Linear property and optimal design of MARS-like cryptographic structure

Nianping WANG; Lirong HONG

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

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Linear property and optimal design of MARS-like cryptographic structure

Papers | 更新时间：2024-06-05

- Linear property and optimal design of MARS-like cryptographic structure
- Journal on Communications Vol. 42, Issue 4, Pages: 169-176(2021)
- 作者机构：
  
  信息工程大学密码工程学院，河南郑州 450001
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61672031)
- DOI：10.11959/j.issn.1000-436x.2021068
  CLC： TN918.1
- Online First：2021-04，
  
  Published：25 April 2021
- 稿件说明：
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Nianping WANG, Lirong HONG. Linear property and optimal design of MARS-like cryptographic structure[J]. Journal on Communications, 2021, 42(4): 169-176.
DOI：

Nianping WANG, Lirong HONG. Linear property and optimal design of MARS-like cryptographic structure[J]. Journal on Communications, 2021, 42(4): 169-176. DOI： 10.11959/j.issn.1000-436x.2021068.

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。

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.

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references

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