  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.
