WO2020173063A1 - 一种新型的密码专用的4×4的s盒构造方法 - Google Patents

一种新型的密码专用的4×4的s盒构造方法 Download PDF

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WO2020173063A1
WO2020173063A1 PCT/CN2019/102938 CN2019102938W WO2020173063A1 WO 2020173063 A1 WO2020173063 A1 WO 2020173063A1 CN 2019102938 W CN2019102938 W CN 2019102938W WO 2020173063 A1 WO2020173063 A1 WO 2020173063A1
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boxes
box
construction method
design requirements
password
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王小云
贾珂婷
魏淙洺
孙悦
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Tsinghua University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators

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  • the present invention relates to the technical field of cryptography, in particular to a new type of 4 ⁇ 4 S-box construction method dedicated to cryptography.
  • S-box has a wide range of applications in modern symmetric cipher design, especially block ciphers and hash functions.
  • the S-box is usually used as the only non-linear part to provide obfuscation to ensure the security of the entire cryptographic algorithm.
  • the S-box can be regarded as a Boolean function with n-bit input and m-bit output, called an n ⁇ m S-box.
  • n and m are large, almost all S-boxes are non-linear and have good password strength, but if n and m are too large, the storage capacity of the algorithm will increase.
  • the common S-box size is 8 ⁇ 8 or 4 ⁇ 4.
  • the 4 ⁇ 4 S-box has more advantages in resource-limited environments, so it is often used in lightweight cryptographic algorithms.
  • Many known algorithms such as Serpent, PRESENT, RECTANGLE, etc., all use 4 ⁇ 4 S-boxes. Due to the small scale of the 4 ⁇ 4 S-box, current studies have conducted a more in-depth analysis of its differential and linear characteristics, and divided the S-boxes that meet the safety requirements of 4 ⁇ 4 for difference and 4 for linearity into 16 One AE category, denoted as G0 ⁇ G15.
  • the S-box constructed by mathematical functions performs well in terms of differential distribution, linear deviation distribution and algebraic order.
  • security features such as 1-bit difference and 1-bit linearity also need to be considered.
  • the method of constructing S-boxes through mathematical functions is more difficult to generate 4 ⁇ 4 S-boxes with higher encryption strength.
  • the present invention provides a new type of password-specific 4 ⁇ 4 S-box construction method, which combines the ergodic affine equivalent (AE) class and S-box feature screening to construct A large number of 4 ⁇ 4 S boxes with higher password strength.
  • AE ergodic affine equivalent
  • This new type of password-specific 4 ⁇ 4 S-box construction method includes the following steps:
  • Step 2 Screen out the S boxes that meet the preset design requirements from the S boxes searched in step 1.
  • Step 3 For the S-boxes that have been screened in step 2, by traversing P 1 (S(P 0 (x+a)))+b, all S-boxes that meet the preset design requirements are obtained; among them, P 0 and P 1 Is a 4 ⁇ 4 permutation matrix, a and b are 4-bit vectors;
  • Step 4 On the basis of step 3, the traversed S-boxes are further screened, and the S-boxes with 0 fixed points are selected as the final target.
  • the preset design requirements include differential probability, linear approximation probability, the number of input and output 1-bit differences, the number of input and output 1-bit linear masks, and the number of algebras.
  • the smallest representative element of each type of S-box that satisfies the preset design requirements selected in the second step is selected by traversing P 1 (S(P 0 (x+a)) )+b Obtain all S boxes that meet the preset design requirements.
  • the new type of password-specific 4 ⁇ 4 S-box construction method provided by the present invention can construct a large number of higher passwords by combining traversal AE class with S-box feature screening Intensity 4 ⁇ 4 S-box.
  • Fig. 1 is a schematic flowchart of a new type of password-specific 4 ⁇ 4 S-box construction method provided by an embodiment of the present invention.
  • This embodiment provides a new type of password-specific 4 ⁇ 4 S-box construction method.
  • the new type of password-specific 4 ⁇ 4 S-box construction method includes the following steps:
  • Step 2 Filter out the S-boxes searched in Step 1 to meet the safety requirements of the design (differential probability not less than 2 -2 , linear approximation probability not less than 2 -2 , input and output 1 bit difference number, input and output 1
  • the number of bit linear masks and the number of algebras are 3). If the 1-bit input and output differential value is 0, the number of 1-bit linear masks is 4, and the number of algebras is 3, there are two types of S-boxes.
  • the smallest representative elements are 03589CE7ADF46B12 and 03586CB7DAE41F29 (other S-boxes in the class can be obtained by the traversal formula in step 3 of the representative element).
  • Step 3 Obtain all S boxes that meet the above design requirements by traversing P 1 (S(P 0 (x+a)))+b for the S boxes screened in step 2.
  • P 0 and P 1 are 4 ⁇ 4 permutation matrices
  • a and b are 4-bit vectors.
  • Step 4 On the basis of step 3, the S boxes are further screened, and the S boxes with 0 fixed points are selected as the final target.
  • the principle is the same as that of the above-mentioned scheme of this embodiment. But the efficiency is low.
  • the new type of password-specific 4 ⁇ 4 S-box construction method combines the traversal AE class with S-box feature screening, which can construct a large number of higher A 4 ⁇ 4 S-box with cipher strength.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Financial Or Insurance-Related Operations Such As Payment And Settlement (AREA)
  • Storage Device Security (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

