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Partition and mix: generalizing the swap-or-not shuffle
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2023-03-02 , DOI: 10.1007/s10623-023-01199-4
Nam-Su Jho, Jooyoung Lee

Card shuffle algorithms have been studied from a cryptographic point of view with applications to format preserving encryption. In this work, we naturally extend the swap-or-not shuffle, proposed by Hoang, Morris and Rogaway at Crypto 2012, by replacing a perfect matching used in each round by a keyed partition with a certain uniform property. The resulting construction, dubbed the partition-and-mix (or simply \(\textsf{PM}\)) shuffle, is proved to be secure up to \((1-\delta )N\) queries for any \(\delta >0\) and the domain size N, while the number of rounds is significantly reduced compared to the swap-or-not. We give concrete examples of the keyed partitions that provide security as well as allow efficient implementation in practice. Such uniform keyed partitions seem of independent interest. The partition-and-mix shuffle might also be viewed as an alternative block cipher structure that extends the domain of a small block cipher operating on each block of the partition.



中文翻译:

分区和混合:推广交换或不洗牌

纸牌洗牌算法已经从密码学的角度进行了研究,并应用于格式保持加密。在这项工作中,我们自然地扩展了 Hoang、Morris 和 Rogaway 在 Crypto 2012 上提出的交换或不洗牌,通过用具有特定统一属性的键控分区替换每轮中使用的完美匹配。由此产生的结构,被称为分区和混合(或简称为\(\textsf{PM}\) )洗牌,被证明是安全的,直到\((1-\delta )N\)查询任何\(\ delta >0\)和域大小N,而与交换或不交换相比,轮数显着减少。我们给出了提供安全性并允许在实践中有效实施的键控分区的具体示例。这种统一的键控分区似乎具有独立的兴趣。分区和混合洗牌也可以被视为一种替代分组密码结构,它扩展了在分区的每个块上运行的小分组密码的域。

更新日期:2023-03-02
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