Perfect secrecy cryptosystem with nonuniform distribution of keys

Chuanjun TIAN

doi:10.11959/j.issn.1000-436x.2018234

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Perfect secrecy cryptosystem with nonuniform distribution of keys

Papers | 更新时间：2024-06-05

- Perfect secrecy cryptosystem with nonuniform distribution of keys
- Journal on Communications Vol. 39, Issue 11, Pages: 1-9(2018)
- 作者机构：
  
  深圳大学信息工程学院，广东深圳 518060
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61070252)
- DOI：10.11959/j.issn.1000-436x.2018234
  CLC： TN918
- Online First：2018-11，
  
  Published：25 November 2018
- 稿件说明：
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Chuanjun TIAN. Perfect secrecy cryptosystem with nonuniform distribution of keys[J]. Journal on Communications, 2018, 39(11): 1-9.
DOI：

Chuanjun TIAN. Perfect secrecy cryptosystem with nonuniform distribution of keys[J]. Journal on Communications, 2018, 39(11): 1-9. DOI： 10.11959/j.issn.1000-436x.2018234.

摘要

提出了理论上更加严格的无限完善保密性和随机“一次一密”保密通信系统的概念，并将保密通信设计过程划分为基本密码系统设计及其应用设计两个阶段。首先研究了利用正交拉丁方组设计基本密码系统的问题，并举例说明了其非线性加密变换的设计方法；然后讨论了利用一类非均匀分布的随机方法设计应用过程中密钥序列的问题，并在理论上严格证明了基于所设计的基本密码系统的随机“一次一密”无限保密通信系统具有完善保密性。这一成果推广了当前常见的基于“模加法密码系统”的随机“一次一密”完善保密通信系统，因而可将其作为序列密码算法设计的一种更广泛的理想模拟原型。由于所能设计的基本密码系统的数量远超过现有常用方法所能设计的基本密码系统的数量，因此，所得结果对当前序列密码算法的主流设计方法是一种有效的补充与完善。

Abstract

More strictly mathematical concepts of infinite perfect secrecy and random “one-time pad” cryptosystem in theory were presented

and the whole secure communication system was divided into two stages:design of a basic cryptosystem and one of its applications.How to design a basic cryptosystem by using a group of orthogonal Latin squares was first studied and an example to illustrate how to design nonlinear encryption transformations for a basic cryptosystem was given.Then

how to design the sequence of keys by using random method with nonuniform distribution was discussed

and it was strictly proven in theory that the infinite random “one-time pad” cryptosystem based on the designed basic cryptosystem was of perfect secrecy.Since the obtained result generalizes the existing one for random “one-time pad” cryptosystem to be perfect by using a basic cryptosystem with modulo addition

it may be used as a wider ideal simulated prototype to design stream cipher algorithms.Since the number of basic cryptosystems that can be designed is much more than one of the common basic cryptosystems with modulo addition

the obtained result is effective supplement and perfection to mainstream design method for the current stream cryptosystems.

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references

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