类MARS密码结构的线性特性及其优化设计

doi:10.11959/j.issn.1000-436x.2021068

通信学报 ›› 2021, Vol. 42 ›› Issue (4): 169-176.doi: 10.11959/j.issn.1000-436x.2021068

类MARS密码结构的线性特性及其优化设计

王念平, 洪礼荣

信息工程大学密码工程学院，河南郑州 450001

修回日期:2021-02-22 出版日期:2021-04-25 发布日期:2021-04-01
作者简介:王念平（1973- ），男，河南洛宁人，博士，信息工程大学教授、博士生导师，主要研究方向为密码学、信息安全等。
洪礼荣（1995- ），男，福建南安人，信息工程大学硕士生，主要研究方向为分组密码的设计与分析等。
基金资助:
国家自然科学基金资助项目(61672031)

Linear property and optimal design of MARS-like cryptographic structure

Nianping WANG, Lirong HONG

School of Cryptographic Engineering, Information Engineering University, Zhengzhou 450001, China

Revised:2021-02-22 Online:2021-04-25 Published:2021-04-01
Supported by:
The National Natural Science Foundation of China(61672031)

摘要/Abstract

摘要：

首先，提出了类MARS密码结构，给出了该密码结构的若干线性特性，并给出了线性变换的一种优化设计方法。具体地，通过分析一类具有特殊结构的线性逼近的传递规律，证明了无论怎样设计线性变换，t(1≤t≤3)轮线性逼近中至少有一条活动轮函数个数为0的线性逼近；4轮线性逼近中至少有一条活动轮函数个数不超过 1 的线性逼近；t(t＆gt;4)轮线性逼近中至少有一条活动轮函数个数不超过?8t/15?的线性逼近。在此基础上，给出了类 MARS 密码结构中线性变换的一种优化设计方法，该优化设计使活动轮函数个数的下界与 MARS密码结构相比更加接近可能的最大值。

关键词: 类MARS密码结构, 线性逼近, 活动轮函数, 线性变换

Abstract:

A MARS-like cryptographic structure was proposed and some linear properties of this cryptographic structure were given.An optimal design method of linear transformation in MARS-like cryptographic structure was also given.Concretely, by analyzing the transfer law of a class of linear approximation with special structure, regardless of the selected linear bijection, the existence of the linear approximation with 0 active round function in the t(1≤t≤3) round had been demonstrated.Furthermore, there was at least one with no more than 1, ?8t/15? active round function among the 4, t(t＆gt;4)-round of linear approximation, respectively.On this basis, an optimal design method was proposed to make the lower bound of the number of active round function closer to the maximum possible value than the MARS cryptographic structure for the linear transformation in the MARS-like cryptographic structure.

Key words: MARS-like cryptographic structure, linear approximation, active round function, linear transformation

中图分类号:

TN918.1

王念平, 洪礼荣. 类MARS密码结构的线性特性及其优化设计[J]. 通信学报, 2021, 42(4): 169-176.

Nianping WANG, Lirong HONG. Linear property and optimal design of MARS-like cryptographic structure[J]. Journal on Communications, 2021, 42(4): 169-176.

图/表 4

参考文献 16

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类MARS密码结构的线性特性及其优化设计

Linear property and optimal design of MARS-like cryptographic structure

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图/表 4

参考文献 16

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线性逼近的轮数	MARS密码结构的下界	特殊的类MARS密码结构的下界	L(t)的值	线性逼近的轮数	MARS密码结构的下界	特殊的类MARS密码结构的下界	L(t)的值
1	0	0	0	17	6	7	9
2	0	0	0	18	6	8	9
3	0	0	0	19	7	8	10
4	1	1	1	20	8	8	10
5	2	1	2	21	8	9	11
6	2	1	3	22	8	10	11
7	2	2	3	23	8	10	12
8	2	3	4	24	9	11	12
9	3	3	4	25	10	11	13
10	4	4	5	26	10	12	13
11	4	4	5	27	10	13	14
12	4	5	6	28	10	14	14
13	4	6	6	29	11	14	15
14	5	7	7	30	12	14	16
15	6	7	8	31	12	14	16
16	6	7	8	32	12	15	17

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