本发明公开了一种新型的密码专用的4×4的S盒构造方法，其包括：首先对每一个仿射等价(AE)类Gi，选用其中已知的S盒S i，按照预设搜索方式搜索得到一系列新的S盒，搜索方式为S'(x)＝M 1(S i(M 0 T(x)))，其中，i＝0,…,15；x为输入，S'为新搜索到的S盒，M 0和M1为4×4的行递增可逆矩阵，满足矩阵的行的数值从上到下逐渐递增；然后从搜索到的S盒中筛选出满足设计需求的S盒；再然后对筛选后的S盒通过遍历P1(S(P 0(x+a)))+b得到全部满足上述设计需求的S盒；其中，P 0和P 1为4×4置换矩阵，a、b为4比特向量；最后选择固定点数目为0的S盒作为最终目标。本发明通过将遍历AE类与S盒特征筛选结合，可构造大量具有更高密码强度的4×4的S盒。

Description

一种新型的密码专用的4×4的S盒构造方法
本申请要求于2019年2月26日提交中国专利局、申请号为201910140294.0，发明名称为“一种新型的密码专用的4×4的S盒构造方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明涉及密码学技术领域，尤其涉及一种新型的密码专用的4×4的S盒构造方法。
背景技术
S盒在现代对称密码设计，特别是分组密码和哈希函数中具有广泛的应用。在分组密码中，S盒通常作为唯一的非线性部分提供混淆作用，保障整个密码算法的安全性。S盒可看作是n比特输入，m比特输出的布尔函数，称为n×m的S盒。当n和m很大时，几乎所有的S盒都是非线性的，且具有良好的密码强度，但n、m过大会增加算法的存储量。常见的S盒大小是8×8或4×4。和8×8的S盒相比，4×4的S盒在资源有限的环境中更具优势，因此常应用于轻量级密码算法。目前已知的很多算法，如Serpent、PRESENT、RECTANGLE等，均采用4×4的S盒。由于4×4的S盒的规模较小，目前已有研究对其差分、线性等特征进行了较深入的分析，并将其中满足差分为4，线性为4安全性要求的S盒划分为16个AE类，记为G0～G15。
构造具有良好的密码强度的S盒是分组密码算法设计中的重要环节。目前常见的S盒构造方法：1)通过数学函数构造S盒，是利用有限域上的模逆或者模幂映射；2)进行随机搜索，筛选满足特定的安全特性的。
通过数学函数构造的S盒在差分分布、线性偏差分布和代数次数方面表现较好。但对于规模较小的4×4的S盒，除了差分、线性和代数次数这些特征外，还需要考虑1比特差分、1比特线性等安全特征。通过数学函数构造S盒的方法在产生具有更高密码强度的4×4的S盒方面比较困难。
发明内容
针对上述现有技术中存在的不足之处，本发明提供一种新型的密码专用的4×4的S盒构造方法，通过将遍历仿射等价(AE)类与S盒特征筛选结合，构造大量具有更高密码强度的4×4的S盒。
该新型的密码专用的4×4的S盒构造方法包括以下步骤：
步骤一、对每一个AE类Gi，选用其中已知的S盒S i，按照预设搜索方式搜索得到一系列新的S盒，所述预设搜索方式为S’(x)＝M 1(S i(M 0 T(x)))，其中，i＝0,…,15，x为输入，S’为新搜索到的S盒，M 0和M 1为4×4的行递增可逆矩阵，满足矩阵的行的数值从上到下逐渐递增；
步骤二、从步骤一所搜索到的S盒中筛选出满足预设设计需求的S盒；
步骤三、对经过步骤二筛选后的S盒通过遍历P 1(S(P 0(x+a)))+b得到全部满足所述预设设计需求的S盒；其中，P 0和P 1为4×4置换矩阵，a、b为4比特向量；
步骤四、在步骤三的基础上进一步对遍历到的S盒进行筛选，选择固定点数目为0的S盒作为最终目标。
进一步地，每个AE类的可选的已知S盒的十六进制表示如下：
G0:0123468A5BCF7E9D      G1:0123468A5BCFED97
G2:0123468A5BCF79DE      G3:0123468B5CD7F9EA
G4:0123468B5C9DEA7F      G5:0123468B5CD7AF9E
G6:0123468B5CD79FAE      G7:0123468C59BDEA7F
G8:0123468A5BCFDE79      G9:0123468B59CED7AF
G10:0123468C59BDE7AF     G11:0123468C59DFA7BE
G12:0123468B5C9DE7AF     G13:0123468B59CEDA7F
