Differential and Linear Cryptanalysis

Cryptanalysis is the process of transforming or decoding communications from non-readable to readable format without having access to the real key. OR we may say it is the technique of retrieving the plain text of the communication without having access to the key. Cryptoanalysis is the art, science, or practice of decrypting encrypted messages. The secret key used for encryption and decoding is considered to be unknown to the cryptologists, mathematicians, and other scientists participating in the process. In contrast to a brute force attack, this form of analysis seeks vulnerabilities in a cryptosystem. 

Cryptanalysis frequently comprises a direct evaluation of the cryptosystem in use, which is essentially an advanced concentrated mathematical attempt at decryption utilizing knowledge about the encryption scheme that is already available. They can employ intercepted encrypted messages (ciphertext), intercepted complete, partial, likely, or similar original messages (plaintext), or information (encrypted or original) that is known to be used adaptively in subsequent trials. 

Process of cryptanalysis

Cryptanalysis is used to break cryptographic security systems and gain access to the contents of the encrypted messages, even if the cryptographic key is unknown.

Types of Cryptanalytic Attacks:

1. Ciphertext only attack:

1. In this type of cryptanalytic attack, the attacker has the knowledge of only the ciphertext.
2. The attacker has to detect the plain text using the ciphertext only.
3. This type of attack is not very easy to be implemented.

2. Known plain text only attack:

1. In this type of cryptanalytic attack, the attacker has the knowledge of some plain text as well as ciphertext.
2. The attacker tries to decrypt the messages using these two.
3. This type of attack is somewhat easy to implement.

Different Forms of Cryptanalysis:

Cryptanalysis basically has two forms:

1. Linear Cryptanalysis:

Linear cryptanalysis is a general type of cryptanalysis based on discovering affine approximations to a cipher’s action in cryptography. Block and stream ciphers have both been subjected to attacks. Linear cryptanalysis is one of the two most common attacks against block ciphers, with differential cryptanalysis being the other.

2. Differential Cryptanalysis:

Differential cryptanalysis is a sort of cryptanalysis that may be used to decrypt both block and stream ciphers, as well as cryptographic hash functions. In the widest sense, it is the study of how alterations in information intake might impact the following difference at the output. In the context of a block cipher, it refers to a collection of strategies for tracking differences across a network of transformations, finding where the cipher displays non-random behavior, and using such attributes to recover the secret key (cryptography key).

Difference between Linear Cryptanalysis and Differential Cryptanalysis

S. No.	Linear Cryptanalysis	Differential Cryptanalysis
1.	Linear cryptanalysis was basically invented by Matsui and Yamagishi in the year 1992.	Differential cryptanalysis was first defined in the year 1990 by Eli Biham and Adi Shamir.
2.	Linear cryptanalysis always works on a single bit (one bit at a time).	Differential cryptanalysis can work on multiple bits at a time.
3.	In the case of Linear cryptanalysis, ciphertext attack is a very big disadvantage.	In the case of differential cryptanalysis plain text attack is a very big disadvantage.
4.	The use of linear cryptanalysis is to figure out what is the linear relationship present between some plaintext bits, ciphertext bits, and unknown key bits very easily.	The use of differential cryptanalysis is to get clues about some critical bits, reducing the need for an extensive search.
5.	Subsets of input attributes refer to the internal structures of a single input.	The underlying structure of each individual input is unimportant in this case since the input attributes are differential.
6.	The cryptanalyst decrypts each ciphertext using all available subkeys and analyses the resultant intermediate ciphertext to determine the random outcome for one encryption cycle.	After several encryption rounds, Cryptanalyst analyses the changes in the intermediate ciphertext obtained. The practice of combining assaults is known as differential linear cryptanalysis.
7.	Any random plaintext is selected in Linear Cryptanalysis.	Plaintext is Carefully chosen in Differential Cryptanalysis.
8.	Plaintext is used one by one in linear Cryptanalysis.	Plaintext is used in pairs in Differential Cryptanalysis.
9.	Complexity of attack is low in linear Cryptanalysis.	Complexity of attack is High in Differential Cryptanalysis
10.	Mathematical relation between plaintexts used has Linear approximation (such as a series of XOR operations).	Mathematical relation between plaintexts used has  Specific differences (such as XOR).
11.	Goal of the attack is to identify the linear relation between some bits of the plaintext, some bits of the cipher text and some bits of the unknown key.	Goal of the attack is to  Identify some bits of the unknown key.