In this era of Networking, everyone is connected. We share various data via the Internet. Cryptography comes into the picture when we have to share sensitive data through an insecure network. It allows us to share sensitive information in an encrypted and secure manner.

Cryptanalysis studies techniques for decoding encrypted data without having access to private data. The fundamental methods of Cryptanalysis are differential and linear cryptanalysis, and numerous cryptographic attacks have been created based on these methods till now. This article will cover the differences between differential and linear Cryptanalysis.

What is Cryptanalysis?

Cryptosystems encrypt and decrypt data to protect interactions between systems, devices, and apps using cryptographic algorithms, often called ciphers.

While cryptography is concerned with producing secret codes, cryptanalysis examines the cryptographic algorithm. To retrieve the secret key, a cryptanalyst must identify statistical and algebraic techniques based on mathematical errors in the design.

Cryptanalytic Attacks

Based on the attacker's access, there are different cryptanalytic attacks, such as

📌 Known plaintext/Ciphertext attacks.

📌 Chosen plaintext/Ciphertext attacks.

📌 Adaptive chosen plaintext/Ciphertext attacks.

📌 Chosen Key Attack.

You can use the number of plaintext-ciphertext pairings or combinations necessary to retrieve a secret key to determine the success of an attack. The cypher is considered broken when the number of operations needed for the attack is fewer than 2n, where n is the size of the secret key.

Cryptanalysis Variants

There are many two types of Cryptanalysis.

📍 Linear.

📍 Differential.

A block cypher resilient to one attack may be breached by one or more of its variants or combinations.

The following diagram shows the variants of Cryptanalysis.

What is Differential Cryptanalysis?

Differential cryptanalysis is a general kind that primarily works with cryptographic hash functions, stream ciphers, and block ciphers. It studies how differences in information input can affect the resultant difference in the output.

In the case of a block cypher, it refers to a collection of methods for the following functions:

Tracking differences through the network of transformation.

Identifying instances in which the cypher displays non-random behaviour.

Taking advantage of these characteristics to find the secret key.

The main objective of linear cryptanalysis is to find high-probability instances of linear expressions involving secret key bits, plaintext bits, and "ciphertext" bits. It is a known plaintext attack based on the assumption that the attacker is aware of a collection of plaintexts and their related ciphertexts.

Difference Between Differential and Linear Cryptanalysis

The main differences between Differential and Linear Cryptanalysis are as follows.

Key Points

Differential Cryptanalysis

Linear Cryptanalysis

Discovery

It was discovered in 1990 by Eli Biham and Adi Shamir.

It was discovered in 1992 by Matsui and Yamagishi.

Definition

It is the study of how differences in information input can affect the resultant difference in the output.

It finds high-probability instances of linear expressions involving secret key bits, plaintext bits, and ciphertext bits.

Decryption

Multiple rounds of encryption are used to get the changes to the middle ciphertext in differential cryptanalysis.

In linear cryptanalysis, each cipher is broken using all feasible subkeys for a single round of encryption, and the intermediate ciphertext is then studied to examine the random outcomes.

Disadvantage

Plain text attack is a very major drawback in the context of differential cryptanalysis.

Ciphertext attack is a significant drawback for linear cryptanalysis.

Role of Attacker

The attacker's job is to examine changes in a few selected plaintexts and the variations in the outputs that arise from encrypting each one to recover some of the keys.

In linear cryptanalysis, the attacker's role is to determine the linear relationship between plaintext, ciphertext, and unknown security key bits.

Structure

Since the input qualities differ, the underlying structure of each input is irrelevant in this situation.

The internal structures of a single input are referred to as subsets of input attributes.

Uses

Differential cryptanalysis is used to uncover information about some crucial bits, nullifying the necessity for an extensive search.

With the help of linear cryptanalysis, it is possible to determine the linear relationship between specific plaintext, ciphertext quickly, and unknown key bits.

The known plaintext or ciphertext attack is based on the assumption that the attacker knows a pair of plaintexts and their related ciphertexts. They will find the high-probability instances of linear expressions involving secret key bits, plaintext bits, and "ciphertext" bits.

What is a Block Cipher?

A block cipher is a method. A block cipher encrypts data in blocks to create ciphertext using a cryptographic key and algorithm. We require a block cypher mode of operation to encode and decode messages of any size and content without leaving ourselves vulnerable to attack.

What is the Piling-up lemma?

The piling-up lemma is a cryptanalysis principle applied to linear cryptanalysis to create linear approximations to block cipher actions. According to the lemma, the bias of a linear Boolean function (XOR-clause) of independent binary random variables is correlated to the product of the input biases.

Conclusion

We discussed Cryptanalysis, types of Cryptanalytic attacks, and types of cryptanalysis. We also discussed Linear and Differential Cryptanalysis. Further, we discussed the difference between Linear and Differential Cryptanalysis.

We hope this blog has helped you. We recommend you visit our articles on different topics of Cryptography, such as