptanalysis, being the other side of the development exercise will gain the importance in the view of the plethora of applications demanding assured security.