基于非平衡Feistel网络的置换发生器：伪随机性条件分析
Permutation Generators Based on Unbalanced Feistel Network: Analysis of the Conditions of Pseudorandomness
摘要：
分组密码是将明文转换为密文的双射函数。分组密码是密码系统中的主要组成部分，因为密码系统的安全性取决于分组密码的安全性。Feistel网络是构造分组密码最广泛使用的方法。该结构具有这样的性质，即它可以将函数变换为双射函数。但现有的Feistel网络不适合构造输入输出规模较大的分组密码。构造具有大输入输出大小的分组密码的一种方法是使用非平衡Feistel网络，该网络是先前Feistel网络的推广。目前对非平衡Feistel网络的研究还很少，以前的工作主要是针对非平衡Feistel网络的一些特殊结构。因此，以前的工作并没有提供一个理论基础，构造分组密码是安全的，有效的使用非平衡Feistel网络。在这篇论文中，我们分析了使用非平衡Feistel网络的伪随机置换生成器的最小轮数。也就是说，在将不平衡Feistel网络分类为源重结构和目标重结构之后，我们分析了使用每种结构的伪随机置换生成器的最小轮数。因此，为了利用非平衡Feistel网络构造一个安全有效的分组密码，我们应该遵循本文的结果。此外，我们提出了一种新的非平衡Feistel网络，它具有一些优点，例如它可以扩展以前的分组密码与小的输入输出大小到一个新的分组密码与大的输入输出大小。我们还分析了使用这种结构的伪随机置换生成器的最小轮数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
