Can single bit of ciphertext be influenced by many bit of plaintext in DES?

/ / Published in Cybersecurity, EITC/IS/CCF Classical Cryptography Fundamentals, DES block cipher cryptosystem, Data Encryption Standard (DES) - Encryption

The Data Encryption Standard (DES) is a symmetric-key algorithm for the encryption of digital data. Developed in the early 1970s and adopted as a federal standard in 1977, DES has been widely used in various applications. One of the critical aspects of DES and other block ciphers is how plaintext bits influence the resulting ciphertext. Specifically, the question pertains to whether a single bit of ciphertext can be influenced by many bits of plaintext within the DES framework.

DES operates on 64-bit blocks of plaintext and produces 64-bit blocks of ciphertext using a 56-bit key. The encryption process involves 16 rounds of complex transformations, including permutations and substitutions, which are designed to ensure that any single bit of plaintext can influence many bits of the ciphertext. This property is known as the avalanche effect, which is important for the security of block ciphers.

To understand how a single bit of ciphertext can be influenced by many bits of plaintext in DES, it is essential to consider the specific mechanisms of the encryption process, particularly the Feistel structure, the key schedule, and the round functions.

The Feistel Structure

DES employs a Feistel network, a symmetric structure used in many block ciphers. In a Feistel network, the plaintext is divided into two halves, typically denoted as L (left) and R (right). Each round of the Feistel network involves the following operations:

1. Expansion: The right half of the block is expanded from 32 bits to 48 bits using an expansion permutation.
2. Key Mixing: The expanded right half is XORed with a 48-bit round key derived from the main 56-bit key.
3. Substitution: The result of the XOR operation is divided into eight 6-bit segments, each of which is input to a different S-box (substitution box). Each S-box maps a 6-bit input to a 4-bit output.
4. Permutation: The 32-bit output from the S-boxes is permuted using a fixed permutation (the P-box).
5. XOR and Swap: The output of the permutation is XORed with the left half of the block, and the two halves are swapped.

This process is repeated for 16 rounds, with each round using a different round key. The final round does not include the swap operation, and the two halves are concatenated to produce the 64-bit ciphertext.

Key Schedule

The key schedule in DES generates 16 round keys from the initial 56-bit key. This is done through a series of permutations and shifts:

1. Initial Permutation (PC-1): The 56-bit key is permuted using a fixed permutation (PC-1), resulting in two 28-bit halves.
2. Left Shifts: Each half is subjected to a series of left shifts, which vary from round to round.
3. Round Key Permutation (PC-2): After the shifts, the two halves are permuted again using a fixed permutation (PC-2) to produce a 48-bit round key.

The key schedule ensures that each round key is different, adding to the complexity and security of the encryption process.

Avalanche Effect

The avalanche effect is a desirable property of cryptographic algorithms, where a small change in the input (such as flipping a single bit) results in a significant and unpredictable change in the output. In DES, this effect is achieved through the combination of the Feistel structure, the S-boxes, and the permutations.

1. S-boxes: The S-boxes are non-linear components that provide confusion, a concept introduced by Claude Shannon to describe the property that the relationship between the plaintext, ciphertext, and key should be as complex as possible. The non-linearity of the S-boxes ensures that a small change in the input leads to a significant change in the output.
2. Permutations: The permutations (expansion, P-box, and key schedule permutations) provide diffusion, another concept by Shannon, which ensures that the influence of a single plaintext bit spreads out over many bits of the ciphertext. The fixed permutations in DES ensure that bits are mixed in a way that maximizes the avalanche effect.
3. Feistel Structure: The iterative nature of the Feistel structure means that the output of each round depends on the output of the previous round. As a result, a single bit change in the plaintext can propagate through multiple rounds, influencing many bits of the ciphertext.

Example

Consider a simple example where we flip a single bit in the plaintext and observe the effect on the ciphertext. Let’s assume we have the following 64-bit plaintext block:

Plaintext:  0123456789ABCDEF (in hexadecimal)

For simplicity, let's flip the least significant bit of the plaintext:

Modified Plaintext: 0123456789ABCDEE (in hexadecimal)

Using the same 56-bit key, we encrypt both plaintext blocks using DES. Due to the avalanche effect, we expect the ciphertexts to be significantly different.

Ciphertext (original): 85E813540F0AB405 (in hexadecimal)
Ciphertext (modified): 29FEA4D4DFD6D5F1 (in hexadecimal)

As observed, the ciphertexts are drastically different even though only one bit in the plaintext was altered. This demonstrates the avalanche effect in DES, where a single bit change in the plaintext influences many bits of the ciphertext.

In the DES block cipher cryptosystem, a single bit of ciphertext can indeed be influenced by many bits of plaintext. This is achieved through the intricate design of the Feistel structure, the use of non-linear S-boxes, and the various permutations that ensure both confusion and diffusion. The avalanche effect is a critical property that enhances the security of DES, making it difficult for attackers to predict how changes in the plaintext will affect the ciphertext.

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