G14:0123468B59CF7DAE     G15:0123468A5BCF7D9E
进一步地，所述预设设计需求包括差分概率、线性逼近概率、输入输出1比特差分个数、输入输出1比特线性掩码个数，以及代数次数。
进一步地，所述步骤三中是根据所述步骤二中筛选出的满足所述预设设计需求的每类S盒的最小代表元，通过遍历P 1(S(P 0(x+a)))+b得到全部满足所述预设设计需求的S盒。
相比于现有的数学函数构造S盒的方法，本发明提供的新型的密码专用的4×4的S盒构造方法通过将遍历AE类与S盒特征筛选结合，可以构造大量具有更高密码强度的4×4的S盒。
附图说明
图1为本发明实施例提供的新型的密码专用的4×4的S盒构造方法的流程示意图。
具体实施方式
为使本发明实施例的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明的一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例，都属于本 发明保护的范围。
请参阅图1，本实施例提供一种新型的密码专用的4×4的S盒构造方法，该新型的密码专用的4×4的S盒构造方法包括以下步骤：
步骤一、对每一个AE类Gi，选用其中已知的S盒S i(i＝0,…,15)，搜索得到一系列新的S盒，搜索方式为S’(x)＝M 1(S i(M 0 T(x)))，其中x为输入，S’为新搜索的S盒，M 0和M 1为4×4的行递增可逆矩阵，满足矩阵的行的数值从上到下逐渐递增。
每个AE类的可选的已知S盒的十六进制表示如下：
G0:0123468A5BCF7E9D      G1:0123468A5BCFED97
G2:0123468A5BCF79DE      G3:0123468B5CD7F9EA
G4:0123468B5C9DEA7F      G5:0123468B5CD7AF9E
G6:0123468B5CD79FAE      G7:0123468C59BDEA7F
G8:0123468A5BCFDE79      G9:0123468B59CED7AF
G10:0123468C59BDE7AF     G11:0123468C59DFA7BE
G12:0123468B5C9DE7AF     G13:0123468B59CEDA7F
G14:0123468B59CF7DAE     G15:0123468A5BCF7D9E
步骤二、从步骤一搜索到的S盒中筛选出满足设计所要求的安全性(差分概率不小于2 -2、线性逼近概率不小于2 -2、输入输出1比特差分个数、输入输出1比特线性掩码个数、代数次数为3)的S盒，如满足1比特输入输出差分值为0，1比特线性掩码输入输出个数为4，代数次数为3的S盒有两类，最小代表元分别为03589CE7ADF46B12和03586CB7DAE41F29(类中其它S盒可通过代表元经步骤三的遍历公式得到)。
步骤三、对步骤二筛选后的S盒通过遍历P 1(S(P 0(x+a)))+b得到全部满足上述设计要求的S盒。其中P 0和P 1为4×4置换矩阵，a、b为4比特向量。
步骤四、在步骤三的基础上进一步对S盒进行筛选，选择固定点数目为0的S盒作为最终目标。
值得一提的是，本实施例的上述方案采用的是先搜索S’(x)＝M 1(S i(M 0 T(x)))筛选出满足设计所要求的安全性的S盒，再遍历P 1(S(P 0(x+a)))+b的方式得到全部S盒；当然也可以直接对AE类进行穷搜筛选，其原理与本实施例的上述方案的原理相同，但效率较低。
相比于现有的数学函数构造S盒的方法，本实施例提供的新型的密码专用的4×4的S盒构造方法通过将遍历AE类与S盒特征筛选结合，可以构造大量具有更高密码 强度的4×4的S盒。
此外，需要说明的是，本发明实施例中，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、物品或者终端设备不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、物品或者终端设备所固有的要素。在没有更多限制的情况下，由语句“包括一个……”限定的要素，并不排除在包括所述要素的过程、方法、物品或者终端设备中还存在另外的相同要素。
以上仅为本发明的优选实施例而已，并不用于限制本发明，对于本领域技术人员来说，本发明可有各种更改和变化。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (4)

