密钥非均匀分布的完善保密通信系统

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

Abstract

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.

Key words: single key cryptosystem, perfect secrecy, nonlinear basic cryptosystem, one-time pad cryptosystem, orthog-onal Latin square

CLC Number:

TN918

Chuanjun TIAN. Perfect secrecy cryptosystem with nonuniform distribution of keys[J]. Journal on Communications, 2018, 39(11): 1-9.

References 20

[1]	SHANNON C E . Communication theory of secrecy system[J]. Bell System Technical Journal, 1949,28(4): 656-715.
[2]	章照止 . 现代密码学基础[M]. 北京: 北京邮电大学出版社, 2004.
	ZHANG Z Z . The foundation of modern cryptography[M]. Beijing: Beijing University of Posts and TelecommunicationsPress, 2004.
[3]	DIFFIE W , HELLMAN M . New directions in cryptography[J]. IEEE Trans.On Info Theory, 1976,IT-22(6): 644-654.
[4]	胡向东, 魏琴芳 . 应用密码学[M]. 北京: 电子工业出版社, 2006.
	HU X D , WEI Q F . Applied cryptography[M]. Beijing: Electronic Industry PressPress, 2006.
[5]	温巧燕, 钮心忻, 杨义先 . 现代密码学中的布尔函数[M]. 北京: 科学出版社, 2000.
	WEN Q Y , NIU X X , YANG Y X . Boolean functions in modern cryptography[M]. Beijing: Science PressPress, 2000.
[6]	丁存生, 肖国镇 . 流密码学及其应用[M]. 北京: 国防工业出版社, 1994.
	DING C S , XIAO G Z . Stream cryptography and its application[M]. Beijing: National Defense Industry PressPress, 1994.
[7]	魏仕民, 陈恺, 肖国镇 ,等. 关于密码体制的完善保密性[J]. 通信学报, 2001,22(7): 44-47.
	WEI S M , CHEN K , XIAO G Z ,et al. On perfect secrecy of cryptosystem[J]. Journal on Communications, 2001,22(7): 44-47.
[8]	亢保元 . 关于密码体制的完善保密性[J]. 中南大学学报, 2004,35(3): 453-456.
	KANG B Y . On perfect secrecy of cryptosystem[J]. Journal of Central South University, 2004,35(3): 453-456.
[9]	王云光 . 关于密码体制的完善保密性[J]. 大连理工大学学报, 2003,43(S1): 69-71.
	WANG Y G . Study of perfect secrecy of cryptosystem[J]. Journal of Dalian University of Technology, 2003,43(S1): 69-71.
[10]	STINSON D R . Cryptography theory and practice[M]. New York: CRC PressPress, 2005.
[11]	王勇, 朱芳来 . 完善保密的再认识[J]. 计算机工程, 2007,33(19): 155-157.
	WANG Y , ZHU F L . Reconsideration of perfect secrecy[J]. Computer Engineering, 2007,33(19): 155-157.
[12]	雷凤宇, 崔国华, 徐鹏 ,等. 完善保密体制的条件和存在性证明[J]. 计算机科学, 2010,37(5): 99-102.
	LEI F Y , CUI G H , XU P ,et al. On the condition and the proof of the existence of perfect secrecy cryptosystem[J]. Computer Science, 2010,37(5): 99-102.
[13]	亢保元, 王育明 . 完善保密密码体制的条件与设计[J]. 通信学报, 2004,22(7): 44-47.
	KANG B Y , WANG Y M . On the condition and design of perfect secrecy cryptosystem[J]. Journal on Communications, 2004,25(2): 44-47.
[14]	JUHA P . Symmetric blind decryption with perfect secrecy[J]. Journal of Computer Networks and Communications, 2017.
[15]	欧阳录 . 幻方与幻立方的当代理论[M]. 湖南: 湖南教育出版社, 2004.
	OUYANG L . The contemporary theory of magic cube and phantom cube[M]. Hunan: Hunan Education PressPress, 2004.
[16]	吴正声, 孙志人 . 组合数学初步[M]. 南京: 南京师范大学出版社, 2001.
	WU Z S , SUN Z R . Preliminary combinatorial mathematics[M]. Nanjing: Nanjing Normal University PressPress, 2001.
[17]	张里千 . 关于正交拉丁方的最大数目(I)[J]. 数学进展, 1963,6(2): 201-204.
	ZHANG L Q . On the maximum number of orthogonal Latin squares (I)[J]. Advances in Mathematics, 1963,6(2): 201-204.
[18]	李超 . 用线性取余变换造正交拉丁方和幻方[J]. 应用数学学报, 1996,19(2): 231-238.
	LI C . Constructing orthogonal Latin squares and magic square by using linear congruent transformation[J]. Acta Mathematicae Applicatae Sinica, 1996,19(2): 231-238.
[19]	陶照民 . 偶阶幻方和奇阶正交拉丁方的构造方法[J]. 应用数学学报, 1983,6(3): 276-281.
	TAO Z M . The general methods for constructing even order magic squares and odd order orthogonal Latin squares[J]. Acta Mathematicae Applicatae Sinica, 1983,6(3): 276-281.
[20]	田传俊 . 频率不相关性及其在单钥密码系统中的应用[J]. 深圳大学学报, 2015,32(1): 32-39.
	TIAN C J . Frequency irrelevance and its applications in one-key crypto systems[J]. Journal of Shenzhen University Science and Engineering, 2015,32(1): 32-39.

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