Block cipher is a bijective function that transform a plaintext to a ciphertext. Block cipher is a principle component of a cryptosystem because the security of a cryptosystem is depends on the security of a block cipher.
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 previous feistel network is unsuitable to construct a block cipher that have large input-output size.
One way to construct a block cipher with large input-output size is to use an unbalanced feistel network that is a generalization of a previous feistel network. But there have been little research on unbalanced feistel networks. And previous works were about some particular structure of unbalanced feistel networks. So previous works didn't provide a theoretical base to construct a block cipher that is secure and efficient using unbalanced feistel networks.
In this thesis, I will analyze the minimal number of rounds of pseudorandom permutation generators that use unbalanced feistel networks. That is, after categorizing unbalanced feistel networks as source-heavy structure and target-heavy structure, I will analyze the minimal number of rounds of pseudorandom permutation generator that use each structure. Therefore in order to construct a block cipher that is secure and efficient using unbalanced feistel networks, we should follows the results of this thesis.
I will propose new unbalanced feistel networks that has some advantage such that it can extend a previous block cipher to a block cipher with large input-output size. And I will analyze the minimal number of rounds of pseudorandom permutation generator that use this structure.
