General concepts of cryptanalysis methods

Токстаджон Козокова

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GENERAL CONCEPTS OF CRYPTANALYSIS METHODS

Qozoqova Toʻxtajon Qaxramon qizi

Tashkent University of Information Technologies

qozoqovat1516@gmail.com

Abstract.

A thesis about cryptanalysis methods could explore any of these types

of attacks in detail, compare their advantages and disadvantages, analyze their

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complexity and effectiveness, and propose new methods or improvements. A thesis
could also focus on a specific cipher or class of ciphers, such as symmetric-key ciphers,
public-key ciphers, stream ciphers, block ciphers, etc., and study their resistance or
vulnerability to different types of

attacks.

Keywords:

Cryptanalysis, Ciphertext-only attack, Known-plaintext attack,

Chosen-ciphertext attack, RSA.

Cryptanalysis is the process of analyzing information systems in order to

understand hidden aspects of the systems, such as the secret key or the
plaintext Cryptanalysis is used to breach cryptographic security systems and gain
access to the contents of encrypted messages, even if the cryptographic key is
unknown[1]

There are many types of cryptanalysis methods, depending on the amount of

information available to the attacker, the type of cipher being attacked, and the goal of
the attack. Some of the most common types are:

•

Ciphertext-only attack:

The attacker only has access to one or more

ciphertexts, and tries to recover the plaintext or the key. This is the most difficult type
of attack, as it requires a lot of computational power and statistical analysis. An
example of this type of attack is frequency analysis, which exploits the fact that some
letters or symbols are more common than others in a given language[12]

•

Known-plaintext attack:

The attacker has access to one or more pairs of

plaintext and ciphertext, and tries to recover the key or other plaintexts. This type of
attack is easier than a ciphertext-only attack, as it reduces the search space for the
key. An example of this type of attack is linear cryptanalysis, which exploits a linear
relation between some bits of the plaintext, some bits of the ciphertext, and some bits
of the key[1][3]

•

Chosen-plaintext attack

: The attacker can choose one or more plaintexts

obtain their corresponding ciphertexts, and try to recover the key or other plaintexts.
This type of attack is even easier than a known-plaintext attack, as it allows the attacker
to tailor the plaintexts to their advantage. An example of this type of attack is
differential cryptanalysis, which exploits a difference between two plaintexts and their
corresponding ciphertexts that depends only on some bits of the key[1][3]

•

Chosen-ciphertext attack

: The attacker can choose one or more ciphertexts

and obtain their corresponding plaintexts, and tries to recover the key or other
ciphertexts. This type of attack is similar to chosen-plaintext attack, but in reverse. An
example of this type of attack is an adaptive chosen-ciphertext attack, which exploits a
weakness in some public-key encryption schemes that allows the attacker to modify a
ciphertext and obtain a valid plaintext. [1-4]

A ciphertext-only attack and a known-plaintext attack are two types of

cryptanalysis attacks that aim to break a cryptographic system. The main difference
between them is the amount and type of information that the attacker has access to.
In a ciphertext-only attack, the attacker only has access to a collection of ciphertexts
and tries to recover the plaintext or the key. This is the most difficult type of attack, as
the attacker has to rely on statistical analysis, guessing, or brute force search to find
patterns or clues in the ciphertexts. For example, an attacker may use frequency

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analysis to break a simple substitution cipher by comparing the letter frequencies in the
ciphertext with those of the expected plaintext language[1]

•

In a known-plaintext attack, the attacker has access to some ciphertexts and

their corresponding plaintexts, and tries to find the key or decrypt other ciphertexts.
This type of attack is easier than a ciphertext-only attack, as the attacker can use the
known pairs to reduce the search space or exploit weaknesses in the encryption
algorithm. For example, an attacker may use a linear equation solver to break a linear
congruential cipher by finding the key parameters from the known pairs [2]

•

The difference between these two types of attacks can be significant

depending on the encryption system under consideration. Some systems may be
vulnerable to both types of attacks, while others may be resistant to one but not the
other. For instance, RSA with OAEP encryption is resistant to known-plaintext attacks,
as the plaintext candidate is automatically verified by the decryption
algorithm. However, RSA with PKCS#1 v1.5 padding is vulnerable to chosen-
ciphertext attacks, as the attacker can modify the ciphertext and obtain feedback from
the decryption algorithm. [1][3]

Nowadays, statistics cryptanalysis is a widely used technique for breaking

cryptographic systems. Statistics cryptanalysis is based on the idea that natural
languages have certain patterns and frequencies that can be exploited to reveal
information about the plaintext or the key. Statistics cryptanalysis can be applied to
various types of ciphers, such as substitution ciphers, transposition ciphers, stream
ciphers, and block ciphers[5][6][7]. Some examples of statistics cryptanalysis are:

•

Frequency analysis: This is one of the oldest and simplest methods of statistics

cryptanalysis. It relies on the fact that different letters or symbols have different
probabilities of occurring in a given language. For example, in English, the letter E is
the most common, followed by T, A, O, I, and N. By counting the frequencies of the
ciphertext symbols and comparing them with the expected frequencies of the plaintext
language, an attacker can guess the mapping between the plaintext and ciphertext
symbols. Frequency analysis can be used to break simple substitution ciphers, such as
Caesar cipher or Vigenère cipher[5][9]

•

Linear cryptanalysis: This is a more advanced method of statistics

cryptanalysis that was introduced by Matsui in 1993. It exploits a linear relation
between some bits of the plaintext, ciphertext, and key of a block cipher. The linear
relation holds for a fraction of plaintexts, and therefore has a bias. If the bias is large
enough, an attacker can use it to recover information about the key or decrypt other
ciphertexts. Linear cryptanalysis can be used to break block ciphers such as DES or
Serpent[5][10]

•

Differential cryptanalysis: This is another advanced method of statistics

cryptanalysis that was introduced by Biham and Shamir in 1990. It exploits a difference
between two plaintexts and the corresponding difference between their ciphertexts
under a block cipher. The difference can be measured by XORing the plaintexts or
ciphertexts. The probability of a certain difference occurring depends on the structure
of the cipher and the key. If the probability is high enough, an attacker can use it to
recover information about the key or decrypt other ciphertexts. Differential
cryptanalysis can be used to break block ciphers such as DES or AES[5][11]

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Statistics cryptanalysis is constantly evolving and adapting to new cryptographic

systems and challenges. Some recent developments in statistics cryptanalysis are:

•

Multidimensional linear cryptanalysis: This is an extension of linear

cryptanalysis that uses multiple linear approximations that form a linear subspace. The
advantage of this method is that it can capture the joint behavior of several not
necessarily independent binary variables, and potentially recover more bits of
information about the key using less data. Multidimensional linear cryptanalysis was
proposed by Hermelin et al. in 2018[10]

•

Neural-aided statistical attack: This is a novel method that combines statistics

cryptanalysis with deep learning techniques. The idea is to use neural networks to learn
the statistical properties of a cipher and use them to assist in key recovery attacks.
Neural-aided statistical attack was proposed by Chen et al. in 2022, and applied to
round-reduced versions of Speck32/64, DES, and Speck96/96.[2]

References:

1.

https://crypto.stackexchange.com/questions/55861/whats-the-difference-

between-a-known-plaintext-attack-and-a-ciphertext-only-att

2.

https://www.geeksforgeeks.org/cryptanalysis-and-types-of-attacks/

3.

https://www.geeksforgeeks.org/cryptanalysis-and-types-of-attacks/

4.

https://www.geeksforgeeks.org/cryptanalysis-and-types-of-attacks/

5.

https://link.springer.com/article/10.1007/s00145-018-9308-x