# Permutation Generators Based on Unbalanced Feistel Network: Analysis of the Conditions of Pseudorandomness

## TL;DR

This paper analyzes the minimal rounds needed for unbalanced Feistel network-based permutation generators to achieve pseudorandomness and proposes a new unbalanced Feistel structure to extend block cipher sizes.

## Contribution

It provides a theoretical analysis of round requirements for unbalanced Feistel networks and introduces a new structure for large input-output size block ciphers.

## Key findings

- Minimal rounds for source-heavy structures determined
- Minimal rounds for target-heavy structures determined
- Proposed new unbalanced Feistel network extends small to large block sizes

## Abstract

A block cipher is a bijective function that transforms a plaintext to a ciphertext. A block cipher is a principle component in a cryptosystem because the security of a cryptosystem depends on the security of a block cipher. A Feistel network is the most widely used method to construct a block cipher. This structure has a property such that it can transform a function to a bijective function. But the previous Feistel network is unsuitable to construct block ciphers that have large input-output size. One way to construct block ciphers with large input-output size is to use an unbalanced Feistel network that is the generalization of a previous Feistel network. There have been little research on unbalanced Feistel networks and previous work was about some particular structures of unbalanced Feistel networks. So previous work didn't provide a theoretical base to construct block ciphers that are secure and efficient using unbalanced Feistel networks. In this thesis, we analyze the minimal number of rounds of pseudo-random permutation generators that use unbalanced Feistel networks. That is, after categorizing unbalanced Feistel networks as source-heavy structures and target-heavy structures, we analyze the minimal number of rounds of pseudo-random permutation generators that use each structure. Therefore, in order to construct a block cipher that is secure and efficient using unbalanced Feistel networks, we should follow the results of this thesis. Additionally, we propose a new unbalanced Feistel network that has some advantages such that it can extend a previous block cipher with small input-output size to a new block cipher with large input-output size. We also analyze the minimum number of rounds of a pseudo-random permutation generator that uses this structure.