What is a Feistel cipher?

While constructing a block cipher, we often use a Feistel cipher. A Feistel cipher is a structure that is used to construct a block cipher. It is named after the cryptographer Horst Feistel. A Feistel cipher is also known as a Feistel network.

Construction Details Of A Feistel Cipher

A Feistel cipher is used to construct an iterative block cipher. In an iterative block cipher, the input plaintext goes through several rounds. In each round, a round function is applied to the block of plaintext and a round key is used.

Let’s say, there are n rounds in an iterative block cipher and there are n round keys K0, … K_n-1. And, we are constructing the iterative block cipher using a Feistel cipher. In a Feistel cipher, firstly the input plaintext is divided into two parts, let’s say L₀ and R₀. Then, for each round i, we calculate L_i+1 and R_i+1 like the following:

L_i+1 = R_i
R_i+1 = L_i ⊕ F(R_i, K_i)

F is a round function that is applied on R_i with the help of a round key K_i. And, ⊕ is the XOR operation.

In other words, a round function F is applied on Ri first with the help of a round key Ki. Then, the output of the round function is XOR’ed with Li. The result is then interchanged with Ri and fed into the next round.

Where are Feistel ciphers used?

Feistel ciphers or modified Feistel ciphers are used in constructing many block ciphers. For example, DES, Triple DES, Blowfish, Twofish, etc. are block ciphers that are constructed using Feistel ciphers or modified Feistel ciphers.

I hope this helps. However, readers who want to know more about how different cryptographic algorithms work and how they are used in various secure network protocols can refer to the book “Cryptography And Public Key Infrastructure.”