如何在其它群上生成伪随机置换：Even-Mansour和Feistel的再认识
How to Generate Pseudorandom Permutations Over Other Groups: Even-Mansour and Feistel Revisited
摘要：
Alagic和Russell最近的研究结果给出了一些证据，证明如果在$(\mathbb{Z}/2)^n$之外的其他组上考虑，Even-Mansour密码可能对具有量子查询的量子对手是安全的。这就引出了一个问题，即其他经典方案是否可以推广到任意群，以及经典结果是否仍然适用于这些推广方案。本文推广了Even-Mansour密码和Feistel密码。我们表明，即使和曼苏尔的原始概念的保密性得到一个关键的，组的变体的Even-曼苏尔密码。我们推广了Kilian和Rogaway的结果，即Even-Mansour密码是伪随机的，超伪随机的，也是在一个密钥，组的情况下。使用滑动攻击，我们匹配上面找到的边界。在将Feistel密码推广到任意群之后，我们通过证明任意群上的$3$轮Feistel密码不是超伪随机的来解决Patel、Ramzan和Sundaram的一个公开问题。最后，我们推广了Gentry和Ramzan的一个结果，证明了Even-Mansour密码可以用Feistel密码作为公共置换来实现。在最后一个结果中，我们还考虑了群上的单密钥情况，并推广了它们的界。
英文摘要：
Recent results by Alagic and Russell have given some evidence that the Even-Mansour cipher may be secure against quantum adversaries with quantum queries, if considered over other groups than $(\mathbb{Z}/2)^n$. This prompts the question as to whether or not other classical schemes may be generalized to arbitrary groups and whether classical results still apply to those generalized schemes. In this paper, we generalize the Even-Mansour cipher and the Feistel cipher. We show that Even and Mansour's original notions of secrecy are obtained on a one-key, group variant of the Even-Mansour cipher. We generalize the result by Kilian and Rogaway, that the Even-Mansour cipher is pseudorandom, to super pseudorandomness, also in the one-key, group case. Using a Slide Attack we match the bound found above. After generalizing the Feistel cipher to arbitrary groups we resolve an open problem of Patel, Ramzan, and Sundaram by showing that the $3$-round Feistel cipher over an arbitrary group is not super pseudorandom. Finally, we generalize a result by Gentry and Ramzan showing that the Even-Mansour cipher can be implemented using the Feistel cipher as the public permutation. In this last result, we also consider the one-key case over a group and generalize their bound.
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。
