| 本文已被：浏览 1243次 下载 3803次 |
码上扫一扫！ |
|
|
| SPN型密码的通用子空间迹分析 |
|
宋蝉1,2, 张蕾1,2,3, 吴文玲1,2
|
|
1.中国科学院 软件研究所, 北京 100190;2.中国科学院大学, 北京 100049;3.密码科学技术国家重点实验室, 北京 100878
|
|
| 摘要: |
| SPN结构是目前最广泛使用的一种分组密码整体结构, AES、ARIA等分组密码算法均采用此结构, 对此类SPN型密码的安全性分析是密码分析中的一个研究热点. 将子空间迹密码分析方法应用到典型二维SPN型密码和典型三维SPN型密码中, 可分别得到其相应的子空间迹和基于子空间迹的通用性质, 该性质与密钥、S盒以及列混淆矩阵的定义均无关, 可具体描述为: 针对一个状态可形式化为n×m二维数组的典型二维SPN型密码, 属于类对角子空间同一陪集的所有明文经过5轮加密得到的密文中属于混淆子空间同一陪集的不同密文对数量一定为$ {2^{n - 1}} $的倍数; 针对一个状态可形式化为l×n×m三维数组的典型三维SPN型密码, 属于类对角子空间同一陪集的所有明文经过7轮加密得到的密文中属于混淆子空间同一陪集的不同密文对数量一定为$ {2^{nl - 1}} $的倍数. 此外, 不仅对该性质进行了证明, 还在PHOTON算法的内部置换以及小规模版本Rijndael算法、3D算法、Saturnin算法上进行了实验验证, 结果与该性质完全一致. |
| 关键词: SPN型密码 子空间迹 倍数性质 PHOTON置换 3D算法 |
| DOI：10.13328/j.cnki.jos.006761 |
| 分类号:TP309 |
| 基金项目:国家自然科学基金(62072445) |
|
| General Subspace Trail Cryptanalysis of SPN Ciphers |
|
SONG Chan1,2, ZHANG Lei1,2,3, WU Wen-Ling1,2
|
|
1.Institute of Software, Chinese Academy of Sciences, Beijing 100190, China;2.University of Chinese Academy of Sciences, Beijing 100049, China;3.State Key Laboratory of Cryptology, Beijing 100878, China
|
| Abstract: |
| SPN construction is the most widely used overall construction of block ciphers at present, which is adopted by block ciphers such as AES and ARIA. The security analysis of SPN ciphers is a research hotspot in cryptanalysis. The application of the subspace trail cryptanalysis to the typical two-dimensional SPN ciphers and typical three-dimensional SPN ciphers can yield the corresponding subspace trails and general properties based on the subspace trails separately. These properties are independent of the secret key and the detailed definitions of the S-box and MixColumns matrix. They can be specifically described as follows: For a typical two-dimensional SPN cipher whose state can be formalized into a two-dimensional array of n×m, the number of different ciphertext pairs belonging to the same coset of the mixed subspace in the ciphertexts obtained by five rounds of encryption of all plaintexts belonging to the same coset of the quasi-diagonal subspace must be a multiple of 2n–1. For a typical three-dimensional SPN cipher whose state can be formalized into a three-dimensional array of l×n×m, the number of different ciphertext pairs belonging to the same coset of the mixed subspace in the ciphertexts obtained by seven rounds of encryption of all plaintexts belonging to the same coset of the quasi-diagonal subspace must be a multiple of 2nl–1. In addition, this study not only proves these properties but also makes experimental verification on the internal permutations of PHOTON and small-scale variants of Rijndael, 3D, and Saturnin algorithms. The experimental results are completely consistent with these properties. |
| Key words: SPN cipher subspace trail multiple property PHOTON’s permutation 3D algorithm |