  1. 一种新型的密码专用的4×4的S盒构造方法，其特征在于，所述构造方法包括以下步骤：
    步骤一、对每一个仿射等价(AE)类Gi，选用其中已知的S盒S i，按照预设搜索方式搜索得到一系列新的S盒，所述预设搜索方式为S’(x)＝M 1(S i(M 0 T(x)))，其中，i＝0,…,15；x为输入，S’为新搜索到的S盒，M 0和M 1为4×4的行递增可逆矩阵，满足矩阵的行的数值从上到下逐渐递增；
    步骤二、从步骤一所搜索到的S盒中筛选出满足预设设计需求的S盒；
    步骤三、对经过步骤二筛选后的S盒通过遍历P 1(S(P 0(x+a)))+b得到全部满足所述预设设计需求的S盒；其中，P 0和P 1为4×4置换矩阵，a、b为4比特向量；
    步骤四、在步骤三的基础上进一步对遍历到的S盒进行筛选，选择固定点数目为0的S盒作为最终目标。
  2. 如权利要求1所述的新型的密码专用的4×4的S盒构造方法，其特征在于，每个AE类的可选的已知S盒的十六进制表示如下：
    G0:0123468A5BCF7E9D G1:0123468A5BCFED97
    G2:0123468A5BCF79DE G3:0123468B5CD7F9EA
    G4:0123468B5C9DEA7F G5:0123468B5CD7AF9E
    G6:0123468B5CD79FAE G7:0123468C59BDEA7F
    G8:0123468A5BCFDE79 G9:0123468B59CED7AF
    G10:0123468C59BDE7AF G11:0123468C59DFA7BE
    G12:0123468B5C9DE7AF G13:0123468B59CEDA7F
    G14:0123468B59CF7DAE G15:0123468A5BCF7D9E。
  3. 如权利要求1所述的新型的密码专用的4×4的S盒构造方法，其特征在于，所述预设设计需求包括差分概率、线性逼近概率、输入输出1比特差分个数、输入输出1比特线性掩码个数，以及代数次数。
  4. 如权利要求1所述的新型的密码专用的4×4的S盒构造方法，其特征在于，所述 步骤三中是根据所述步骤二中筛选出的满足所述预设设计需求的每类S盒的最小代表元，通过遍历P 1(S(P 0(x+a)))+b得到全部满足所述预设设计需求的S盒。
PCT/CN2019/102938 2019-02-26 2019-08-28 一种新型的密码专用的4×4的s盒构造方法 Ceased WO2020173063A1 (zh)

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CN111756521B (zh) * 2020-06-25 2022-05-27 桂林电子科技大学 基于Feistel-SP结构的密码S盒设计方法
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